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3 years ago

What is the solution to the compound inequality? -8< 2x-4<2

Mathematics

1 answer:

DanielleElmas [232]3 years ago

4 0

Answer:

–2 < x < 3

Step-by-step explanation:

–8 < 2x – 4 < 2

Add 4 to all parts:

–8 + 4 < 2x – 4 + 4 < 2 + 4

Simplify:

–4 < 2x < 6

Divide all parts by 2:

(–4 ÷ 2) < (2x ÷ 2) < (6 ÷ 2)

Simplify:

–2 < x < 3

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muminat

Answer:

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Step-by-step explanation:

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3 years ago

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2 years ago

What is the equation of the line that is parallel to the line x = -2 and passes through the point (5.4)?

Leno4ka [110]

Lines parallel to each others only occur when two slopes of equations are same. The definition of parallel lines is:

$\large \boxed{m_1 = m_2}$

We are given the equation of a line which is x = -2. For x = a, the equation forms a verical line and has an undefined slope. These below are basic that you may need to learn when learning about the line graph:

y = a —> horizontal line; slope is 0.
x = a —> vertical line; slope is undefined.
For y = a, any a-values would have same x-values. For example, if we are given y = 2 then any domains or x-values can have the range of 2.
For x = a, any a-values would have same y-values or range.

Back to the question. We want to find the equation of a line that is parallel to the line x = -2 and passes through (5,4) point. Recall the definition of parallel line that both slopes of equations must equal. Since x = a for any a-values would give an undefined slope. That means our parallel would be x = b.

Because the line passes through (5,4) - for any a-values from x = a would give out the set of all real numbers for range. Therefore the equation of a line is x = 5.

Answer

The equation of a line that is parallel to x = -2 and passes through (5,4) is x = 5.

I hope this helps! If you have any doubts or questions, don't hestitate to ask in comment! Good luck on your assignment and have a great day!

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3 years ago

Very fast please! How do you work out: 5x3/4

Harlamova29_29 [7]

As it is only 5, it is 5/1 so you do 5 x 3 = 15 then 1 x 4 = 4. So 15/4

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3 years ago

HELPPPP ME PLZZZZ!!!!!!

mihalych1998 [28]

<h3>Answers:</h3>

14. Each leg is $21\sqrt{2}$ units long.

15 (a). The longer leg is $7\sqrt{3}$ units long

15 (b). The hypotenuse is $14$ units long

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

Explanations:

For a 45 degree right triangle, aka 45-45-90 triangle, the hypotenuse is equal to sqrt(2) times the short leg. Algebraically we can say

$y = x\sqrt{2}$ where x is the leg and y is the hypotenuse

Let's solve for x

$y = x\sqrt{2}\\\\x\sqrt{2} = y\\\\x = \frac{y}{\sqrt{2}}\\\\x = \frac{y\sqrt{2}}{\sqrt{2}*\sqrt{2}} \ \text{rationalizing denominator}\\\\x = \frac{y\sqrt{2}}{2}\\\\$

Now plug in the given hypotenuse y = 42, this leads to,

$x = \frac{y\sqrt{2}}{2}\\\\x = \frac{42\sqrt{2}}{2}\\\\x = \frac{42}{2}\sqrt{2}\\\\x = 21\sqrt{2}\\\\$

---------------------------

For a 30-60-90 triangle, the hypotenuse is double that of the short leg. So the hypotenuse is 2*7 = 14.

The longer leg is equal to sqrt(3) times the short leg. The longer leg is $7\sqrt{3}$

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3 years ago