Question

1. the perimeter of a rectangle is equal to 2 times the length plus twice the width.
2. the density of an object is the quotient of its mass and its volume.
3. simple interest is computed by finding the product of the principal amount p, the interest rate r, and the time t.
4. the surface area of a rectangular prism is 2 times the sum of the width, w, times height, h, and length, l, times width and length times height.

examples 4 and 5
write a sentence for each equation.

1. j + 16 = 35
2. 4m = 52
3. 7(p + 23)=102
4. r² - 15 = t + 19
5. $\frac{2}{5}v+\frac{3}{4}=\frac{2}{3}x^{2}$
6. $\frac{1}{3}-\frac{4}{5}z=\frac{4}{3}y^{3}$
7. g + 10 = 3g
8. 2(t + 4q)=2q + 4t
9. 4(a + b)=9a
10. 8(2y - 6x)=4 + 2x
11. $\frac{1}{2}(f + y)=f - 5$
12. k² - n² = 2b

example 6
write a sentence for each formula. then interpret the equation in the context of the situation.

1. geometry the formula for the volume of a cylinder is v = πr²h, where v is the volume, r is the length of the radius of the base, and h is the height of the cylinder.
2. geometry the formula for the volume of a cube is v = s³, where v is the volume and s is the side length.
3. finance the simple - interest formula is given by i = prt, where p = principal, r = rate, and t = time.
4. finance the compound - interest formula is...

Explanation:

19.

Step1: Translate the equation

The sum of a number \(j\) and 16 is 35.

Step1: Translate the equation

Four times a number \(m\) is 52.

Step1: Translate the equation

Seven times the sum of a number \(p\) and 23 is 102.

Answer:

The sum of a number \(j\) and 16 is 35.

20.