Mathematics, 05.10.2019 02:30, BookiesBaby8533

Quinn is building an enclosed pen in his backyard he wants the perimeter to be no more than 50 feet he also wants the length to be at least 5 feet longer than the width

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answered: chelsiem25

Option B width = 5 feet and length = 12 feet

The solution in the attached figure

Step-by-step explanation:

The options of the questions are

Which combination of width and length will meet Quinn’s requirements for the pen?

A. width = 7 feet and length = 20 feet

B. width = 5 feet and length = 12 feet

C. width = 15 feet and length = 10 feet

D. width = 11 feet and length = 15 feet

Let

x -----> the length of the enclosed pen in feet

y-----> the width of the enclosed pen in feet

we know that

The perimeter is equal to

P=2(x+y)

In this problem

$2(x+y)\leq 50$

Simplify

$(x+y)\leq 25$ ----> inequality A

$x\geq y+5$ ---> inequality B

using a graphing tool

The solution is the triangular shaded area

see the attached figure N 1

Remember that

The values of x and y cannot be a negative number

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequality

Verify each case

case A) width = 7 feet and length = 20 feet

For y=7, x=20

Check inequality A

$(20+7)\leq 25$

$(27)\leq 25$ ----> is not true

therefore

This combination of width and length will not meet Quinn’s requirements for the pen

case B) width = 5 feet and length = 12 feet

For y=5, x=12

Check inequality A

$(12+5)\leq 25$

$(17)\leq 25$ ----> is true

Check inequality B

$12\geq 5+5$

$12\geq 10$ -----> is true

therefore

This combination of width and length will meet Quinn’s requirements for the pen

case C) width = 15 feet and length = 10 feet

For y=15, x=10

Check inequality A

$(10+15)\leq 25$

$(25)\leq 25$ ----> is true

Check inequality B

$10\geq 15+5$

$10\geq 20$ -----> is not true

therefore

This combination of width and length will not meet Quinn’s requirements for the pen

case D) width = 11 feet and length = 15 feet

For y=11, x=15

Check inequality A

$(15+11)\leq 25$

$(26)\leq 25$ ----> is not true

therefore

This combination of width and length will not meet Quinn’s requirements for the pen

Note If the ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area

see the attached figure N 2 to better understand the problem

Quinn is building an enclosed pen in his backyard he wants the perimeter to be no more than 50 feet

answered: Guest

Hello!

the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

$\frac{a^{m} }{a^{n} }=a^{m-n}$

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

$\frac{3^{4} }{3^{1}}$

then, calculating we have:

$\frac{3^{4} }{3^{1}}=3^{4-1}=3^{3}$

hence, the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

have a nice day!

answered: Guest

step-by-step explanation:

What is the first step in sketching the graph of a rational function

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Quinn is building an enclosed pen in his backyard he wants the perimeter to be no more than 50 feet...