Mathematics, 18.02.2020 07:45 love123jones

Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Cynthia plans to make the area of her tree house at least 13 square feet. Write and solve an inequality to find the area of Andrew's tree house. Let x be the area of Andrew's tree house. Describe how you know which tree house is larger without solving the inequality.

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Answer from: anayajhughes0603

The area of Andrew's tree house must be greater than or equal to 117 square feet

Step-by-step explanation:

Let

x -----> the area of Andrew's tree house in square feet

y ----> the area of Cynthia's tree house in square feet

we know that

Cynthia plans to make the area of her tree house at least 13 square feet.

The word "at least" means "greater than or equal to"

$y\geq 13$ ----> inequality A

Cynthia plans to build a tree house that is 1/3 the size of Andrew's tree house

Remember that

When two figures are similar, the ratio of its areas is equal to the scale factor squared

In this problem the scale factor is given

The scale factor is 1/3

The scale factor squared is 1/9

That means

The area of Andrew's tree house is 9 times greater than the area of Cynthia's tree house

The area of Cynthia's tree house is 9 times smaller than the area of Andrew's tree house

$y=\frac{1}{9}x$ ----> equation B

substitute equation B in the inequality A

$\frac{1}{9}x\geq 13$

solve for x

$x\geq 117\ ft^2$

The area of Andrew's tree house must be greater than or equal to 117 square feet

we know that Andrew's tree house is larger than Cynthia's tree house, because the problem states that Cynthia's tree house is 1/3 the size of Andrew's tree house

That means

The size of Andrew's tree house is 3 times greater than the size of Cynthia's tree house, without solving the inequality

Answer from: Quest

87%

step-by-step explanation:

apex answer

Answer from: Quest

x =-.20752

step-by-step explanation:

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know logb c = loga c/loga b

we want to convert to base 10 so a = 10

by default, we do not write the 10 c = 4 and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

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