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3 years ago

Let f(x) = 7x - 13. Find f-1(x).

1 answer:

4 0

$f(x)=7x-13 \\ \\ y=7x-13 \ \ \ |+13 \\
y+13=7x \ \ \ |\div 7 \\
x=\frac{1}{7}y+\frac{13}{7} \\ \\
\boxed{f^{-1}(x)=\frac{1}{7}x+\frac{13}{7}}$

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3 years ago

What is the measure of the vertex angle of an isosceles

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Answer:

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2 years ago

You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar

Verizon [17]

Answer:

$Length=10.5\ ft$

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Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

$P=2(x+y)$

we have

$P=42\ ft$

$42=2(x+y)$

simplify

$21=(x+y)$

$y=21-x$ ------> equation A

Remember that the area of rectangle is equal to

$A=xy$ ----> equation B

substitute equation A in equation B

$A=x(21-x)$

$A=21x-x^{2}$ ----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point $(10.5,110.25)$

see the attached figure

$x=10.5\ ft$

Find the value of y

$y=21-10.5=10.5\ ft$

The garden is a square

the area is equal to

$A=(10.5)(10.5)=110.25\ ft^{2}$ ----> is equal to the y-coordinate of the vertex is correct

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2 years ago