Question

1 geometry the formula for the volume of a cone is $v = \frac{1}{3}\pi r^2 h$, where $v$ represents the volume, $r$ represents the radius of the base, and $h$ represents the height. what is the height of a cone with a volume of 110 cubic centimeters and a base with a radius of 5 centimeters?

a.
b.
c.
d.

2 twice a number $m$ minus three equals the sum of $m$ and five.

a. $2(m - 3) = m + 5$
c. $2m - 3 = 5m$
b. $2m - 3 = m + 5$
d. $2(m - 3) = 5m$

3 the sum of twice a number $x$ and 13 is two less than three times $x$.

a. $2(x + 13) = 3x - 2$
c. $2x + 13 = 3x - 2$
b. $2x + 13 = 2 - 3x$
d. $2x + 13 = 3(x - 2)$

4 eighty - five plus five times $x$ is equal to ten.

a. $85 + 5x = 10$
c. $5x - 85 = 10$
b. $85 - 5x = 10$
d. $(85 - 5)x = 10$

translate the equation into a verbal sentence.

5 $3y + 8 = 32$

a. three times a number $y$ minus 8 equals 32.
b. three times a number $y$ plus 8 equals 32.
c. three times a number $y$ times 8 equals 32.
d. three times a number $y$ divided by 8 equals 32.

Explanation:

Question 2

Step1: Analyze the left - hand side of the equation

The phrase "Twice a number \(m\) minus three" means we first multiply \(m\) by 2 (which is \(2m\)) and then subtract 3 from it. So the left - hand side of the equation is \(2m - 3\).

Step2: Analyze the right - hand side of the equation

The phrase "the sum of \(m\) and five" means we add \(m\) and 5 together, so the right - hand side of the equation is \(m + 5\).

Step3: Form the equation

Putting the left - hand side and the right - hand side together, we get the equation \(2m-3=m + 5\).

Step1: Analyze the left - hand side of the equation

The phrase "The sum of twice a number \(x\) and 13" means we first find twice of \(x\) (which is \(2x\)) and then add 13 to it. So the left - hand side of the equation is \(2x+13\).

Step2: Analyze the right - hand side of the equation

The phrase "two less than three times \(x\)" means we first find three times of \(x\) (which is \(3x\)) and then subtract 2 from it. So the right - hand side of the equation is \(3x - 2\).

Step3: Form the equation

Putting the left - hand side and the right - hand side together, we get the equation \(2x + 13=3x-2\).

Step1: Analyze the left - hand side of the equation

The phrase "Eighty - five plus five times \(x\)" means we add 85 and \(5x\) together. So the left - hand side of the equation is \(85 + 5x\).

Step2: Analyze the right - hand side of the equation

The right - hand side of the equation is 10.

Step3: Form the equation

Putting the left - hand side and the right - hand side together, we get the equation \(85+5x = 10\).

Answer:

b. \(2m - 3=m + 5\)

Question 3