Question
The length of each side of a nonagon is 8 in. Find its perimeter
- 32 in
- 64 in
- 72 in
- 80 in
Hint:
A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.
The correct answer is: 72 in
Explanation:
- We have been given the length of each side of a nonagon that is 8 in.
- We have to find the perimeter of the given nonagon.
Step 1 of 1:
We have length of each side of a nanagon 8in
Now the perimeter will be
9 × 8in
72in
Hence, Option C is correct.
Related Questions to study
The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given the two sides of a regular pentagon in the form of expressions that is -
- 4x + 7 and x + 16
- We have to find the length of a side of the pentagon.
The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
Now, We know that all sides of regular polygon are equal.
So,
X + 16 = 4x + 7
3x = 16 - 7
3x = 9
x = 3
And the measure of length will be
= x + 16
= 3 + 16
= 19
The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given the two sides of a regular pentagon in the form of expressions that is -
- 4x + 7 and x + 16
- We have to find the length of a side of the pentagon.
The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
Now, We know that all sides of regular polygon are equal.
So,
X + 16 = 4x + 7
3x = 16 - 7
3x = 9
x = 3
And the measure of length will be
= x + 16
= 3 + 16
= 19
Two angles of a regular polygon are given to be
Find the value of and measure of each angle.
Hint:
- A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.
- We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
- We have to find the value of x and measure of each angle.
We know that a regulat polygon is equiangular
So,
2x + 27 = 3x - 3
x = 27 + 3
x = 30
And the value of each angle will be
= 2x + 27
= 2(30) + 27
= 87
Two angles of a regular polygon are given to be
Find the value of and measure of each angle.
Hint:
- A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.
- We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
- We have to find the value of x and measure of each angle.
We know that a regulat polygon is equiangular
So,
2x + 27 = 3x - 3
x = 27 + 3
x = 30
And the value of each angle will be
= 2x + 27
= 2(30) + 27
= 87
Solve the equation. Write a reason for each step.
8(−x − 6) = −50 − 10x
Ans:- x = 1
Explanation :-
Given ,8(-x − 6) = -50-10x.
By left distributive property - 8x − 48 = - 50 -10x
Adding 48 on both sides by additive property of equality both sides remain equal.
- 8x − 48 + 48 = - 50 -10x + 48
- 8x = -10x - 2
Adding 10x on both sides by additive property of equality both sides remain equal.
- 8x +10x = -10x - 2 +10x
2x = - 2
Dividing 2
x = -1
∴ x = -1
Solve the equation. Write a reason for each step.
8(−x − 6) = −50 − 10x
Ans:- x = 1
Explanation :-
Given ,8(-x − 6) = -50-10x.
By left distributive property - 8x − 48 = - 50 -10x
Adding 48 on both sides by additive property of equality both sides remain equal.
- 8x − 48 + 48 = - 50 -10x + 48
- 8x = -10x - 2
Adding 10x on both sides by additive property of equality both sides remain equal.
- 8x +10x = -10x - 2 +10x
2x = - 2
Dividing 2
x = -1
∴ x = -1
Find the measure of each angle of an equilateral triangle using base angle theorem.
Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- An equilateral triangle is a triangle with all the three sides of equal length.
- We have to find the measure of each angle of an equilateral triangle using base angle theorem.
Let a triangle be ABC
Here,
AB = AC
Using base angle theorem
And,
So,
Therefore,
Step 2 of 2:
We know that the sum of all angles of a triangle is 1800.
Now,
So,
Find the measure of each angle of an equilateral triangle using base angle theorem.
Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- An equilateral triangle is a triangle with all the three sides of equal length.
- We have to find the measure of each angle of an equilateral triangle using base angle theorem.
Let a triangle be ABC
Here,
AB = AC
Using base angle theorem
And,
So,
Therefore,
Step 2 of 2:
We know that the sum of all angles of a triangle is 1800.
Now,
So,
The length of each side of a regular pentagon is . Find the value of if its perimeter is .
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given in the question the length of each side of a regular pentagon which is (x+5) cm
- We have also been given the perimeter that is 50 cm.
- We have to find the value of x.
We have given a perimeter of a regular pentaogn 50.
A pentagon has sides.
The length of the side is x+5
So,
5(x + 5) = 50
x + 5 = 10
x = 5
Hence, Option A is correct.
The length of each side of a regular pentagon is . Find the value of if its perimeter is .
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given in the question the length of each side of a regular pentagon which is (x+5) cm
- We have also been given the perimeter that is 50 cm.
- We have to find the value of x.
We have given a perimeter of a regular pentaogn 50.
A pentagon has sides.
The length of the side is x+5
So,
5(x + 5) = 50
x + 5 = 10
x = 5
Hence, Option A is correct.
Name the property of equality the statement illustrates.
Every segment is congruent to itself.
Ans :- Option A
Explanation :-
The reflexive property states that any real number, a, is equal to itself. That is, a = a.
Similarly the segment is congruent to itself .
∴Option A
Name the property of equality the statement illustrates.
Every segment is congruent to itself.
Ans :- Option A
Explanation :-
The reflexive property states that any real number, a, is equal to itself. That is, a = a.
Similarly the segment is congruent to itself .
∴Option A
Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given a diagram of a triangle in the question named ABC we have also been given 𝑚∠𝐵 = 55°.
- We have to find out 𝑚∠A.
We have given figure
Here, AB = AC
It means the given triangle is an isosceles triangle.
Now,
By base angle theorem
And it is given
So,
Step 2 of 2:
We know that the sum of angle of a triangle is 1800
Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given a diagram of a triangle in the question named ABC we have also been given 𝑚∠𝐵 = 55°.
- We have to find out 𝑚∠A.
We have given figure
Here, AB = AC
It means the given triangle is an isosceles triangle.
Now,
By base angle theorem
And it is given
So,
Step 2 of 2:
We know that the sum of angle of a triangle is 1800
If f(x) satisfies the relation 2f(x) +f(1-x) = x2 for all real x , then f(x) is
We have given that
2f(x) +f(1-x) = x2 - - -- - - - - -(i)
We have to find the value of f(x)
By replacing x by (1-x) in equation (i)we get,
2f(1-x) + f(x) = (1-x)2
2f(1-x) + f(x) = 1 + x2 – 2x - - - - - -(ii)
Multiplying the equation(i) by 2 we get,
4f(x) + 2f(1-x) = 2x2 - - - - - - (iii)
Subtracting equation (ii) from (iii)
3f(x) = x2 + 2x -1
So,
Therefore option (b) is correct.
If f(x) satisfies the relation 2f(x) +f(1-x) = x2 for all real x , then f(x) is
We have given that
2f(x) +f(1-x) = x2 - - -- - - - - -(i)
We have to find the value of f(x)
By replacing x by (1-x) in equation (i)we get,
2f(1-x) + f(x) = (1-x)2
2f(1-x) + f(x) = 1 + x2 – 2x - - - - - -(ii)
Multiplying the equation(i) by 2 we get,
4f(x) + 2f(1-x) = 2x2 - - - - - - (iii)
Subtracting equation (ii) from (iii)
3f(x) = x2 + 2x -1
So,
Therefore option (b) is correct.
If f:R->R be a function whose inverse is (𝑥+5)/3 , then what is the value of f(x)
f-1(x) = (x+5)/3
For solving this let us take
y = f-1(x)
y = (x+5)/3
Further solving we get,
x = 3y – 5
f(y) = 3y – 5
Therefore,
f(x) = 3x – 5
If f:R->R be a function whose inverse is (𝑥+5)/3 , then what is the value of f(x)
f-1(x) = (x+5)/3
For solving this let us take
y = f-1(x)
y = (x+5)/3
Further solving we get,
x = 3y – 5
f(y) = 3y – 5
Therefore,
f(x) = 3x – 5
Hint:
- The base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given in the question a diagram of a triangle named ABC and 𝑚∠𝐴 = 60°.
- We have to find the 𝑚∠𝐴 𝑎𝑛𝑑 𝑚∠𝐶.
In the given figure, AB = AC.
So, ABC is an isosceles triangle.
So, According to base-angle theorem, the angles opposite the congruent sides are congruent.
So,
Step 2 of 2:
Now we know that the sum of angle of triangle is equal to 1800.
So,
Since,
So,
Therefore,
Hint:
- The base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given in the question a diagram of a triangle named ABC and 𝑚∠𝐴 = 60°.
- We have to find the 𝑚∠𝐴 𝑎𝑛𝑑 𝑚∠𝐶.
In the given figure, AB = AC.
So, ABC is an isosceles triangle.
So, According to base-angle theorem, the angles opposite the congruent sides are congruent.
So,
Step 2 of 2:
Now we know that the sum of angle of triangle is equal to 1800.
So,
Since,
So,
Therefore,
Let A= {x, y, z} and B= { p, q, r, s}, What is the number of distinct relations from B to A ?
A= {x, y, z}
B= { p, q, r, s},
For finding the district relations from B to A we have to take the cartesian product of B and A
B×A = {p, q, r, s} × {x, y, z}
= {(p, x) , (p, y) , (p, z) , (q, x) , (q, y), (q, z) , (r, x) , (r, y), (r, z) , (s, x), (s, y), (s, z)}
Therefore there are 12 distinct relations .
Let A= {x, y, z} and B= { p, q, r, s}, What is the number of distinct relations from B to A ?
A= {x, y, z}
B= { p, q, r, s},
For finding the district relations from B to A we have to take the cartesian product of B and A
B×A = {p, q, r, s} × {x, y, z}
= {(p, x) , (p, y) , (p, z) , (q, x) , (q, y), (q, z) , (r, x) , (r, y), (r, z) , (s, x), (s, y), (s, z)}
Therefore there are 12 distinct relations .
Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f(g)
f(x) = x + 1
g(x) = 2x – 3
We have to find the value of
i) f(x) + g(x)
ii) f(x) – g(x)
iii) f(g(x))
Therefore,
i) f(x) + g(x) = x + 1 + 2x – 3
= 3x – 2
ii f(x) – g(x) = x + 1 – (2x – 3)
= x + 1 – 2x + 3
= 4 – x
iii) f(g(x)) = f(2x -3)
= (2x – 3) + 1
= 2x – 2
Therefore, f+g = 3x – 2
f – g = 4 – x
f(g) = 2x – 2
Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f(g)
f(x) = x + 1
g(x) = 2x – 3
We have to find the value of
i) f(x) + g(x)
ii) f(x) – g(x)
iii) f(g(x))
Therefore,
i) f(x) + g(x) = x + 1 + 2x – 3
= 3x – 2
ii f(x) – g(x) = x + 1 – (2x – 3)
= x + 1 – 2x + 3
= 4 – x
iii) f(g(x)) = f(2x -3)
= (2x – 3) + 1
= 2x – 2
Therefore, f+g = 3x – 2
f – g = 4 – x
f(g) = 2x – 2
Name the property of equality the statement illustrates.
If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.
The symmetric property states that for any real numbers, a and b, if a = b then b = a. Similarly with angles If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.
∴Option B
Name the property of equality the statement illustrates.
If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.
The symmetric property states that for any real numbers, a and b, if a = b then b = a. Similarly with angles If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.
∴Option B
Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
f = {(1,1), (2,3), (0,–1), (–1, –3)}
And also we have given that
f(x) = ax + b
We have to find the value of a and b .
First of all if the f is a function then its points will satisfy f(x) = ax + b
f(1) = 1
f(2) = 3
f(0) = -1
f(-1) = -3
i) (1,1)
f(1) = a (1) + b
1 = a + b
ii) (2,3)
f(2) = a (2) + b
3 = 2a + b
Subtract equation (i) from (ii)
2a – a + b – b = 3 – 1
a = 2
Putting this value in equation (i)
1 = 2 + b
b = 1 – 2
b = -1
Therefore, value of a = 2 and b = -1 .
Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
f = {(1,1), (2,3), (0,–1), (–1, –3)}
And also we have given that
f(x) = ax + b
We have to find the value of a and b .
First of all if the f is a function then its points will satisfy f(x) = ax + b
f(1) = 1
f(2) = 3
f(0) = -1
f(-1) = -3
i) (1,1)
f(1) = a (1) + b
1 = a + b
ii) (2,3)
f(2) = a (2) + b
3 = 2a + b
Subtract equation (i) from (ii)
2a – a + b – b = 3 – 1
a = 2
Putting this value in equation (i)
1 = 2 + b
b = 1 – 2
b = -1
Therefore, value of a = 2 and b = -1 .
Planet Wiener receives $2.25 for every hotdog sold. They spend $105 for 25 packages of hot dogs and 10 packages of buns. Think of the linear function that demonstrates the profit based on the number of hotdogs sold
Rate of Change:___________
Initial Value:______________
Independent Variable:______
Dependent Variable:________
EQ of Line:________________
SOL – Let Dependent Variable : x given by no of hotdog sold
Independent Variable : y given by profit earned
It is given that Planet Wiener receives $2.25 for every hotdog sold.
We know that Slope of the line = Rate of Change
So, m = 2.25 ---- (1)
Planet Wiener spends $105 for 25 packages of hot dogs and 10 packages of buns. (See it as an investment made before earning any profit. So, these $105 will actually be considered in ‘-’)
This initial value is obtained when no of hotdogs sold, x = 0 i.e., it will act as y – intercept, c = - 105 ---- (2)
Using slope intercept form equation of a line is given by
y = mx + c where m is slope and c is y – intercept.
Planet Wiener receives $2.25 for every hotdog sold. They spend $105 for 25 packages of hot dogs and 10 packages of buns. Think of the linear function that demonstrates the profit based on the number of hotdogs sold
Rate of Change:___________
Initial Value:______________
Independent Variable:______
Dependent Variable:________
EQ of Line:________________
SOL – Let Dependent Variable : x given by no of hotdog sold
Independent Variable : y given by profit earned
It is given that Planet Wiener receives $2.25 for every hotdog sold.
We know that Slope of the line = Rate of Change
So, m = 2.25 ---- (1)
Planet Wiener spends $105 for 25 packages of hot dogs and 10 packages of buns. (See it as an investment made before earning any profit. So, these $105 will actually be considered in ‘-’)
This initial value is obtained when no of hotdogs sold, x = 0 i.e., it will act as y – intercept, c = - 105 ---- (2)
Using slope intercept form equation of a line is given by
y = mx + c where m is slope and c is y – intercept.