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3 years ago

What is 15(2x – 3y + 5x) = ?

Mathematics

1 answer:

bekas [8.4K]3 years ago

6 0

Answer: 105x + -45y

Step-by-step explanation: Since there are three terms inside the parentheses in this problem, the 15 distributes through all three terms.

Before distributing however, change the -3y to plus a negative 3y.

So we have 15(2x) + 15(-3y) + 15(5x).

This simplifies to 30x + -45y + 75x.

Now combine like terms to get 105x + -45y.

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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th

Bond [772]

Answer:

The time that the rocket will hit the ground will be:

x = 17.40 seconds

Step-by-step explanation:

Given the expression

$f\left(x\right)\:=-16x^2+272x+110$

Here:

x represents the time in seconds

y represents the height of the rocket

We know that when the rocket will hit the ground, the height will get y = 0

i.e.

$0\:=-16x^2+272x+110$

solving for x to determine the time that the rocket takes when it will hit the ground.

$-16x^2+272x+110=0$

subtract 110 from both sides

$-16x^2+272x+110-110=0-110$

$-16x^2+272x=-110$

Divide both sides by -16

$\frac{-16x^2+272x}{-16}=\frac{-110}{-16}$

$x^2-17x=\frac{55}{8}$

$\mathrm{Add\:}\left(-\frac{17}{2}\right)^2\mathrm{\:to\:both\:sides}$

$x^2-17x+\left(-\frac{17}{2}\right)^2=\frac{55}{8}+\left(-\frac{17}{2}\right)^2$

$x^2-17x+\left(-\frac{17}{2}\right)^2=\frac{633}{8}$

$\left(x-\frac{17}{2}\right)^2=\frac{633}{8}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solving

$x-\frac{17}{2}=\sqrt{\frac{633}{8}}$

$x=\frac{\sqrt{1266}}{4}+\frac{17}{2}$

x = 17.40 seconds

also solving

$x-\frac{17}{2}=-\sqrt{\frac{633}{8}}$

$x=-\frac{\sqrt{1266}}{4}+\frac{17}{2}$

x = -0.40 seconds

As time can not be negative.

Thus, the value of x = 17.40 seconds

Therefore, the time that the rocket will hit the ground will be:

x = 17.40 seconds

4 0

3 years ago

Half of a number plus 12 is 46

asambeis [7]

Let the number = x
x/2 + 12 = 46
x/2 = 46 - 12
x/2 = 34
x = 34 * 2
x = 68

So, your final answer is 68

Hope this helps!

4 0

3 years ago

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Simplify the following fraction: 10/24

mestny [16]

Answer:

5/12

Step-by-step explanation:

inside 2s table there 10 and 24

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3 years ago

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What is the range of the function f(x) = sqrt x+3 – 7?

anyanavicka [17]

The values produced by the function

$f(x)=\sqrt{x+3}-7$

will not be any lower than -7, but may be that low when x=-3.

That is, the range is

... f(x) ≥ -7 . . . . matches the 1st selection

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3 years ago

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5/6k=-20 what is the correct answer ??

damaskus [11]

<span>5/6k=-20

k=-24

Hope this helps</span>

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3 years ago

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