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3 years ago

What is f(x)=3x^2-18x+23 into vertex form

1 answer:

5 0

$3x^2-18x+23=3(x^2-6x)+23=3(x^2-6x+9-9)+23$
$\quad=3((x-3)^2-9)+23=3(x-3)^2-27+23=3(x-3)^2-4$

The vertex is then $(3,-4)$ .

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PLEASE HELP! 50 POINTS

Alex73 [517]

5.1 ANSWERS.pdf

2. Page 3. Practice: Use your calculator to sketch a graph of each

5 0

2 years ago

Solve for g. Show your work! g+6-3=31

Zielflug [23.3K]

Answer:

g=28, that may not be how the teacher would want you to show your work, but that's how I find the answer!

Step-by-step explanation:

6-3=3

31-3=28

28=g

So therefore 28+6-3=31

6 0

3 years ago

The area of a rectangular piece of cardboard is represented by

Liula [17]

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

$A = wl$

w(2w + 3) = 9

From this, we get that:

$l = 2w + 3, A = 9$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

In this question:

$w(2w+3) = 9$

$2w^2 + 3w - 9 = 0$

Thus a quadratic equation with $a = 2, b = 3, c = -9$

Then

$\Delta = 3^2 - 4(2)(-9) = 81$

$w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5$

$w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3$

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

5 0

2 years ago

What is 35.125 as a mixed number??

Sever21 [200]

The number can be separated into 35+0.125
0.125 can be rewritten as,
$\frac{125}{1000}$
So, the number can be rewritten;
35+ $\frac{125}{1000}$
35 $\frac{125}{1000}$

5 0

3 years ago

A shoe box in the shape of a rectangular prism has a length of 12 inches, a width of 6 1/2 inches, and a height of 4 1/2 inches.

katovenus [111]

12 x 6 1/2 x 4 1/2 = 351in^3

3 0

3 years ago