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2 years ago

17. The length of a rectangle is 12 in, and the perimeter is 56 in. Find the width of the rectangle.

Mathematics

1 answer:

Ivahew [28]2 years ago

4 0

Answer:

Step-by-step explanation:

P = 2(L + W)

P = 56

L = 12

now sub...we are looking for w

56 = 2(12 + W)

56 = 24 + 2W

56 - 24 = 2W

32 = 2W

32/2 = W

16 = W <==== the width is 16 inches

check...

P = 2(L + W)

56 = 2(12 + 16)

56 = 2(28)

56 = 56 (correct)

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Which pair of funtions is not a pair of inverse functions? please help!!

antiseptic1488 [7]

Answer:

$f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Step-by-step explanation:

we know that

To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.

we will proceed to verify each case to determine the solution of the problem

case A) $f(x)=\frac{x+1}{6} , g(x)=6x-1$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y+1}{6}$

Isolate the variable y

$6x=y+1$

$y=6x-1$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=6x-1$

therefore

f(x) and g(x) are inverse functions

case B) $f(x)=\frac{x-4}{19} , g(x)=19x+4$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y-4}{19}$

Isolate the variable y

$19x=y-4$

$y=19x+4$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=19x+4$

therefore

f(x) and g(x) are inverse functions

case C) $f(x)=x^{5}, g(x)=\sqrt[5]{x}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=y^{5}$

Isolate the variable y

fifth root both members

$y=\sqrt[5]{x}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=\sqrt[5]{x}$

therefore

f(x) and g(x) are inverse functions

case D) $f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y}{y+20}$

Isolate the variable y

$x(y+20)=y$

$xy+20x=y$

$y-xy=20x$

$y(1-x)=20x$

$y=20x/(1-x)$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=20x/(1-x)$

$\frac{20x}{1-x}\neq \frac{20x}{x-1}$

therefore

f(x) and g(x) is not a pair of inverse functions

7 0

2 years ago

Read 2 more answers

Factor the expression completely. 625x4 - 256y4

scoundrel [369]

Answer:

(625 • (x4)) - 28y4

54x4 - 28y4 3.1 Factoring: 625x4-256y4

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 625 is the square of 25

Check : 256 is the square of 16

Check : x4 is the square of x2

Check : y4 is the square of y2

Factorization is : (25x2 + 16y2) • (25x2 - 16y2) 3.2 Factoring: 25x2 - 16y2

Check : 25 is the square of 5

Check : 16 is the square of 4

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (5x + 4y) • (5x - 4y)this is the answer: (25x2 + 16y2) •(5x + 4y) • (5x - 4y)

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2 years ago

A line passes through the point (-8,3) and has a slope of -3/4. What is this equation in slope intercept form

kupik [55]

I did the math and I believe the answer is, the y-intercept is 12.3.

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2 years ago

Factor completely 5ax2 − 20x3 2a − 8x. (a 4x)(5x2 2) (a 4x)(5x2 − 2) (a − 4x)(5x2 2) (a − 4x)(5x2 − 2).

antiseptic1488 [7]

The complete factor of the polynomial 5ax² − 20x³ + 2a − 8x is (5x² + 2) (y − 4x). Then the correct option is C.

<h3>What is polynomial?</h3>

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Factor completely 5ax² − 20x³ + 2a − 8x.

Take 5x² common from the first two terms and 2 from the last two terms. we have

5ax² − 20x³ + 2a − 8x

5x²(a − 4x) + 2 (a − 4x)

Take (a - 4) common, then we have

(5x² + 2) (y − 4x)

The complete factor of the polynomial 5ax² − 20x³ + 2a − 8x is (5x² + 2) (y − 4x). Then the correct option is C.

More about the polynomial link is given below.

brainly.com/question/17822016

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2 years ago

1\100 of 3756 in dollars

maksim [4K]

Answer: 37.56

What the fraction 1/100 is saying is it is dividing them 3756 by a 100.

3756/100= 37.56

3 0

3 years ago