Which are like terms to the term 2x.

The quadratic parent function has been reflected down, stretched vertically by a factor of 1/3, shifted vertically by 9 units an

zmey [24]

Answer:

1a) f(x) = -1/3(x + 12)² + 9

1b) f(x) = -1/3x² - 8x - 39

General Formulas and Concepts:

Algebra I

Equality Properties

Expand by FOIL (First Outside Inside Last)

Standard Form: ax² + bx + c = 0

Transformations Graph: f(x) = a(bx - c)² + d

a = vertical shrink/stretch

b = horizontal shrink/stretch

c = horizontal movement left/right

d = vertical movement up/down

Step-by-step explanation:

Step 1: Define

Reflected down and vertically stretched by 1/3: a = -1/3

Shifted vertically by 9 units: d = 9

Shifted horizontally by -12 units: c = -12

Step 2: Write Vertex Form

Define: f(x) = a(bx - c)² + d
Substitute: f(x) = -1/3(x + 12)² + 9

Step 3: Write Standard Form

Define: f(x) = -1/3(x + 12)² + 9
Expand: f(x) = -1/3(x² + 24x + 144) + 9
Distribute -1/3: f(x) = -1/3x² - 8x - 48 + 9
Combine like terms: f(x) = -1/3x² - 8x - 39

And we have our final answers!

8 0

3 years ago

What are 4 key word that indicate that the problem involves an inequality?

Maslowich

Answer:

Less than, at max, greater than, at least

Or,

Not greater/more than, not less than

4 0

4 years ago

What is the area of a pizza with a diameter of 12 inches? Round to the nearest tenth. Use 3.14 for pi.

Flauer [41]

Answer:

$\boxed {\boxed {\sf a \approx 113.0 \ in^2}}$

Step-by-step explanation:

Assuming this pizza is a circle, we can use this formula for area:

$a= \pi r^2$

1. Find Radius

We are given the diameter: 12 inches, but the formula uses radius.

The radius is half the diameter, or:

$r=\frac{d}{2}$

$r=\frac{12 \ in}{2}$

$r= 6 \ in$

2. Calculate Area

Substitute the radius (6 inches) in for r. The question also asks us to use 3.14 for pi.

$a= (3.14)(6 \ in)^2$

Solve the exponent.

(6 in)²= 6 in* 6 in= 36 in²

$a= (3.14)(36 \ in^2)$

Multiply.

$a= 113.04 \ in^2$

3. Round

The question asks us to round to the nearest tenth.

The 4 in the hundredth place tells us to leave the 0 in the tenth place.

$a \approx 113.0 \ in^2$

The area of the pizza is about 113.0 square inches.

7 0

3 years ago

Find the value of x in each case.

MissTica

Answer:

The angle X in every part of the triangle is 22.5⁰

7 0

3 years ago

Slope and y intercept

morpeh [17]

Answer:

$y=\frac{25}{1}x+75$

The beginning balance of Sophie's account is 75

Step-by-step explanation:

Using the slope intercept form aka $y=mx+b$

The slope of a line describes how steep a line is.

We can see that the y-axis goes up by 25.

25, 50, 75, 100, 125, 150 etc

$ is how much you have in your bank account.

We can see that Sophie starts off with 75 dollars.

In the first week, we see that Sophie has 100 dollars. In the second week, we see that Sophie has 125.

<h3>how to find the slope</h3>

$slope formula\\m=\frac{rise(y)}{run(x)}=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

The first week (1, 100)

The second week (2,125)

$(x_{1}, y_{1})= 1, 100\\(x_{2}, y_{2})= 2, 125\\m=\frac{125-100}{2-1}=\frac{25}{1} \\Up 25 (aka, 1 line), over 1(aka 2 lines)$

7 0

3 years ago