Maths-
General
Easy

Question

In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, in degrees Celsius, and is given by S(T)  = 0.6T + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

  1. The speed of sound, in meters per second, at 0°C 
  2. The speed of sound, in meters per second, at 0.6°C 
  3. The increase in the speed of sound, in meters per second, that corresponds to an increase of 1°C 
  4. The increase in the speed of sound, in meters per second, that corresponds to an increase of 0.6°C

The correct answer is: The speed of sound, in meters per second, at 0°C


    Solution:-
    Given :- Speed of sound= S m/s
    Temperature = T °C
    S(T) = 0.6T + 331.4
    We can compare this equation with the equation of straight line y= mx + c.
    And T represents x-axis
    We get y-intercept, c= 331.4, when x= 0
    Similarly , we will get S(T)= 331.4 when T=0
    Therefore, the speed of sound in meters per second at 0°C will be 331.4 m/s
    So, correct answer is Option A.

    Related Questions to study

    General
    Maths-

    Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

    Solution:-
    • We have given that Jackie has two jobs. She works as a tutor and lifeguard.
    • Payment as a tutor =  $12 per hour
    Payment as a lifeguard = $9.50 per hour
    • x = Number of hours she tutors.
    y = Number of hours she works as lifeguard.
    • Then amount as tutor will be calculate by multiplying number of hours, x and payment per hour, which will be 12x and same for lifeguard i. e 9.5y   
    Therefore, total amount earned per week will be 12x + 9.5y
    • Minimum payment she requires= $220 per week.
    Therefore,       12x + 9.5y ≥ 220
    • Maximum work in a week= 20 hours
    Therefore,        x + y ≤ 20
    Therefore, the correct option is C) 12x + 9.5y ≥ 220
    x +y  ≤ 20

    Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

    Maths-General
    Solution:-
    • We have given that Jackie has two jobs. She works as a tutor and lifeguard.
    • Payment as a tutor =  $12 per hour
    Payment as a lifeguard = $9.50 per hour
    • x = Number of hours she tutors.
    y = Number of hours she works as lifeguard.
    • Then amount as tutor will be calculate by multiplying number of hours, x and payment per hour, which will be 12x and same for lifeguard i. e 9.5y   
    Therefore, total amount earned per week will be 12x + 9.5y
    • Minimum payment she requires= $220 per week.
    Therefore,       12x + 9.5y ≥ 220
    • Maximum work in a week= 20 hours
    Therefore,        x + y ≤ 20
    Therefore, the correct option is C) 12x + 9.5y ≥ 220
    x +y  ≤ 20
    General
    Maths-


    The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
    Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

    • For solving the above question,
    Let x be the original price, in dollars, of the Glenview Street property.
    • After the 40% discount, the price of the property became 0.6x dollars
    • And after the additional 20% off the discounted price, the price of the property became 0.8(0.6x).
    • Thus, in terms of the original price of the property, x, the purchase price of the property is 0.48x.
    •  It follows that
    0.48x = 140,000.
    Solving this equation for x gives
    x = 291,666.6 .
    • Therefore, of the given choices, $291,700 best approximates the original price of the Glenview Street property.
    • Option A is incorrect because it is the result of dividing the purchase price of the property by 0.4, as though the purchase price were 40% of the original price.
    • Option C is incorrect because it is the closest to dividing the purchase price of the property by 0.6, as though the purchase price were 60% of the original price.
    • Option D is incorrect because it is the result of dividing the purchase price of the property by 0.8, as though the purchase price were 80% of the original price.


    The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
    Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

    Maths-General
    • For solving the above question,
    Let x be the original price, in dollars, of the Glenview Street property.
    • After the 40% discount, the price of the property became 0.6x dollars
    • And after the additional 20% off the discounted price, the price of the property became 0.8(0.6x).
    • Thus, in terms of the original price of the property, x, the purchase price of the property is 0.48x.
    •  It follows that
    0.48x = 140,000.
    Solving this equation for x gives
    x = 291,666.6 .
    • Therefore, of the given choices, $291,700 best approximates the original price of the Glenview Street property.
    • Option A is incorrect because it is the result of dividing the purchase price of the property by 0.4, as though the purchase price were 40% of the original price.
    • Option C is incorrect because it is the closest to dividing the purchase price of the property by 0.6, as though the purchase price were 60% of the original price.
    • Option D is incorrect because it is the result of dividing the purchase price of the property by 0.8, as though the purchase price were 80% of the original price.
    General
    Maths-


    The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
    The relationship between the monthly rental price r, in dollars, and the property’s purchase price p, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

    • We have given that the linear function that represents the relationship will be in the linerar form like
    r(p) = ap + b,
    where a and b are constants
    and r(p) = monthly rental price( in dollars) of a property
    price = p thousands of dollars.
    • According to the table, (70, 515) and (450, 3,365) are ordered pairs that should satisfy the function, which leads to the system of equations below.
    • 70a + b = 515
    • 450a + b= 3365
    • Subtracting side by side the first equation from the second
    450a+b-70a-b=3365-515
    380a = 2850;
    • Solving for a gives
    a= 2,850/380= 7.5
    • Substituting 7.5 for a in the first equation of the system gives
    525 + b = 515;
    • Solving for b gives
    b = −10.
    • Therefore, the linear function that represents the relationship is
    r(p) = 7.5p − 10.
    Choices A, B, and C are incorrect because the coefficient of p, or the rate at which the rental price, in dollars, increases for every thousand-dollar increase of the purchase price is different from what is suggested by these choices.


    The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
    The relationship between the monthly rental price r, in dollars, and the property’s purchase price p, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

    Maths-General
    • We have given that the linear function that represents the relationship will be in the linerar form like
    r(p) = ap + b,
    where a and b are constants
    and r(p) = monthly rental price( in dollars) of a property
    price = p thousands of dollars.
    • According to the table, (70, 515) and (450, 3,365) are ordered pairs that should satisfy the function, which leads to the system of equations below.
    • 70a + b = 515
    • 450a + b= 3365
    • Subtracting side by side the first equation from the second
    450a+b-70a-b=3365-515
    380a = 2850;
    • Solving for a gives
    a= 2,850/380= 7.5
    • Substituting 7.5 for a in the first equation of the system gives
    525 + b = 515;
    • Solving for b gives
    b = −10.
    • Therefore, the linear function that represents the relationship is
    r(p) = 7.5p − 10.
    Choices A, B, and C are incorrect because the coefficient of p, or the rate at which the rental price, in dollars, increases for every thousand-dollar increase of the purchase price is different from what is suggested by these choices.
    parallel
    General
    Maths-


    In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one
    of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated
    professional activity is research?

    Solution:- Option A is correct.
    After analysis of table given in the question according to the table, 74 orthopedic surgeons indicated that research is their major professional activity.
    Since a total of 607 surgeons completed the survey, it follows that the probability that the randomly selected surgeon is an orthopedic surgeon whose indicated major professional activity is research is 74 out of 607,
    equals 74 divided by 607 almost equal to 0.122
    Options B, C, and D are incorrect and may be the result of finding the probability that
    • For option B the randomly selected surgeon is an orthopedic surgeon whose major professional activity is teaching .
    • For option C an orthopedic surgeon whose major professional activity is either teaching or research.
    • For option D a general surgeon or orthopedic surgeon whose major professional activity is research.
    Therefore the correct option is Option A) 0.122
     


    In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one
    of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated
    professional activity is research?

    Maths-General
    Solution:- Option A is correct.
    After analysis of table given in the question according to the table, 74 orthopedic surgeons indicated that research is their major professional activity.
    Since a total of 607 surgeons completed the survey, it follows that the probability that the randomly selected surgeon is an orthopedic surgeon whose indicated major professional activity is research is 74 out of 607,
    equals 74 divided by 607 almost equal to 0.122
    Options B, C, and D are incorrect and may be the result of finding the probability that
    • For option B the randomly selected surgeon is an orthopedic surgeon whose major professional activity is teaching .
    • For option C an orthopedic surgeon whose major professional activity is either teaching or research.
    • For option D a general surgeon or orthopedic surgeon whose major professional activity is research.
    Therefore the correct option is Option A) 0.122
     
    General
    Maths-

    1 half left parenthesis 2 x plus y right parenthesis equals 21 over 2
    y equals 2 x
    The system of equations above has solution (x, y). What is the value of x ?

    Solution:- 

    • We have given two equations

    (2x + y) = 21 over 2                      --------(1)

    y = 2x                                        --------(2)

    • We can solve this by Substitution method, Substitute value of y from equation 2 in equation 1

    2x + 2x = 21 over 2

    • Further solving we get

    4x = 21 over 2

    • Divide both sides by 4 we gwt,

    x = 21 over 8

    • Substituting value of x in equation 2 we get,

    y = 21 × 2 over 8 = 42 over 8

    • Therefore

    x=21 over 8

    y=42 over 8

    • Therefore value of x is 21 over 8.

    1 half left parenthesis 2 x plus y right parenthesis equals 21 over 2
    y equals 2 x
    The system of equations above has solution (x, y). What is the value of x ?

    Maths-General

    Solution:- 

    • We have given two equations

    (2x + y) = 21 over 2                      --------(1)

    y = 2x                                        --------(2)

    • We can solve this by Substitution method, Substitute value of y from equation 2 in equation 1

    2x + 2x = 21 over 2

    • Further solving we get

    4x = 21 over 2

    • Divide both sides by 4 we gwt,

    x = 21 over 8

    • Substituting value of x in equation 2 we get,

    y = 21 × 2 over 8 = 42 over 8

    • Therefore

    x=21 over 8

    y=42 over 8

    • Therefore value of x is 21 over 8.
    General
    Maths-

    In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

    • We have given that 34.6% of 26 students in Mr. Camp’s class reported that they had at least two siblings.
    34.6% of 26 = 8.996=9
    there must have been 9 students in the class who reported having at least two siblings and remaining 26- 9 = 17 students who reported that they had fewer than two siblings.
    • It is also given that the average eighth-grade class size in the state is 26 and that Mr. Camp’s class is representative of all eighth-grade classes in the state. This means that in each eighth-grade class in the state there are about 17 students who have fewer than two siblings. Therefore, the best estimate of the number of eighth-grade students in the state who have fewer than two siblings is
    17 × (number of eighth-grade classes in the state),
    or        17 × 1,800 = 30,600.
    • Option A is incorrect because 16,200 is the best estimate for the number of eighth-grade students in the state who have at least, not fewer than, two siblings.
    Option B is incorrect because 23,400 is half of the estimated total number of eighth-grade students in the state; however, since the students in Mr. Camp’s class are representative of students in the eighth grade classes in the state and more than half of the students in Mr. Camp’s class have fewer than two
    • siblings, more than half of the students in each eighth-grade class in the state have fewer than two siblings, too.
    • Option D is incorrect because 46,800 is the estimated total number of eighth-grade students in the state.

    In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

    Maths-General
    • We have given that 34.6% of 26 students in Mr. Camp’s class reported that they had at least two siblings.
    34.6% of 26 = 8.996=9
    there must have been 9 students in the class who reported having at least two siblings and remaining 26- 9 = 17 students who reported that they had fewer than two siblings.
    • It is also given that the average eighth-grade class size in the state is 26 and that Mr. Camp’s class is representative of all eighth-grade classes in the state. This means that in each eighth-grade class in the state there are about 17 students who have fewer than two siblings. Therefore, the best estimate of the number of eighth-grade students in the state who have fewer than two siblings is
    17 × (number of eighth-grade classes in the state),
    or        17 × 1,800 = 30,600.
    • Option A is incorrect because 16,200 is the best estimate for the number of eighth-grade students in the state who have at least, not fewer than, two siblings.
    Option B is incorrect because 23,400 is half of the estimated total number of eighth-grade students in the state; however, since the students in Mr. Camp’s class are representative of students in the eighth grade classes in the state and more than half of the students in Mr. Camp’s class have fewer than two
    • siblings, more than half of the students in each eighth-grade class in the state have fewer than two siblings, too.
    • Option D is incorrect because 46,800 is the estimated total number of eighth-grade students in the state.
    parallel
    General
    Maths-

    Which of the following is equivalent to the sum of the expressions a2 - 1 and a + 1 ?

    Solution:- (A) a2 + a
    • Given two equations are a2 - 1 and  a + 1.
    Let  A = a2 – 1 and B = a + 1
    • We have to find equivalent sum of both the expressions.
    • Lets X be the sum of both the sums,
    X = A + B
    • Lets put the values of A and B in the equation
    X = (a2 – 1) + (a + 1)
    X =  a2 – 1 + a + 1
    • We can see that there are two terms -1 and 1, if we add both of them their sum will be 0.
    X=  a2 + a
    • Therefore, the correct option is (A) a2 + a

    Which of the following is equivalent to the sum of the expressions a2 - 1 and a + 1 ?

    Maths-General
    Solution:- (A) a2 + a
    • Given two equations are a2 - 1 and  a + 1.
    Let  A = a2 – 1 and B = a + 1
    • We have to find equivalent sum of both the expressions.
    • Lets X be the sum of both the sums,
    X = A + B
    • Lets put the values of A and B in the equation
    X = (a2 – 1) + (a + 1)
    X =  a2 – 1 + a + 1
    • We can see that there are two terms -1 and 1, if we add both of them their sum will be 0.
    X=  a2 + a
    • Therefore, the correct option is (A) a2 + a
    General
    Maths-

    Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower?

    Step by step solution:-
    We have to find the power, in watts, is equal to 2 horsepower.
    For solving this question,
    Let us take x be the number of watts that is equal to 2 horsepower.
    Since we have given that 5 horsepower is equal to 3730 watts,
    5 horse power ~ 3730 watts
    So, 2 horse power = x watts
    This follows,2 over 5 equals x over 3730
    Multiplying both sides of equation by 3730
    left parenthesis 3730 right parenthesis 2 over 5 equals x over 3730 left parenthesis 3730 right parenthesis
    left parenthesis 3730 right parenthesis 2 over 5 equals x
    straight X equals 7450 over 5
    x =  1492
    Therefore, 2 horsepower equals 1492 watts.

    Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower?

    Maths-General
    Step by step solution:-
    We have to find the power, in watts, is equal to 2 horsepower.
    For solving this question,
    Let us take x be the number of watts that is equal to 2 horsepower.
    Since we have given that 5 horsepower is equal to 3730 watts,
    5 horse power ~ 3730 watts
    So, 2 horse power = x watts
    This follows,2 over 5 equals x over 3730
    Multiplying both sides of equation by 3730
    left parenthesis 3730 right parenthesis 2 over 5 equals x over 3730 left parenthesis 3730 right parenthesis
    left parenthesis 3730 right parenthesis 2 over 5 equals x
    straight X equals 7450 over 5
    x =  1492
    Therefore, 2 horsepower equals 1492 watts.
    General
    Maths-

    2(p + 1) + 8(p - 1) = 5p
    What value of p is the solution of the equation above?

    2(p+1)+8(p-1) = 5p

    • Lets solve the brackets first

    2p + 2 + 8p – 8 = 5p              ------------[  a(b + c) = ab + ac ]

    • Adding the like terms

    10p – 6 = 5p                          --------------[2p + 8p=10p , 2 – 8 = - 6]

    • Subtract 5p from both sides

    5p – 6 = 0

    • Add 6 from both sides

    5p = 6

    • Divide both sides by 5

    p = 6/5

    • Therefore the value of p is 6/5

    2(p + 1) + 8(p - 1) = 5p
    What value of p is the solution of the equation above?

    Maths-General

    2(p+1)+8(p-1) = 5p

    • Lets solve the brackets first

    2p + 2 + 8p – 8 = 5p              ------------[  a(b + c) = ab + ac ]

    • Adding the like terms

    10p – 6 = 5p                          --------------[2p + 8p=10p , 2 – 8 = - 6]

    • Subtract 5p from both sides

    5p – 6 = 0

    • Add 6 from both sides

    5p = 6

    • Divide both sides by 5

    p = 6/5

    • Therefore the value of p is 6/5
    parallel
    General
    Maths-

    fraction numerator a minus b over denominator a end fraction equals c
    In the equation above, if a is negative and b is positive, which of the following must be true?

    • We have given the equation
    fraction numerator a minus b over denominator a end fraction equals c
    • The equation can be rewritten as 1 minus b over a equals c,
      or .1 minus c equals b over a
    • Since a less than 0 and b greater than 0, it follows that b divided by a less than stack 0 with _ below with _ below
    • And as b/a < 0
      • 1-c < 0, or equivalent to c > 1.
      • Option B is incorrect. If c = 1, then a – b = a, or b = 0. But it is given that b > 0, so c = 1 cannot be true.
      • Option C  is incorrect. If c = -1, then a - b = -a, or 2a = b. But this equation contradicts the premise that a < 0 and b > 0, so c = -1 cannot be true.
      •  Option D is incorrect. For example, if c = -2, then a - b = -2a, or 3a = b. But this contradicts the fact that  and  have opposite signs, so c < -1 cannot be true.

    fraction numerator a minus b over denominator a end fraction equals c
    In the equation above, if a is negative and b is positive, which of the following must be true?

    Maths-General
    • We have given the equation
    fraction numerator a minus b over denominator a end fraction equals c
    • The equation can be rewritten as 1 minus b over a equals c,
      or .1 minus c equals b over a
    • Since a less than 0 and b greater than 0, it follows that b divided by a less than stack 0 with _ below with _ below
    • And as b/a < 0
      • 1-c < 0, or equivalent to c > 1.
      • Option B is incorrect. If c = 1, then a – b = a, or b = 0. But it is given that b > 0, so c = 1 cannot be true.
      • Option C  is incorrect. If c = -1, then a - b = -a, or 2a = b. But this equation contradicts the premise that a < 0 and b > 0, so c = -1 cannot be true.
      •  Option D is incorrect. For example, if c = -2, then a - b = -2a, or 3a = b. But this contradicts the fact that  and  have opposite signs, so c < -1 cannot be true.
    General
    Maths-

    square root of k plus 2 end root minus x equals 0
    In the equation above, k is a constant. If x = 9, what is the value of K ?

    Solution:-
    • Given equation is square root of k plus 2 end root minus x equals 0.
    • k is constant and x = 9
    • Lets solve the equation, add x to both sides of equation, we get,
    square root of k plus 2 end root equals x
    • As the value of x is given we will put it into the equation to find the value of k.square root of k plus 2 end root equals 9
    • Squaring on both sides we get,
    k+2 = 81
    • Subtract 2 from both sides we get,
    k = 79
    • Therefore the value of k is 79, correct option is (D)79.
     

    square root of k plus 2 end root minus x equals 0
    In the equation above, k is a constant. If x = 9, what is the value of K ?

    Maths-General
    Solution:-
    • Given equation is square root of k plus 2 end root minus x equals 0.
    • k is constant and x = 9
    • Lets solve the equation, add x to both sides of equation, we get,
    square root of k plus 2 end root equals x
    • As the value of x is given we will put it into the equation to find the value of k.square root of k plus 2 end root equals 9
    • Squaring on both sides we get,
    k+2 = 81
    • Subtract 2 from both sides we get,
    k = 79
    • Therefore the value of k is 79, correct option is (D)79.
     
    General
    Maths-

    square root of x plus 28 end root minus 2 square root of x plus 1 end root equals 0
    What value of x satisfies the equation above?

    We proceed in the following way,
    square root of x plus 28 end root minus 2 square root of x plus 1 end root equals 0
    square root of x plus 28 end root equals 2 square root of x plus 1 end root
    (We make sure that both the square roots are not on the same side o the equation.)
    Squaring both sides, we get
    left parenthesis square root of x plus 28 end root right parenthesis squared equals left parenthesis 2 square root of x plus 1 end root right parenthesis squared
    Since,open parentheses square root of x squared end root close parentheses equals x text  and  end text left parenthesis a b right parenthesis squared equals a squared b squared
    x plus 28 equals 2 squared left parenthesis x plus 1 right parenthesis
    not stretchy rightwards double arrow x plus 28 equals 4 left parenthesis x plus 1 right parenthesis
    Expanding the above equation, we get
    x plus 28 equals 4 x plus 4
    Simplifying, we have
    x minus 4 x equals 4 minus 28
    not stretchy rightwards double arrow negative 3 x equals negative 24
    not stretchy rightwards double arrow 3 x equals 24
    Dividing both sides by 3, we get
    x = 8
    Hence, the value of x which satisfies the given equation is 8.
    Thus, the correct option is A).

    square root of x plus 28 end root minus 2 square root of x plus 1 end root equals 0
    What value of x satisfies the equation above?

    Maths-General
    We proceed in the following way,
    square root of x plus 28 end root minus 2 square root of x plus 1 end root equals 0
    square root of x plus 28 end root equals 2 square root of x plus 1 end root
    (We make sure that both the square roots are not on the same side o the equation.)
    Squaring both sides, we get
    left parenthesis square root of x plus 28 end root right parenthesis squared equals left parenthesis 2 square root of x plus 1 end root right parenthesis squared
    Since,open parentheses square root of x squared end root close parentheses equals x text  and  end text left parenthesis a b right parenthesis squared equals a squared b squared
    x plus 28 equals 2 squared left parenthesis x plus 1 right parenthesis
    not stretchy rightwards double arrow x plus 28 equals 4 left parenthesis x plus 1 right parenthesis
    Expanding the above equation, we get
    x plus 28 equals 4 x plus 4
    Simplifying, we have
    x minus 4 x equals 4 minus 28
    not stretchy rightwards double arrow negative 3 x equals negative 24
    not stretchy rightwards double arrow 3 x equals 24
    Dividing both sides by 3, we get
    x = 8
    Hence, the value of x which satisfies the given equation is 8.
    Thus, the correct option is A).
    parallel
    General
    Maths-

    y ≤3x +1
    x – y  >1
    Which of the following ordered pairs ( x, y)satisfies the system of inequalities above?

    Solution:- Option D is correct.
    Method 1:-
    We have given two inequalities
    y ≤3x +1
    x – y  >1
    Any point (x, y) that is a solution to the given system of inequalities must
    satisfy both inequalities in the system. Since the second inequality in the system can be rewritten as y < x − 1, the system is equivalent to the following system.
    y ≤3x +1
    x – y  >1
    Since ,            3x + 1 > x − 1 for x > −1
    and                 3x + 1 ≤ x − 1 for x ≤ −1,
    it follows that y < x − 1 for x > −1 and y ≤ 3x + 1 for x ≤ −1. Of the given choices,
    only (2, −1) satisfies these conditions because −1 < 2 − 1 = 1
    Method 2:-
    Substituting (2, −1) into the first inequality gives
    −1 ≤ 3(2) + 1, or −1 ≤ 7,
    which is a true statement.
    Substituting (2, −1) into the second inequality gives
    2 − (−1) > 1, or 3 > 1,
    which is a true statement.
    Therefore, since (2, −1) satisfies both inequalities,
    it is a solution to the system.
    • If we considered Option A , it is incorrect because substituting −2 for x and −1
    for y in the first inequality gives −1 ≤ 3(−2) + 1, or −1 ≤ −5, which is false.
    • If we considered option B , it is incorrect because substituting −1 for x and 3 for
              y in the first inequality gives 3 ≤ 3(−1) + 1, or 3 ≤ −2, which is false.
    • If we considered option C, it is incorrect because substituting 1 for x and 5 for
             y in the first inequality gives 5 ≤ 3(1) + 1, or 5 ≤ 4, which is false.

    y ≤3x +1
    x – y  >1
    Which of the following ordered pairs ( x, y)satisfies the system of inequalities above?

    Maths-General
    Solution:- Option D is correct.
    Method 1:-
    We have given two inequalities
    y ≤3x +1
    x – y  >1
    Any point (x, y) that is a solution to the given system of inequalities must
    satisfy both inequalities in the system. Since the second inequality in the system can be rewritten as y < x − 1, the system is equivalent to the following system.
    y ≤3x +1
    x – y  >1
    Since ,            3x + 1 > x − 1 for x > −1
    and                 3x + 1 ≤ x − 1 for x ≤ −1,
    it follows that y < x − 1 for x > −1 and y ≤ 3x + 1 for x ≤ −1. Of the given choices,
    only (2, −1) satisfies these conditions because −1 < 2 − 1 = 1
    Method 2:-
    Substituting (2, −1) into the first inequality gives
    −1 ≤ 3(2) + 1, or −1 ≤ 7,
    which is a true statement.
    Substituting (2, −1) into the second inequality gives
    2 − (−1) > 1, or 3 > 1,
    which is a true statement.
    Therefore, since (2, −1) satisfies both inequalities,
    it is a solution to the system.
    • If we considered Option A , it is incorrect because substituting −2 for x and −1
    for y in the first inequality gives −1 ≤ 3(−2) + 1, or −1 ≤ −5, which is false.
    • If we considered option B , it is incorrect because substituting −1 for x and 3 for
              y in the first inequality gives 3 ≤ 3(−1) + 1, or 3 ≤ −2, which is false.
    • If we considered option C, it is incorrect because substituting 1 for x and 5 for
             y in the first inequality gives 5 ≤ 3(1) + 1, or 5 ≤ 4, which is false.
    General
    Maths-

    The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is 1 third the corresponding original dimension, what is the height of the reproduction, in inches ?

    We are given that the height of the original painting is 29 inches and width is 36.25 inches
    Reproduction made has dimensions 1 third rd of corresponding original dimensions so ,
    The reproduction’s height is 1 third of the original height.
    Reproduction height= original height / 3
    = 29 over 3
    = 9.6
    Height of the reproduction is 29 over 3 or in decimals 9.66 or 9.67 can be taken as the correct answer.

    The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is 1 third the corresponding original dimension, what is the height of the reproduction, in inches ?

    Maths-General
    We are given that the height of the original painting is 29 inches and width is 36.25 inches
    Reproduction made has dimensions 1 third rd of corresponding original dimensions so ,
    The reproduction’s height is 1 third of the original height.
    Reproduction height= original height / 3
    = 29 over 3
    = 9.6
    Height of the reproduction is 29 over 3 or in decimals 9.66 or 9.67 can be taken as the correct answer.
    General
    Maths-

    Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?

    Solution:- Option(C) A quadratic function with no real zeros.
    Lets consider option A, it says that A linear function whose rate of change is not zero.
    • Rate of change = Slope of the line
    We know that, equation of line is y = mx + c ,
    In the question we have given that function has no x-intercept. That means it should not intersect the x-axis. i.e.it should be parallel to the x-axis.
    Now, x-axis is the line such that its slope, m= 0 and y-intercept, c=0.
    But as in the given option rate of change is not zero that means slope m≠0. So the line will not be parallel to x-axis. Hence, it will have x-intercept at some point.
    So, Option A is not correct.
    Lets consider option B, it says that a quadratic function with real zero,
    We know that, A zero or root of a function is the value of x at which the function is zero.
    So, when we draw graph then, (x, y) = (x, f(x))
    So, at real zero value of x is (x1 , 0) where x1 is real zero.
    If the function has real zeros it will intersect x-axis at some point because function will be equal to zero at the value of the real zero.
    So, Option B is not correct.
    Lets consider option C, it says that a quadratic function with no real zeroes.
    So, function with no real zeroes, will not be equal to 0 at any real value of x. Hence there will be no x-intercept.
    So, Option C is Correct .
    Reason for option D will be same as of Option B.

    Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?

    Maths-General
    Solution:- Option(C) A quadratic function with no real zeros.
    Lets consider option A, it says that A linear function whose rate of change is not zero.
    • Rate of change = Slope of the line
    We know that, equation of line is y = mx + c ,
    In the question we have given that function has no x-intercept. That means it should not intersect the x-axis. i.e.it should be parallel to the x-axis.
    Now, x-axis is the line such that its slope, m= 0 and y-intercept, c=0.
    But as in the given option rate of change is not zero that means slope m≠0. So the line will not be parallel to x-axis. Hence, it will have x-intercept at some point.
    So, Option A is not correct.
    Lets consider option B, it says that a quadratic function with real zero,
    We know that, A zero or root of a function is the value of x at which the function is zero.
    So, when we draw graph then, (x, y) = (x, f(x))
    So, at real zero value of x is (x1 , 0) where x1 is real zero.
    If the function has real zeros it will intersect x-axis at some point because function will be equal to zero at the value of the real zero.
    So, Option B is not correct.
    Lets consider option C, it says that a quadratic function with no real zeroes.
    So, function with no real zeroes, will not be equal to 0 at any real value of x. Hence there will be no x-intercept.
    So, Option C is Correct .
    Reason for option D will be same as of Option B.
    parallel

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