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3 years ago

5

John says the transformation rule (x, y) > (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the im

age (0, –2). What was his error?

1 answer:

erik [133]3 years ago

5 0

If he used the rule (x + 4, y + 7) then pre-image (4, 5) would result in image (4 + 4, 5 + 7) = (8, 12).

He should have used the rule (x - 4, y - 7)

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The graph of the quadratic function y = ax^2 + bx + c is given.<br> Find a + b + c.

andrey2020 [161]

Answer:

$\frac{145}{24}\approx 6$ ***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

$(0,3)$

$(2,8)$

$(6,5)$

Step-by-step explanation:

I see that the graph crosses at $(0,3)$ , $(2,8)$ , and $(6,5)$ .

The equation $y=ax^2+bx+c$ tells us the $y$ -intercept is $c$ since when $x=0$ we have $y=a(0)^2+b(0)+c=0+0+c=c$ .

The $y$ -intercept for our graph is $3$ . Therefore, $c=3$ .

So far we have the equation:

$y=ax^2+bx+3$ .

Let's enter the other points creating a system of linear equations to solve:

$8=a(2)^2+b(2)+3$

$5=a(6)^2+b(6)+3$

Let's simplify:

$8=4a+2b+3$

$5=36a+6b+3$

Let's subtract 3 on both sides:

$5=4a+2b$

$2=36a+6b$

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

$-15=-12a-6b$

$2=36a+6b$

Now adding the equations results in:

$-13=24a$

Divide both sides by 24:

$\frac{-13}{24}=a$

Now using one of the equations we can find $b$ :

$5=4a+2b$ with $a=\frac{-13}{24}$

$5=4\frac{-13}{24}+2b$

$5=\frac{-13}{6}+2b$

Add 13/6 on both sides:

$5+\frac{13}{6}=2b$

$\frac{30+13}{6}=2b$

$\frac{43}{6}=2b$

Divide both sides by 2:

$\frac{43}{2(6)}=b$

$\frac{43}{12}=b$

So we have the equation:

$y=\frac{-13}{24}x^2+\frac{43}{12}+3$

Let's evaluate $a+b+c$ now:

$\frac{-13}{24}+\frac{43}{12}+3$

$\frac{-13+86+72}{24}$

$\frac{73+72}{24}$

$\frac{145}{24}$

4 0

3 years ago

rectangular stained glass window is 2 feet by 4 feet. A clear glass border is constructed around the stained glass window. The w

Mice21 [21]

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

4x^2+12x=7
4x^2+12x-7=0
D=12^2-4x4x(-7)=256
X1=(-12-16)/(2x4)=-3.5 impossible
X2=(-12+16)/(2x4)=0.5

A

7 0

3 years ago

What is the answer?

iVinArrow [24]

Answer:42

Step-by-step explanation:

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3 years ago

Help me with this math work please

Aloiza [94]

Your photo is super blurry! I can’t read parts of the problems, so I can’t exactly help you. Sorry! Good luck.

7 0

2 years ago

Read 2 more answers

In the data set below, what is the range? 9, 4, 9, 2, 8, 2, 1

noname [10]

First put these in order from least to greatest.

1,2,2,4,8,9,9 is the correct order
Range is when we subtract the greatest value of our data set from the smallest so in our case it would be 9-1 which leaves us with our answer that 8 is your range.

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3 years ago