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3 years ago

14

Arnie is mixing red and yellow paint to make two different shades of orange. To make 1 cup of dark orange paint, he needs 7 ounc

es of red paint and 1 ounce of yellow paint. To make 2 cup of light orange paint, he needs 13 ounces of yellow paint. Answer part a and b.

1 answer:

nordsb [41]3 years ago

4 0

Answer:

If this is how many ounces of yellow: 14oz

If this is how many ounses of red: 8oz

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Evaluate the expression for the given value. 0. 5w+3x, when w=6, x=5

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Answer:

18

Step-by-step explanation:

0.5(w) + 3x

0.5(6) + 3(5)

= 18

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sal is making bracalets for a fundraser he uses 6 inches of yarn per bracalet how many bracalets can sal make with 5 ft of yarn

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Answer:

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Step-by-step explanation:

we need to convert 5 ft to inches

1 ft = 12 inches

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4 years ago

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Step-by-step explanation:

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3 years ago

If sin theta = 2/3 and sex theta < 0 , find cos theta and tan theta

FromTheMoon [43]

Answer:

$\displaystyle cos\theta=-\frac{\sqrt{5}}{3}$

$\displaystyle tan\theta=-\frac{2\sqrt{5}}{5}$

Step-by-step explanation:

<u>Trigonometric Formulas</u>

To solve this problem, we must recall some basic relations and concepts.

The main trigonometric identity relates the sine to the cosine:

$sin^2\theta+cos^2\theta=1$

The tangent can be found by

$\displaystyle tan\theta=\frac{sin\theta}{cos\theta}$

The cosine and the secant are related by

$\displaystyle cos\theta=\frac{1}{sec\theta}$

They both have the same sign.

The sine is positive in the first and second quadrants, the cosine is positive in the first and fourth quadrants.

The sine is negative in the third and fourth quadrants, the cosine is negative in the second and third quadrants.

We are given

$\displaystyle sin\theta=\frac{2}{3}$

Find the cosine by solving

$sin^2\theta+cos^2\theta=1$

$\displaystyle \left(\frac{2}{3}\right)^2+cos^2\theta=1$

$\displaystyle cos^2\theta=1-\left(\frac{2}{3}\right)^2=1-\frac{4}{9}=\frac{5}{9}$

$\displaystyle cos\theta=\sqrt{\frac{5}{9}}=-\frac{\sqrt{5}}{3}$

$\boxed{\displaystyle cos\theta=-\frac{\sqrt{5}}{3}}$

We have placed the negative sign because we know the secant ('sex') is negative and they both have the same sign.

Now compute the tangent

$\displaystyle tan\theta=\frac{sin\theta}{cos\theta}=\frac{\frac{2}{3}}{-\frac{\sqrt{5}}{3}}=-\frac{2}{\sqrt{5}}$

Rationalizing

$\displaystyle tan\theta=-\frac{2}{\sqrt{5}}=-\frac{2\sqrt{5}}{5}$

$\boxed{\displaystyle tan\theta=-\frac{2\sqrt{5}}{5}}$

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