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3 years ago

Which equation can be used to describe g(x) in terms of f(x)?

Mathematics

1 answer:

ollegr [7]3 years ago

7 0

F(x) is a parabola opening upward, while g(x) is a parabola facing downward.

So there needs to be a negative out front of the f(x) term. The negative will flip the parabola. That means the answer is either A or B

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After we flip the parabola, we need to translate the vertex (0,0) to the point (2,1) so that it matches up with the vertex of g(x)

To move from (0,0) to (2,1) we shift 2 units to the right and 1 unit up.

To move 2 units to the right, replace 'x' with 'x-2'
To move 1 unit up, you tack on a "+1"

So f(x) turns into -f(x) and then we replace the x with x-2 to get -f(x-2). Finally we tack on a "+1" to get -f(x-2)+1

The g(x) function is g(x) = -f(x-2)+1

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Therefore the final answer is choice B

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Which shows one way to determine the factors of x3 11x2 – 3x – 33 by grouping? x2(x 11) 3(x – 11) x2(x – 11) – 3(x – 11) x2(x 11

Aloiza [94]

The one way to determine factors of x³ + 11x² – 3x – 33 will be $x^2(x+11)-3(x+11)_$ .

<h3>What is a factorization?</h3>

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The steps involved in the factorization are;

1. For each pair of parentheses, we create a common factor.

2. We use x2 as a common factor for the first parenthesis.

3. We use common factor 3 for the second parenthesis.

$x^3 + 11x^2 - 3x -33 \\\\ x^2(x+11)-3(x+11)_$

We will find the final solution as $x^2(x+11)-3(x+11)_$ .

Hence the one way to determine factors of x³ + 11x² – 3x – 33 will be $x^2(x+11)-3(x+11)_$ .

To learn more about the factorization refer to the link;

brainly.com/question/24182713

3 0

1 year ago

Solve.<br> X = -7<br> 4x - 4y = 12<br> (x,y)

Fynjy0 [20]

Answer:

(-7, -10)

$x=-7\\y=-10$

Step-by-step explanation:

$4x-4y=12$

Substitute x for -7.

$4(-7)-4y=12$

Multiply 4 by -7.

$-28-4y=12$

Add 28 on both sides.

$-4y=40$

Divide -4 on both sides.

$y=-10$

4 0

2 years ago

Explain how to solve 3^x-4=6 using the change of base formula log base b of y equals log y over log b. include the solution for

Alexxandr [17]

Answer:

x = log 10/log 3

Step-by-step explanation:

3^x - 4 = 6

3^x = 10

We take log base 3 of both sides since log_3 3^x is simply x.

log_3 3^x = log_3 10

x = log_3 10

We have an answer for x, but it is a log base 3. We want log base 10.

Now we use the change of base formula.

log_b y = log y/log b

x = log 10/log 3

7 0

3 years ago

Please help <br><br><br> thank u

zzz [600]

I think the answer Is B

3 0

3 years ago

Scenario: Kevin is baking cupcakes for a fundraiser at his school. Yesterday, he prepared 30 cupcakes in 45 minutes. Today, he p

attashe74 [19]

a) As the constants are equal, the situation represents a proportional relationship.

b) The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the constants for each situation are:

k = 30/45 = (30/15)/(45/15) = 2/3 = 20/30.

Since the constants are equal, the situation represents a proportional relationship.

The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

5 0

2 years ago