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pashok25 [27]
3 years ago
10

What value of x is in the solution set of 4x – 12 < 16 + 8x? -10 -9 -8 -7

Mathematics
1 answer:
Akimi4 [234]3 years ago
3 0

Answer:

Step-by-step explanation:

4x - 12 ≤ 16 + 8x

4x - 8x ≤ 16 + 12

- 4x ≤ 28

<em>x ≥ - 7 or [ - 7, ∞ )</em>

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7.Find the lengths of the missing sides in the triangle. If your answer is not an integer, leave it in simplest radical form. Th
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We have to find, the sides which is opposite, adjacent and hypotenuse here.

We know that the side opposite to right angle is always hypotenuse. So, hypotenuyse = y.

The side adjacent to the given angle 45^o is x. So, here adjacent = x.

The opposite side is opposite to the given angle. So, opposite = 4.

Now we will use SOHCAHTOA that is sin(x) =\frac{Opposite}{Hypotenuse} , cos(x) =\frac{Adjacent}{Hypotenuse} , tan(x) =\frac{Opposite}{Adjacent}, where x is the angle given.

To get x, we will use tan. So we will get,

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We know the value of tan(45^o) = 1. By substituting the value we will get,

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To find x, we have to move x here to the left side by multiplying it to both sides. We will get,

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So we have got the value of x here.

Now to find y, we will use the trigonometric function sine.

sin(45^o) =\frac{4}{y}

we know the value of sin(45^o) =\frac{\sqrt{2}}{2}

By substituting the value we will get,

\frac{\sqrt{2}}{2}  = \frac{4}{y}

By cross multiplying we will get,

(\sqrt{2}) (y) = (4)(2)

\sqrt{2}y = 8

We will get y by dividing both sides by \sqrt{2}, we will get,

\frac{\sqrt{2}y}{\sqrt{2}}   =\frac{8}{\sqrt{2} }

y =\frac{8}{\sqrt{2}  }

Now we will rationalize the denominator by multiplying \sqrt{2} to the top and bottom.

y =\frac{8\sqrt{2}}{(\sqrt{2})(\sqrt{2})}

y =\frac{8\sqrt{2}}{2}

y = 4\sqrt{2}

So we have got the required values of x and y.

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3 years ago
Read 2 more answers
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Veronika [31]

Answer:

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