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3 years ago

HELP QUICK!!! EX POINTS.

Mathematics

1 answer:

Rashid [163]3 years ago

7 0

Answer:

x = 10.

Step-by-step explanation:

8/12 = (x + 4)/(2x + 1) Simplify 8/12:

2/3 = (x + 4)/(2x + 1) Cross multiply:

2(2x + 1) = 3(x + 4)

4x + 2 = 3x + 12

x = 10.

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4 years ago

Q13<br> Please help me solve this….

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Choice C

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Step-by-step explanation:

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Using identity 1, we can solve for cos(s) and cos(t)

$sin(s)=-\frac{\sqrt{3}}{3}, sin^{2}(s)=\frac{3}{9}=\frac{1}{3}\\cos^{2}(s)=1-sin^{2}(s)=1-\frac{1}{3}=\frac{2}{3}; cos(s)=\pm\sqrt{\frac{2}{3}}\\\\$

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Since both angles lie in quadrant IV, both cos(s) and cos(t) must be positive so we only consider the positive signs of both values

Using identity 2, we can solve for cos(s-t)

$cos(s-t)=cos(s)cos(t)+sin(s)sin(t)=\frac{\sqrt{2}}{\sqrt{3}}.\frac{\sqrt{31}}{6}+(-\frac{\sqrt{3}}{3})(-\frac{\sqrt{5}}{6})$

Multiplying numerator and denominator of the first term by $\sqrt{3}$ gives us the final expression as

$\frac{\sqrt{3}}{\sqrt{3}}\frac{\sqrt{2}}{\sqrt{3}}.\frac{\sqrt{31}}{6}+(-\frac{\sqrt{3}}{3})(-\frac{\sqrt{5}}{6})=\frac{\sqrt{186}}{18}+\frac{\sqrt{15}}{18}= \frac{\sqrt{186}+\sqrt{15}}{18}$

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