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Lerok [7]
3 years ago
12

Describe how the graph of y= x – 12 is like the graph of y= x and how it is different

Mathematics
1 answer:
puteri [66]3 years ago
6 0
The two graphs have the same slope.  But the graph of <span>y= x – 12 is 12 units below the graph of y = x.  We call that a "vertical translation."

</span>
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Factor to the given polynomial completely.<br><br> 4x³+24x²-288x
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Answer: \Large\boxed{4x(x+12)(x-6)}

Step-by-step explanation:

<u>Given expression</u>

4x³ + 24x² - 288x

<u>Factorize 4x out from the expression</u>

4x · x² + 4x · 6x - 4x · 72

4x (x² + 6x - 72)

<u>Cross multiply to factorize the remaining polynomial expression</u>

<em>The meaning is to allow the factored product of the constant to add up to the first-degree term</em>

x             12

x             -6

<u>Combine the result</u>

\Large\boxed{4x(x+12)(x-6)}

Hope this helps!! :)

Please let me know if you have any questions

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1 year ago
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A new factory is growing fast and hiring a lot of new workers. Every week, the total number of workers doubles in size. If it ta
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9 weeks

Step-by-step explanation:

divide the full capacity by 2 to get 9 because 9 x 2 is 18 and half of the full capacity would be half capacity

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3 years ago
3 times the sum of a number and 2
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Answer:

is this actually a question

Step-by-step explanation:

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The arch beneath a bridge is​ semi-elliptical, a​ one-way roadway passes under the arch. The width of the roadway is 38 feet and
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Answer:

Only truck 1 can pass under the bridge.

Step-by-step explanation:

So, first of all, we must do a drawing of what the situation looks like (see attached picture).

Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:

\frac{x^2}{a^2}+\frac{y^2}{b^2}

where:

a= wider side of the ellipse

b= shorter side of the ellipse

in this case:

a=\frac{38}{2}=19ft

and

b=12ft

so we can go ahead and plug this data into the ellipse formula:

\frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}

and we can simplify the equation, so we get:

\frac{x^2}{361}+\frac{y^2}{144}

So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.

in order to do this let's solve the equation for y:

\frac{y^{2}}{144}=1-\frac{x^{2}}{361}

y^{2}=144(1-\frac{x^{2}}{361})

we can add everything inside parenthesis so we get:

y^{2}=144(\frac{361-x^{2}}{361})

and take the square root on both sides, so we get:

y=\sqrt{144(\frac{361-x^{2}}{361})}

and we can simplify this so we get:

y=\frac{12}{19}\sqrt{361-x^{2}}

and now we can evaluate this equation for x=4 (half the width of the trucks) so:

y=\frac{12}{19}\sqrt{361-(8)^{2}}

y=11.73ft

this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.

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You put the following items into your rucksack. Ham 600 g Cheese 380 g Tomatoes 270 g How much do all the ingredients weigh in t
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