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Ann [662]
3 years ago
6

Five less than nine times a number is the same as nineteen more than the number

Mathematics
1 answer:
Xelga [282]3 years ago
4 0

Answer:


Step-by-step explanation:

The first thing you need to do is develop the equation. Less in this case means subtract.

On the left side you have

9 times a number which is 9*x

5 less than 9 times a number means 9x - 5

Now you shift to the right

x = 3

x + 19  What you get is

9x - 5 = x + 19        Subtract x from both sides of the equation

9x - x - 5 = 19        Combine both x terms on the left

8x - 5 = 19             Add 5 to both sides.

8x - 5 + 5 = 19 + 5 Combine terms

8x = 24                  Divide by 8

x = 24/8

x = 3

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Write the first trigonometric function in terms of the second for θ in the given quadrant.. sec θ, sin θ; θ in quadrant I
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We have sec  = 1/cos

Then we also have  cos^2 = 1 – sin^2

Also we have cos = sqrt (1 – sin^2)

Substitute the derived cosine function to sec then we have

Sec = 1/(sqrt(1-sin^2)

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Help.. solve for the given variable <br>-5(r - 6) + 3(-8 + 8r) = -32
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-5(r - 6) + 3(-8 + 8r) = -32

STEP 1: Simplify both sides of the equation.
<span><span><span><span><span><span>(<span>−5</span>)</span><span>(r)</span></span>+<span><span>(<span>−5</span>)</span><span>(<span>−6</span>)</span></span></span>+<span><span>(3)</span><span>(<span>−8</span>)</span></span></span>+<span><span>(3)</span><span>(<span>8r</span>)</span></span></span>=<span>−32 </span></span>(Distribute)
<span><span><span><span><span><span>−<span>5r</span></span>+30</span>+</span>−24</span>+<span>24r</span></span>=<span>−32</span></span><span><span><span>(<span><span>−<span>5r</span></span>+<span>24r</span></span>)</span>+<span>(<span>30+<span>−24</span></span>)</span></span>=<span>−32 </span></span>(Combine Like Terms)
<span><span><span>19r</span>+6</span>=<span>−32</span></span><span><span><span>19r</span>+6</span>=<span>−32
</span></span>
STEP 2: Subtract 6 from both sides.
<span><span><span><span>19r</span>+6</span>−6</span>=<span><span>−32</span>−6</span></span><span><span>19r</span>=<span>−<span>38

STEP 3: Divide both sides by 19.
19r/19 = -38/19
r = -2

FINAL ANSWER: r  = -2</span></span></span>
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