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Viktor [21]
4 years ago
5

What is 10 (3+8k) + 9 (k+3)

Mathematics
1 answer:
IrinaK [193]4 years ago
5 0
10 (3+8k) + 9 (k +3)

30+80k+9k+27
Collect like terms

30+27+80k+9k
57+89k
Or
89k+57
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Write this in words- 2.0120
babymother [125]
Two point zero one hundred twenty
7 0
4 years ago
If sin theta = 8/17 and cot theta < 0, what is sec theta?
klasskru [66]

Answer:

-\frac{17}{15}

Step-by-step explanation:

By definition, \cot \theta=\frac{1}{\tan \theta} and \sec \theta=\frac{1}{\cos \theta}. Since since \cot \theta is negative, \tan \theta must also be negative, and since \sin \theta is positive, we must be in Quadrant II.

In a right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. The cosine of an angle in a right triangle is equal to its adjacent side divided by the hypotenuse. Therefore, we can draw a right triangle in Quadrant II, where the opposite side to angle theta is 8 and the hypotenuse of the triangle is 17.

To find the remaining leg, use to the Pythagorean Theorem, where a^2+b^2=c^2, where c is the hypotenuse, or longest side, of the right triangle and a and b are the two legs of the right triangle.

Solving, we get:

8^2+b^2=17^2,\\b^2=17^2-8^2,\\b^2=\sqrt{17^2-8^2}=\sqrt{225}=15

Since all values of cosine theta are negative in Quadrant II, all values of secant theta must also be negative in Quadrant II.

Thus, we have:

\sec\theta=\frac{1}{\cos \theta}=-\frac{1}{\frac{15}{17}}=\boxed{-\frac{17}{15}}

6 0
3 years ago
PLEASE HELP!!!! Seventeen consecutive positive integers have a sum of 306. What is the sum of the seventeen consecutive integers
Dima020 [189]

Answer:

595

Step-by-step explanation:

Let the first integer be n. Then each consecutive integer will be (n+1), (n+2)... until (n+16).

First, from the formula k/2(a+x_{k}), where k is the number of elements and xk is the last element, we can find 1+2+3 ... +15+16 = (16/2)(1+16)=136.

Anyways, this means that 17n+136=306.

We can find that n=10

Thus, the first integer is 10, and the 17th integer will be 10+16=26.

Thus, the first integer immediately proceeding 26 is 27. There are a total of 17 digits including 27 so we can add 16 to 27 to find the last digit, which is 43. There are again 17 digits in this set.

Thus, we have: 17/2(27+43)=595.

4 0
4 years ago
Need help ASAP!! Use the graph to find the solution of the system of equations what is the solution?
andreev551 [17]

The solution is the point where the two lines meet. The answer is D.

7 0
4 years ago
NEED HELP ASAP!!!
Marat540 [252]
You would subtract 90% and 35% and get 55%. You subtract that by 20 and yiu will have 35% of the 90% mixture
6 0
3 years ago
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