True or false: if a > b then ac

Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

3 years ago

Read 2 more answers

Thomas made 8700 ml of tomato soup.he packed 1.6L of the soup in his kids lunches .he then froze half of the remaining soup.

kenny6666 [7]

Answer: 3550

Step-by-step explanation:

1.6L equals 1600mL

8700-1600=7100 remaining

7100 divided by 2 = 3550

7 0

3 years ago

Find the value of x and y

djverab [1.8K]

Answer:

x = 8, y = 27

Step-by-step explanation:

Since both opposite lines are equal in length to each other, these opposite lines are parallel to each other. The top line is parallel and same length as the bottom line and the left and right lines are also parallel and equal in length.

Based on that, the two left side angles must equal 180 and the right side two angles must equal 180.

(2y + 24) + (3y + 21) = 180

That's the same as 2y + 24 + 3y + 21 = 180

Simplify to 5y + 45 = 180

Subtract 45 from both sides

5y = 135

y = 27

(16x - 26) + (9x + 6) = 180

16x - 26 + 9x + 6 = 180

25x - 20 = 180

25x = 200

x = 8

7 0

3 years ago

Each day Marisa runs the same distance. She ran 35 miles in the last 5 days. What is the unit rate?

Fudgin [204]

Answer:

7 miles

Step-by-step explanation:

As, we will take unit rate as "x"

So, for one day = x distance

For 5 days = 5(x)

For 5 days she covered 35 miles

So therefore,

5(x) = 35 miles

X= 35/5

X=7 miles

For a day= 7 miles are covered

4 0

4 years ago

Is it necessary to have a common denominator when you multiply two fractions? Explain.

Softa [21]

It is not necessary to have a common denominator when you multiply two fractions

<h3>How to determine the true statement?</h3>

The statement is about the relationship between the denominator of fractions when they are multiplied

Take for instance, we have the following fractions

a/b and x/y

In the above fractions, we have

Numerator = a and x

Denominator = b and y

Where b and y do not have the same value

When they are multiplied, we have

Product = ax/by

The denominators do not have the same value

And we were able to calculate the product

This means that the fraction denominator do not have to be common

True or false: if a > b then ac > bc