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3 years ago

Solve the following equation. 7(x - 2) = 3(x + 4)

Mathematics

2 answers:

scoray [572]3 years ago

8 0

Answer:

x = 6.5

Step-by-step explanation:

You have to apply the distributive property of multiplication:

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

7x - 14 = 3x + 12

7x - 3x = 12 + 14

4x = 26

x = 6.5

katen-ka-za [31]3 years ago

6 0

Answer: 6.5

Step-by-step explanation:

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

7x-14 = 3x + 12

-3x -3x

4x -14 = 12

+14 +14

4x = 26

4x /4 = 26 /4

X = 6.5

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A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 29 ft/s. Its height

Ilia_Sergeevich [38]

Answer:

$\overline{v}_{@\Delta t=0.01s}=-15.22ft/s, \overline{v}_{@\Delta t=0.005s}=-15.11ft/s, \overline{v}_{@\Delta t=0.002s}=-15.044ft/s, \overline{v}_{@\Delta t=0.001s}=-15.022ft/s$

Step-by-step explanation:

Now, in order to solve this problem, we need to use the average velocity formula:

$\overline{v}=\frac{y_{f}-y_{0}}{t_{f}-t_{0}}$

From this point on, you have two possibilities, either you find each individual $y_{f}, y_{0}, t_{f}, t_{0}$ and input them into the formula, or you find a formula you can use to directly input the change of times. I'll take the second approach.

We know that:

$t_{f}-t_{0}=\Delta t$

and we also know that:

$t_{f}=t_{0}+\Delta t$

in order to find the final position, we can substitute this final time into the function, so we get:

$y_{f}=29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}$

so we can rewrite our formula as:

$\overline{v}=\frac{29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}-y_{0}}{\Delta t}$

$y_{0}$ will always be the same, so we can start by calculating that, we take the provided function ans evaluate it for t=1s, so we get:

$y_{0}=29t-22t^{2}$

$y_{0}=29(1)-22(1)^{2}$

$y_{0}=7ft$

we can substitute it into our average velocity equation:

$\overline{v}=\frac{29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}-7}{\Delta t}$

and we also know that the initil time will always be 1, so we can substitute it as well.

$\overline{v}=\frac{29(1+\Delta t)-22(1+\Delta t)^{2}-7}{\Delta t}$

so we can now simplify our formula by expanding the numerator:

$\overline{v}=\frac{29+29\Delta t-22(1+2\Delta t+\Delta t^{2})-7}{\Delta t}$

$\overline{v}=\frac{29+29\Delta t-22-44\Delta t-22\Delta t^{2}-7}{\Delta t}$

we can now simplify this to:

$\overline{v}=\frac{-15\Delta t-22\Delta t^{2}}{\Delta t}$

Now we can factor Δt to get:

$\overline{v}=\frac{\Delta t(-15-22\Delta t)}{\Delta t}$

and simplify

$\overline{v}=-15-22\Delta t$

Which is the equation that will represent the average speed of the ball. So now we can substitute each period into our equation so we get:

$\overline{v}_{@\Delta t=0.01s}=-15-22(0.01)=-15.22ft/s$

$\overline{v}_{@\Delta t=0.005s}=-15-22(0.005)=-15.11ft/s$

$\overline{v}_{@\Delta t=0.002s}=-15-22(0.002)=-15.044ft/s$

$\overline{v}_{@\Delta t=0.001s}=-15-22(0.001)=-15.022ft/s$

5 0

3 years ago

Which expression shows the distance on the number line between −7 and 16?

galben [10]

The distance between any two points is the <em>absolute value of their difference</em>. Only one of those expressions provided represents the difference between -7 and 16; the others alter the numbers in one way or another. Which one of those absolute value expressions contains the <em>difference of -7 and 16</em>?

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4 years ago

Read 2 more answers

PLEASE HELP!

balandron [24]

The inequality equation represented by the parabola graph is;

y < (x - 2)(x - 8)

<h3>How to Interpret a Quadratic Graph?</h3>

We are told that the zeros of a parabola are 2 and 8. This means that the roots of the quadratic equation represented by the graph are 2 and 8. Thus, the factors of this quadratic graph can be written as;

(x - 2) and (x - 8)

Now, one rule about graphing inequalities is that If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.

Otherwise, if the inequality symbol is < or > , the parabola should be drawn with a dotted line to indicate that the region does not include its boundary.

Now, since the parabola is drawn with a dashed line, it means that the inequality sign will be < or > .

Lastly, since the outside of the parabola is shaded, it means that the inequality will be less than. Thus, our inequality equation is;

y < (x - 2)(x - 8)

Read more about Quadratic Graphs at; brainly.com/question/7784687

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2 years ago

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Mariana [72]

The answer is 138.5

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3 years ago

I should be company charge $15 to ship a Package and and 5% of the shipping charge for insurance on the package was the total co

Zolol [24]

If you determine 5% of the total cost ($0.75) then subtract that from the total cost, you would be left with the shipping price of $14.25.

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3 years ago