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2 years ago

Multiply (x – 2)(3x + 4) using the distributive property. Select the answer choice showing the correct distribution.

Mathematics

1 answer:

levacccp [35]2 years ago

5 0

Answer: Choice C)

(x-2)(3x) + (x-2)(4)

======================================

How to get this answer? One easy way that might work is to let y = x-2, which will allow us to do a replacement.

We will go from (x-2)(3x+4) to y(3x+4). Now use the distributive property to multiply the y term by each term inside

y(3x+4) = y*3x + y*4 = (y)*(3x) + (y)*(4)

The last step is to re-introduce y = x-2 back in. So replace y with x-2 like so

(y)*(3x) + (y)*(4) = (x-2)*(3x) + (x-2)(4)

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Write an equation that has a graph with the shape of y = x^2, but shifted left 3 units.

svetoff [14.1K]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf % template detailing
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\$

$\bf \bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

now, with that template in mind, let's see

$\bf y=x^2\implies 
\begin{array}{llll}
y=(&1x&-0)^2\\
&B&C
\end{array}$

so, just change C to +3, thus C/B is 3/1

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2 years ago

Which of the following is the surface area of the right cylinder below?

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Answer:

The one you have selected is the right answer 126 times pi

Step-by-step explanation:

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2 years ago

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Are the expressions 2x+8 and 2(x+4)+4 equivalent

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Answer:

Step-by-step explanation:

2x+8 2(x+4)+4

2(x)+2(4)+4

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3 years ago

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Please help<br> What does X=??

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Answer:

Step-by-step explanation:

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2 years ago

A ride at a carnival has two types of cars for children to ride one type has two seats and one has four seats there are 25 cars

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Answer:

Step-by-step explanation:

To solve this problem you need to create a system of equations. In these equations, use a = 2-seated car and b = 4- seated car

The first equation that you can make can be a + b = 25 because the number of 2-seated cars plus the number of 4-seated cars is going to equal a total of 25 cars.

The next equation you can make is 2a + 4b = 70 because the number of seats provided by the 2-seated cars plus the number of seats provided by the 4-seated cars will equal 70 total seats.

Next, line up the equations and solve:

Step one: Line up the equations

a + b = 25

2a + 4b = 70

Step two: Multiply the top equation by -2 so that you can add both of the equations together

-2(a) + -2(b) = 25(-2) ⇒ -2a - 2b = -50

2a + 4b = 70 ⇒ 2a + 4b = 70

Step three: Add the equations

-2a - 2b = -50

+ 2a + 4b = 70

______________

2b = 20

Step four: Divide both sides by 2 in order to solve for b

2b = 20 ⇒ b = 10

Because b represents the number of 4-seated cars, you now know that there are 10 4-seated cars on the ride.

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