Find the exact value for the expression under the given conditions.
cos(α+β), sin α= -8/17 for α in Quadrant lll and cosβ= -8/15 for β in Quadrant ll.

Answer:

[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]

Step-by-step explanation:

We are given the conditions:

[tex]\displaystyle \sin(\alpha)=-\frac{8}{17}\text{ and } \cos(\beta)=-\frac{8}{15}[/tex]

Where α is in QIII and β is in QII and we want to find the exact value of cos(α + β).

The first ratio gives us the opposite side and the hypotenuse with respect to α . Then the adjacent side is (we can ignore negatives):

[tex]a=\sqrt{(17)^2-(8)^2}=15[/tex]

The second ratio gives us the adjacent side and the hypotenuse with respect to β. Then the opposite side is:

[tex]o=\sqrt{(15)^2-(8)^2}=\sqrt{161}[/tex]

Therefore, for α, ignoring negatives, the adjacent side is 15, the opposite side is 8, and the hypotenuse is 17.

And for β, ignoring negatives, the adjacent side is 8, the opposite side is √(161), and the hypotenuse is 15.

We can rewrite our expression as:

[tex]\displaystyle \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]

Since α is in QIII, sin(α), cos(α) < 0, and tan(α) > 0.

And since β is in QII, cos(β), tan(β) < 0, and sin(β) > 0.

Using this information, substitute:

[tex]\displaystyle \cos(\alpha+\beta)=\left(-\frac{15}{17}\right)\left(-\frac{8}{15}\right)-\left(-\frac{8}{17}\right)\left(\frac{\sqrt{161}}{15}\right)[/tex]

Therefore:

[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]

How many miles will light travel in one day if the speed of light is 300,000,000 meters per second.
(1.62 km = 1 mi)

Sharon paid $19.50 sales tax on a new camera. If the sales tax rate is 6.5%, what was the total cost of the camera including tax? Round to the nearest cent (hundredths place).

1.
What is the solution?
y
3
-3-2-1
2 3x
O (1,2)
O (1,-1)
O 1
02

Find the 17th term in the sequence for which a1 = 10 and d = -3.

What is the approximate circumference of a circle that has a center at (6,2) and passes through the point (20,2)? (Use 3.14 as an approximation for pi)

answers : 126,88,63,44

A data set is normally distributed with a mean of 25 and a standard deviation of 1.

Using the Empirical Rule, what percent of the data is greater than 26?

Group of answer choices

34%

16%

13.5%

23%

FH and IK are parallel lines.

Which angles are vertical angles?

The nationwide mean height of players on a high school basketball team is 71 in., with standard deviation of 5 in. A
random sample of 150 players was used to determine the range of reasonable means.

Ill give brain just helpppp

Please helppp!!!

what is the perimeter of the triangle?

what is the area or the triangle?​

A. 4 in
B. 5 in
C.60 in
D. 1.7 in
FOR BRAINLIST!!!!

. The table shows the dimensions of four boxes. Which is the order of the volumes of the boxes from least to greatest?​

Find the surface area of this net.
5 cm
13 cm
8 cm
A
B
C
12 cm
28
square centimeters

Find the 10th term of the geometric sequence show below

Given a polynomial f(x), if (x + 7) is a factor, what else must be true

In ΔMNO, o = 63 cm, n = 23 cm and ∠N=30°. Find all possible values of ∠O, to the nearest degree.

Identify the area of the figure shown.

Can you guys help? Last one plzzzz

what are the lengths of side a and b​

What is the value of -2(x + 5)?
A. x + 10
B. x - 10
C. -2x - 2
D. -2x - 10​

which angle corresponds to <OJH​

A hospital has 12 floors. On each floor there are 294 beds. The hospital wants one nurse for every 3 patients. How many nurses will the hospital have to hire to make this happen?

An elephant can travel 30 km in 2 hours. How fast is the elephant moving?

Convert the following equation
into standard form.
y = 2x – 4
-2x + y = [?]

Which sequence of transformations will change figure PQRS to figure P′Q′R′S′? (5 points)



Group of answer choices

Counterclockwise rotation about the origin by 180 degrees followed by reflection over the x-axis

Counterclockwise rotation about the origin by 180 degrees followed by reflection over the y-axis

Counterclockwise rotation about the origin by 270 degrees followed by reflection over the x-axis

Counterclockwise rotation about the origin by 270 degrees followed by reflection over the y-axis

couldn't write, added a file

Help fast pls. I will surely mark you brainliest. Answer step by step
Sohail, Amar, raja, and Mira go to a restaurant to have diner, Sohail pays 1/5 of the bills, Amar pays 2/5 of it and the balance is shared equally between raja and Mira. Who pays the maximum amount?

A pizza shop delivers an extra large pizza, which is sold for \$20$20dollar sign, 20, and costs the pizza shop \$12$12dollar sign, 12 to make. The pizza shop has a delivery policy that says if the pizza takes longer than half an hour to arrive, there is no charge. Experience has shown that delivery takes longer than half an hour only 10\%10%10, percent of the time.
Let the random variable XXX be the pizza shop's profit for a randomly selected delivery order for one of these pizzas. Here is the probability distribution for XXX:
Late On-time
X=\text{profit}X=profitX, equals, start text, p, r, o, f, i, t, end text -\$12−$12minus, dollar sign, 12 \$8$8dollar sign, 8
P(X)P(X)P, left parenthesis, X, right parenthesis 0.100.100, point, 10 0.900.900, point, 90
Given that \mu_X=\$6μ
X
​
=$6mu, start subscript, X, end subscript, equals, dollar sign, 6, calculate \sigma_Xσ
X
​
sigma, start subscript, X, end subscript.
Round your answer to two decimal places.
\sigma_X=σ
X
​
=sigma, start subscript, X, end subscript, equals
dollars

Select the point that is a solution to the system of inequalities.
y< x2 + 3
y=x²-4
A. (-2,-4)
B. (0,4)
C. (1,2)
D. (4,0)

You deposited 800 dollars in an account that pays 6% interest compounded monthly. How much will your account be worth after 10 years?

A. 276130.00
B. 849.46
C. 1456
D. 1455.52