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1 year ago

20 POINTS!

Mathematics

1 answer:

Norma-Jean [14]1 year ago

5 0

Answer:

C. $x^{3}$ - 4 $x^{3}$ - 24x + 21

Step-by-step explanation:

(x - 7)( $x^{2}$ + 3x - 3)

x( $x^{2}$ + 3x - 3) + -7( $x^{2}$ + 3x - 3)

( $x^{3}$ + 3 $x^{2}$ - 3x) + (-7 $x^{2}$ + -21x + 21)

$x^{3}$ - 4 $x^{3}$ - 24x + 21

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If g(x)=4x^2-16 we’re shifted 9 united to the right and 1 down, what would the new equation be?

Inessa05 [86]

Shown in the graph

<h2>Explanation:</h2>

Using graph tools we can graph the function:

$g(x)=4x^2-16$

which is the red graph shown below. As you can see, this is a parabola. The rule for vertical and horizontal shifts is as follows:

$Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:$

$\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)$

Therefore, If we shift the red graph 9 units to the right and 1 down, our new function (let's call it $h(x)$ ) will be:

$h(x)=4\left(x-9\right)^{2}-16-1 \\ \\ Simplifying: \\ \\ h(x)=4\left(x-9\right)^{2}-17$

This graph is the blue graph below. Let's verify the transformation taking the vertex of the red graph:

$(0,-16)$

By translating the 9 units to the right and 1 down the vertex is also translated by the same rule, so:

$New \ vertex: \\ \\ (0+9,-16-1) \\ \\ (9,-17)$

<h2>Learn more:</h2>

Cubic function: brainly.com/question/13773618#

#LearnWithBrainly

5 0

3 years ago

he marketing research department at the Fresno Mall plans to survey teenagers about a newly developed soft drink. Each person sa

Nat2105 [25]

50% of those who liked orange flavored soda also like lime flavored soda according to the conditional probability.

According to the statement

we have given that the in the survey 70% of the people surveyed said they like the orange flavored soda and 35% of the people surveyed said they liked the orange flavored soda AND the lime flavored soda.

And we have to find the conditional probability about this given statement.

So, We know that the

Let A and B represents the following events.

A : The people like the orange flavored soda.

B : The people like the lime flavored soda.

It is given that 70% of the people surveyed said they like the orange flavored soda.

so, P(A) = 0.70

And 35% of the people surveyed said they liked the orange flavored soda AND the lime flavored soda.

So, P(A ∩ B ) = 0.35

A. Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

And

B. The formula for conditional probability is is written below:

P(A/B) = P(A ∩ B ) / P (B)

And

C. We need to find the percent of those who liked orange flavored soda also like lime flavored soda.

Use the above written conditional probability formula then

Substitute P(A)=0.70 and P(A∩B)=0.35 in the above formula.

So,

P(B/A) = P(A ∩ B ) / P (A)

P(B/A) = 0.35 / 0.70

P(B/A) = 0.50

So, 50% of those who liked orange flavored soda also like lime flavored soda according to the conditional probability.

Learn more about conditional probability here

brainly.com/question/23382435

Disclaimer: This question was incomplete. Please find the full content below.

Question:

The marketing research department at the Fresno Mall plans to survey teenagers about a newly developed soft drink. 70% of the people surveyed said they like the orange flavored soda. 35% of the people surveyed said they liked the orange flavored soda AND the lime flavored soda. Using this information and the Text Editor, answer the following questions:

1.What is conditional probability?

2.Explain the formula for conditional probability.

3.Explain how to solve this example.

What percent of those who liked orange flavored soda also like lime flavored soda, and how did you come to that conclusion?

#SPJ4

5 0

2 years ago

A display case for the artifact is in the shape of a cube. Each side of the display case is three times longer than the width ww

Katena32 [7]

A cube is a 3d object bounded by 6 square faces.

Each side of the display case is 3 times longer than the width of the artifact.

width of the artifact = w
side of the cube = 3w

<span>a. Write an expression for the volume of the case.
volume of a cube is the measure of its side raised to the power of 3.

Volume = (3w)</span>³

<span>Volume = 27w</span>³<span>

</span>

6 0

3 years ago

What is the total area of the figure below?

ki77a [65]

Answer:

Step-by-step explanation:

28×14=392, which generally already gives you the answer. But the extra area is a trapezoid so we do 4+6=10×2(height)=20, but we have to divide by two since its a trapezoid giving us 10. So 10+392=402

7 0

3 years ago

-3x -4y = 20 x - 10y =16 if (x, y) is the solution to the system of equations above what is the value of x?

balu736 [363]

Multiply first equation by -5 and 2nd by 2, add them

15x+20y=-100
<u>2x-20y=32 +</u>
17x+0y=-68

17x=-68
divide both sides by 17
x=-4

the x value is -4

6 0

3 years ago