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3 years ago

Find the cosine of R.

Mathematics

1 answer:

JulijaS [17]3 years ago

3 0

Answer:

$cos(R) = \frac{\sqrt{15}}{5}$

Step-by-step explanation:

To find the cosine of <R, apply the following trigonometric ratio formula:

$cos(R) = \frac{adjacent}{hypotenuse}$

Adjacent = 3

Hypotenuse = √15

Plug in the values into the formula

$cos(R) = \frac{3}{\sqrt{15}}$

Multiply the numerator and denominator by √15 to rationalize.

$cos(R) = \frac{3 \times \sqrt{15}}{\sqrt{15} \times \sqrt{15}}$

$cos(R) = \frac{3\sqrt{15}}{(\sqrt{15})^2}$

$cos(R) = \frac{3\sqrt{15}}{15}$

$cos(R) = \frac{\sqrt{15}}{5}$

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2 years ago

Sylvia earns $7 per hour at her after school job. After working one week, she received a paycheck for $91.

makvit [3.9K]

Answer:

a.) $hours=13$

b.) $h\leq 15$

c.) $ $$105$

Step-by-step explanation:

a.) If she earns $7 'per' hour, this multiplication. After a week, we need to see how many hours she worked to earn $91, so this goes behind the equal sign. Let h be the unknown number of hours:

$7h=91$

Solve for h. Divide both sides by 7:

$\frac{7h}{7}=\frac{91}{7}\\\\h=13$

Sylvia worked 13 hours at a rate of $7 an hour.

b.) She can work at most 15 hours a week. At 'most' can also mean less than or equal to. Let h be hours:

$h\leq 15$

Sylvia can work less than or equal to 15 hours per week.

c.) If Sylvia can work 15 hours, plug in this value for h into an equation when she earns $7 per hour. Let the product of the hours and money equal t for total:

$t=7(15)\\t=105$