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2 years ago

The function A(b) relates the area of a trapezoid with a given height of 12 and

Mathematics

1 answer:

Flura [38]2 years ago

5 0

Answer:

$B(a)=\frac{a}{6}-9$

Step-by-step explanation:

see the attached figure , to better understand the problem

we have

$A(b)=12(\frac{b+9}{2})$

where

A(b) ---> is the trapezoid's area

b ---> is the other base value

Solve the equation for b

That means ----> isolate the variable b

Divide 12 by 2 right side

$A=6(b+9)$

Divide by 6 both sides

$\frac{A}{6}=b+9$

subtract 9 both sides

$\frac{A}{6}-9=b$

Rewrite

$b=\frac{A}{6}-9$

Convert to function notation

$B(a)=\frac{a}{6}-9$

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A crew must repave a road that is 3/8 miles long. They can repave 1/48 miles per hour. How long will it take the crew to repave

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Answer:

Step-by-step explanation:

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2 years ago

Curtis threw 15 darts at a dartboard. 40% of his darts hit the bull's-eye. How many darts did not hit the bull's-eye?

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2 years ago

Read 2 more answers

A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, the

pochemuha

Answer:

The quadratic function whose graph contains these points is $y=-x^{2}-2x-2$

Step-by-step explanation:

We know that a quadratic function is a function of the form $y=ax^{2}+bx+c$ . The first step is use the 3 points given to write 3 equations to find the values of the constants a,b, and c.

Substitute the points (0,-2), (-5,-17), and (3,-17) into the general form of a quadratic function.

$-2=a*0^{2}+b*0+c\\c=-2$

$-17=a*-5^{2}+b*-5+c\\c=-25a+5b-17$

$-17=a*3^{2}+b*3+c\\ c=-9a-3b-17$

We can solve these system of equations by substitution

Substitute $c=-9a-3b-17$

$-9a-3b-17=25a+5b-17\\-9a-3b-17=-2$

Isolate a for the first equation

$-9a-3b-17=-25a+5b-17\\a=\frac{b}{2}$

Substitute $a=\frac{b}{2}$ into the second equation

$-9\left(-\frac{b}{2}\right)-3b-17=-2$

Find the value of b

$-9\left(-\frac{4b}{17}\right)-3b-17=-2\\ b=-2$

Find the value of a

$a=\frac{b}{2}\\ a=-1$

The solutions to the system of equations are:

b=-2,a=-1,c=-2

So the quadratic function whose graph contains these points is

$y=-x^{2}-2x-2$

As you can corroborate with the graph of this function.

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2 years ago