The perimeter of a rectangle is 120 feet. the width of the rectangle.

Compute the total pay:

stiv31 [10]

Answer:

$112.65

Step-by-step explanation:

7.25 x 8 = 58

58 + 54.65 = 112.65

3 0

3 years ago

PLEASE HELP ME TO UNDERSTAND THESE KINDS OF QUESTIONS I HAVE BEEN STRUGGLING WITH THESE PLEASE EXPLAIN HOW THEY WORK TO ME!!!!!

ASHA 777 [7]

Q1 - meters

Q2 - square feet

4 0

3 years ago

The sum of four consecutive terms of an arithmetic progression is 32 and the ratio of product of the first and the last term to

OverLord2011 [107]

The four consecutive terms are 2,6,10,14.

Explanation:

Let the four consecutive terms of an arithmetic progression be (a - 3d), (a - d),(a + d), (a + 3d)

It is given that the sum of four consecutive terms is 32.

Thus, adding all the four consecutive terms, we have,

$\begin{array}{r}{a-3 d+a-d+a+d+a+3 d=32} \\{4 a=32} \\{a=8}\end{array}$

Thus, the value of a is 8.

It is also given that the ratio of the product of first and last term to the product of the two middle terms is 7:15. Thud, we have,

$\frac{(a-3d)(a+3d)}{(a-d)(a+d)} =\frac{7}{15}$

Simplifying the terms, we have,

$\begin{aligned} \frac{a^{2}-9 d^{2}}{a^{2}-d^{2}} &=\frac{7}{15} \\ 15\left(a^{2}-9 d^{2}\right) &=7\left(a^{2}-d^{2}\right) \\ 15 a^{2}-135 d^{2} &=7 a^{2}-7 d^{2} \\ 8 a^{2} &=128 d^{2} \end{aligned}$

Now, substituting a = 8, we have,

$\begin{aligned} 8(64) &=128 d^{2} \\ 512 &=128 d^{2} \\ 4 &=d^{2} \\ 2 &=d \end{aligned}$

Thus, the value of d is 2.

Now, we shall substitute the value of a and d in the terms (a - 3d), (a - d),(a + d), (a + 3d), we get, the four consecutive terms.

Thus, the four consecutive terms are 2,6,10,14.

8 0

3 years ago

Let F(x) = x^2 – 15 and G(x)= 4 - x Find (F/G)(–7) =

KATRIN_1 [288]

Answer:

$\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation

Step-by-step explanation:

Step 1: Define

Identify

F(x) = x² - 15

G(x) = 4 - x

Step 2: Find

Substitute in functions: $\displaystyle \bigg( \frac{F}{G} \bigg)(x) = \frac{x^2 - 15}{4 - x}$

Step 3: Evaluate

Substitute in x [Function (F/G)(x)]: $\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{(-7)^2 - 15}{4 - (-7)}$
Exponents: $\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{49 - 15}{4 - (-7)}$
Subtract: $\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}$