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mylen [45]
3 years ago
15

Will give brainlst Have a nice day

Mathematics
1 answer:
Zolol [24]3 years ago
4 0

Step-by-step explanation:

9) given

12x = 4(x + 2) + 20 \\ 12x = 4x + 8 + 20 \\ 8x = 28 \\ x = 28 \div 8 \\  = 3.5

10)standard form equation: y=mx+c

where m = slope and c = y-intercept

given m = 8, c = 12,

equation of line :

y = 8x + 12

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ludmilkaskok [199]

Given:

The point (9,-12) is on terminal side of angle theta in standard position.

To find:

The exact value of each of the six trigonometric functions of theta.

Solution:

The given point is (9,-12). Here, x-coordinate is positive and y-coordinate is negative. So, the point lies in 4th quadrant and only cos and sec are positive in 4th quadrant.

We know that,

r=\sqrt{x^2+y^2}

r=\sqrt{9^2+(-12)^2}

r=\sqrt{81+144}

r=\sqrt{225}

r=15

Now,

\sin \theta=\dfrac{y}{r}=\dfrac{-12}{15}=-\dfrac{4}{5}

\cos \theta=\dfrac{x}{r}=\dfrac{9}{15}=\dfrac{3}{5}

\tan \theta=\dfrac{y}{x}=\dfrac{-12}{9}=-\dfrac{4}{3}

\cot \theta=\dfrac{1}{\tan \theta}=-\dfrac{3}{4}

\text{cosec} \theta=\dfrac{1}{\sin \theta}=-\dfrac{5}{4}

\sec \theta=\dfrac{1}{\cos \theta}=\dfrac{5}{3}

Therefore, the values of six trigonometric functions of theta are \sin \theta=-\dfrac{4}{5},\cos \theta=\dfrac{3}{5},\tan \theta=-\dfrac{4}{3},\cot \theta=-\dfrac{3}{4},\text{cosec} \theta=-\dfrac{5}{4},\sec \theta=\dfrac{5}{3}.

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4 years ago
Splitting investments. Joan had $3,000 to invest. She invested part of it in an investment paying 8% and the remainder in an inv
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Answer:

Step-by-step explanation:

From the given information:

Let assume that the invested amount in the investment paying 8% interest is a

Now, since the total amount invested = $3000.

Then, the amount invested in the investment that will be paying 10% interest can be represented as:

= $(3000-a)

Income earned on $a that is being invested in 8% interest = $a × 8/100 = $0.08a

Income earned from $(3000-a)  in the 10% investment is:

= $(3000-a)× 10/100

= $(300 - 0.1a)

Since total income of the two investment = $290;

Then;

0.08a + (300 - 0.1a) = 290

0.08a + 300 - 0.1a = 20-

300 - 0.02a = 290

-0.02a = -10

a = -10/-0.02

x = 500

Thus;

the amount invested in an investment paying 8% interest = $500

the amount invested in an investment paying 10% interest = $(3000 - 500) = $2500

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Answer:

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