Which number represents 50% of 74?<br> A. 35<br> B. 37<br> C. 38<br> D. 39

Enter the correct answer in the box.

Mekhanik [1.2K]

The equation in the vertex form of g(x) is:

$g(x) = (x + 1)^2 - 38$

<h3>How to get the equation of function g?</h3>

We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).

So first, let's rewrite f(x) to its vertex form:

$f(x) = x^2 - 4x - 32$

The vertex is at:

$x = -(-4)/2*1 = 2$

The y-value of the vertex is:

$f(2) = 2^2 - 4*2 - 32 = -36$

Then the vertex form of f(x) is:

$f(x) = (x - 2)^2 - 36$

If we move this vertex 2 units below, and 3 units to the left, then we have:

$g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38$

That is the equation for g(x) in vertex form.

If you want to learn more about quadratic equations:

brainly.com/question/1214333

#SPJ1

6 0

2 years ago

What is the measure of z

Mama L [17]

What? Where’s the rest?

8 0

2 years ago

PLS HELP ILL GIVE BRAINLIEST

inysia [295]

<h3>Answer: 14x - 8</h3>

=======================================================

Explanation:

I'll use the quadratic formula to find the roots or x intercepts. This slight detour allows us to factor without having to use guess-and-check methods.

The equation is of the form ax^2+bx+c = 0

a = 12
b = -11
c = -5

This leads to...

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-11)\pm\sqrt{(-11)^2-4(12)(-5)}}{2(12)}\\\\x = \frac{11\pm\sqrt{361}}{24}\\\\x = \frac{11\pm19}{24}\\\\x = \frac{11+19}{24} \ \text{ or } \ x = \frac{11-19}{24}\\\\x = \frac{30}{24} \ \text{ or } \ x = \frac{-8}{24}\\\\x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}$

Now use those roots to form these steps

$x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}\\\\4x = 5 \ \text{ or } \ 3x = -1\\\\4x - 5 =0 \ \text{ or } \ 3x+1 = 0\\\\(4x-5)(3x+1) = 0$

Refer to the zero product property for more info.

Therefore, the original expression factors fully to (4x-5)(3x+1)

Use the FOIL rule to expand it out and you should get 12x^2-11x-5 again.

----------------------------------------------

We did that factoring so we could find the side lengths of the rectangle.

I'm using the fact that area = length*width

L = length = 4x-5
W = width = 3x+1

The order of length and width doesn't matter.

From here, we can then compute the perimeter of the rectangle

P = 2(L+W)

P = 2(4x-5+3x+1)

P = 2(7x-4)

P = 14x - 8

6 0

2 years ago

A village fete has a children’s running race each year, run in heats of up to ten children. For each heat the first three contes

bekas [8.4K]

Answer: 1) 1/3,654 2) 3/406 3) 72,684,900,288,000 4) 120

<u>Step-by-step explanation:</u>

1) First and Second and Third

$\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}\times \dfrac{1\ remaining\ prize}{27\ remaining\ people}=\dfrac{6}{21,924}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad =\large\boxed{\dfrac{1}{3,654}}$