Question
If 2n + 12 = 26n, what is the value of 6n?
- 8
- 4
- 3
The correct answer is: 3
2n + 12 = 26n
12 = 26n – 2n
24n = 12
(4 x 6) n = 12
6n = 
6n = 3
Related Questions to study
I2x - 4 I = 8
What is the positive solution to the given equation?
I2x - 4 I = 8
What is the positive solution to the given equation?
Two lines intersect as shown. What is the value of x ?
Two lines intersect as shown. What is the value of x ?
The bar graph above shows the total number of scheduled flights and the number of delayed flights for five airlines in a one-month period. Values have been rounded to the nearest 1000 flights.
According to the graph, for the airline with the greatest number of delayed flights, what fraction of the total number of scheduled flights for the airline were delayed?
The bar graph above shows the total number of scheduled flights and the number of delayed flights for five airlines in a one-month period. Values have been rounded to the nearest 1000 flights.
According to the graph, for the airline with the greatest number of delayed flights, what fraction of the total number of scheduled flights for the airline were delayed?
Two numbers, a and b, are each greater than zero, and the square root of a is equal to the cube root of b. For what value of x is a2x-1 equal to b?
• To calculate the square root
To find the square root of the numbers, first find a number that, when multiplied twice by itself, yields the original number, and we must first determine which number was squared to obtain the original number. So, for example, if we need to find the square root of 4, we know that multiplying '2' by '2' yields 4. Hence, √4 = 2.
• To calculate the cube root
We must first find a number that, when multiplied three times by itself, yields the original number, and to find the cube root of a number, say 64, it is simple to see that the cube of 4 equals 64. As a result, the cube root of 64 is 4.
Two numbers, a and b, are each greater than zero, and the square root of a is equal to the cube root of b. For what value of x is a2x-1 equal to b?
• To calculate the square root
To find the square root of the numbers, first find a number that, when multiplied twice by itself, yields the original number, and we must first determine which number was squared to obtain the original number. So, for example, if we need to find the square root of 4, we know that multiplying '2' by '2' yields 4. Hence, √4 = 2.
• To calculate the cube root
We must first find a number that, when multiplied three times by itself, yields the original number, and to find the cube root of a number, say 64, it is simple to see that the cube of 4 equals 64. As a result, the cube root of 64 is 4.
The expression 0.6y represents the result of decreasing the quantity y by p%. What is the value of p?
The expression 0.6y represents the result of decreasing the quantity y by p%. What is the value of p?
In the system of equations above, k is a constant. If the system has no solutions, what is the value of k?
In the system of equations above, k is a constant. If the system has no solutions, what is the value of k?
x2−4x−9=0
The solutions to the given equation can be written in the form 
, where m and k are integers. What is the value of m + k?
x2−4x−9=0
The solutions to the given equation can be written in the form , where m and k are integers. What is the value of m + k?
Tamika is ordering desktop computers for her company. The desktop computers cost $375 each, and tax is an additional 6% of the total cost of the computers. If she can spend no more than $40,000 on the desktop computers, including tax, what is the maximum number of computers that Tamika can purchase?
Tamika is ordering desktop computers for her company. The desktop computers cost $375 each, and tax is an additional 6% of the total cost of the computers. If she can spend no more than $40,000 on the desktop computers, including tax, what is the maximum number of computers that Tamika can purchase?
An angle measure of 540 degrees was written in
radians as 
. What is the value of x ?
An angle measure of 540 degrees was written in
radians as . What is the value of x ?
The populations, in thousands, of Alaska and Hawaii from 1960 to 2016 can be modeled by the functions A and H, where x is the number of years since January 1, 1960, and 0 ≤ x ≤ 55.
Alaska: A(x)=221+9.78x
Hawaii: H(x)=645+14.5x
Based on the model, in which year does the predicted population of Hawaii first exceed 900,000?
The populations, in thousands, of Alaska and Hawaii from 1960 to 2016 can be modeled by the functions A and H, where x is the number of years since January 1, 1960, and 0 ≤ x ≤ 55.
Alaska: A(x)=221+9.78x
Hawaii: H(x)=645+14.5x
Based on the model, in which year does the predicted population of Hawaii first exceed 900,000?
What value of x satisfies the equation above?
What value of x satisfies the equation above?
The populations, in thousands, of Alaska and Hawaii from 1960 to 2016 can be modeled by the functions A and H, where x is the number of years since January 1, 1960, and 0 ≤ x ≤ 55.
Alaska: A(x)=221+9.78x
Hawaii: H(x)=645+14.5x
Based on the model, what is the predicted population of Alaska, on January 1, 1960?
The populations, in thousands, of Alaska and Hawaii from 1960 to 2016 can be modeled by the functions A and H, where x is the number of years since January 1, 1960, and 0 ≤ x ≤ 55.
Alaska: A(x)=221+9.78x
Hawaii: H(x)=645+14.5x
Based on the model, what is the predicted population of Alaska, on January 1, 1960?
Note: Figure not drawn to scale.
In right triangle ABC above, BC= 8. If the cosine of x0 is 
, what is the length of 
?
When a triangle has three angles, one of them must always be 90°. The Pythagoras Theorem, which asserts that the square hypotenuse's longest side is the same as the sum of the squares of the perpendicular and base, is derived for right-angled triangles.
We can determine the value of every angle in a right-angled triangle given the length of at least two of its sides. To do this, we employ a variety of trigonometric functions, including sine, cosine, tangent, cotangent, sec, and cosec.
Properties:
1. Among the three vertices, there is a right-angle vertex.
2. The opposite side of a right-angled vertex is referred to as the hypotenuse.
3. The Pythagoras theorem, which asserts, is used to determine the length of the sides.
4. A right-angled triangle's hypotenuse is its longest side.
5. Acute angles are those other than the right angle with a value of less than 90 degrees.The Cosine Rule states that the square of the length of any one side of a triangle is equal to the sum of the squares of the lengths of the other two sides multiplied by the cosine of the angle that includes those sides.
¶The formula is as follows: a2 = b2 + c2 - 2bc cos x
Note: Figure not drawn to scale.
In right triangle ABC above, BC= 8. If the cosine of x0 is , what is the length of ?
When a triangle has three angles, one of them must always be 90°. The Pythagoras Theorem, which asserts that the square hypotenuse's longest side is the same as the sum of the squares of the perpendicular and base, is derived for right-angled triangles.
We can determine the value of every angle in a right-angled triangle given the length of at least two of its sides. To do this, we employ a variety of trigonometric functions, including sine, cosine, tangent, cotangent, sec, and cosec.
Properties:
1. Among the three vertices, there is a right-angle vertex.
2. The opposite side of a right-angled vertex is referred to as the hypotenuse.
3. The Pythagoras theorem, which asserts, is used to determine the length of the sides.
4. A right-angled triangle's hypotenuse is its longest side.
5. Acute angles are those other than the right angle with a value of less than 90 degrees.The Cosine Rule states that the square of the length of any one side of a triangle is equal to the sum of the squares of the lengths of the other two sides multiplied by the cosine of the angle that includes those sides.
¶The formula is as follows: a2 = b2 + c2 - 2bc cos x
Race Summary
|
Split number |
Race segment (meters) |
Split time (seconds) |
Total race time at end of split (seconds) |
|
1 |
0 - 500 |
109 |
109 |
|
2 |
500 - 1000 |
112 |
221 |
|
3 |
1000 - 1500 |
111 |
332 |
|
4 |
1500 - 2000 |
108 |
440 |
By the end of the season, the coach wants the team to reduce its mean split time by 10% as compared to this race. At the end of the season, what should the team's mean split time be, in seconds?
Race Summary
|
Split number |
Race segment (meters) |
Split time (seconds) |
Total race time at end of split (seconds) |
|
1 |
0 - 500 |
109 |
109 |
|
2 |
500 - 1000 |
112 |
221 |
|
3 |
1000 - 1500 |
111 |
332 |
|
4 |
1500 - 2000 |
108 |
440 |
By the end of the season, the coach wants the team to reduce its mean split time by 10% as compared to this race. At the end of the season, what should the team's mean split time be, in seconds?
