Gordon types 2,590 words in 35 minutes. Find the unit rate.

The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).

garri49 [273]

Answer:

(-1,-6)

Step-by-step explanation:

$f(x)=x^2+6x+3$

$g(x)=f(x-2)$

$g(x)=(x-2)^2+6(x-2)+3$ (Replaced x in f with (x-2))

$g(x)=x^2-4x+4+6x-12+3$ (Used $(x+b)^2=x^2+2bx+b^2$ and distributive property)

$g(x)=x^2-4x+6x+4-12+3$ (Gathered like terms)

$g(x)=x^2+2x-5$ (Simplified)

The vertex of a parabola occurs at $(\frac{-b}{2a},g(\frac{-b}{2a})$ .

Let's find $\frac{-b}{2a}$ first.

$\frac{-2}{2(1)}=-1$

Now we can obtain $g(\frac{-b}{2a})$ which is $g(-1)$ in this case:

$g(x)=x^2+2x-5$

$g(-1)=(-1)^2+2(-1)-5$

$g(-1)=1-2-5$

$g(-1)=-1-5$

$g(-1)=-6$ .

The vertex is (-1,-6).

6 0

3 years ago

How to solve inequalities

Ulleksa [173]

Answer:

Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.

Step 2 Simplify by combining like terms on each side of the inequality.

Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

Step 4 Divide each term of the inequality by the coefficient of the unknown. If the coefficient is positive, the inequality will remain the same. If the coefficient is negative, the inequality will be reversed.

Step 5 Check your answer.

3 0

3 years ago

Read 2 more answers

There are 18 girls and 12 boys in your class. What is the probability that a new kid entering your class will be a boy ?

xenn [34]

C.
12/30=0.4
You should really learn how to do probabilities. They don't go away after like the sixth grade.

6 0

3 years ago

Find two numbers whos diffrence is 16 and the product is 720

antiseptic1488 [7]

Answer:

the numbers who's difference is 16 and the product is 720 is

36 &20

Explanation:

to finding numbers you have to express the equation in a quadratic equation then Factor it.

since the two numbers have a difference of 16 you can say that the first number is x and the second number is x -16 then their product is 720.

x(x-16)=720

x²-16x=720

x²-16x-720=0

(x-36)(x+20)

there are two possible value of x but since you are looking for the positive value of x, choose the positive value of x the first number is 20.

To find the second number

x-16=20

x=20+16

x=36

the second number is 36

Now to check

36-20=16

20*36=720

8 0

3 years ago

Find the difference of(ab+8a+1)-(-6ab+4)

vagabundo [1.1K]

Hey there!

When finding the difference of expressions like these, there's a few things you should keep in mind.

1. When finding the difference of two polynomials, multiply the polynomial that implied to be "negative" by –1 to expand the problem and make it easier to solve.

2. You combine terms based on their unknown terms, like x, y, x², ab, etc. You cannot combine the terms x and x², but you can combine the terms 6b and 8b by adding them.

3. You can rearrange your terms however you see fit. If a polynomial is implied as "positive", you can multiply that entire polynomial by +1 to get rid of the parentheses.

With all that in mind, you can go ahead and solve for your difference, like so:

$(ab+8a+1)-(-6ab+4)$

$(ab+8a+1) (-1(-6ab+4))$

$(ab+8a+1) + (6ab-4)$

$ab+6ab+8a+1-4$

$7ab+8a-3$

$7ab+8a-3$ will be your difference.

Hope this helped you out! :-)

8 0

3 years ago