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3 years ago

10

Ernest's grandma bought a package of socks for christmas that 40% of regular price. the amount of the discount was $6. What was

the regular price of the sock?

1 answer:

lapo4ka [179]3 years ago

6 0

It was 15 because 40%=6,that means that 80%=12,20%=6:2=3 and 80%+20%=12+3=15

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HELP! Find the value of sin 0 if tan 0 = 4; 180 < 0< 270

BabaBlast [244]

Hi there! Use the following identities below to help with your problem.

$\large \boxed{sin \theta = tan \theta cos \theta} \\ \large \boxed{tan^{2} \theta + 1 = {sec}^{2} \theta}$

What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.

$\large{ {4}^{2} + 1 = {sec}^{2} \theta } \\ \large{16 + 1 = {sec}^{2} \theta } \\ \large{ {sec}^{2} \theta = 17}$

As we know, sec²θ = 1/cos²θ.

$\large \boxed{sec \theta = \frac{1}{cos \theta} } \\ \large \boxed{ {sec}^{2} \theta = \frac{1}{ {cos}^{2} \theta} }$

And thus,

$\large{ {cos}^{2} \theta = \frac{1}{17}} \\ \large{cos \theta = \frac{ \sqrt{1} }{ \sqrt{17} } } \\ \large{cos \theta = \frac{1}{ \sqrt{17} } \longrightarrow \frac{ \sqrt{17} }{17} }$

Since the given domain is 180° < θ < 360°. Thus, the cosθ < 0.

$\large{cos \theta = \cancel\frac{ \sqrt{17} }{17} \longrightarrow cos \theta = - \frac{ \sqrt{17} }{17}}$

Then use the Identity of sinθ = tanθcosθ to find the sinθ.

$\large{sin \theta = 4 \times ( - \frac{ \sqrt{17} }{17}) } \\ \large{sin \theta = - \frac{4 \sqrt{17} }{17} }$

Answer

sinθ = -4sqrt(17)/17 or A choice.

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Aleksandr-060686 [28]

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4 years ago

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If the ratio of boys to girls at the school is 2:5 and there are 40 boys how many girls are there?

sukhopar [10]

Answer:

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Step-by-step explanation:

The ratio of boys : girls is 2 : 5.

In other words, boys are 2 parts of the school while girls are 5 parts of the school.

Since there are 40 boys, 2 parts of the school is 40. Thus:

$2p = 40\\p = 20$

1 part is 20.

Since there are 5 parts girls, there are

$5p = 5*20 = 100$

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Answer: 100 girls

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