Answer:
42
Step-by-step explanation:
You have to multiply 7 by 4 and 2 then add them together. 7*4 = 28 and 7*2 = 14. 28 + 14 = 42. (Make sure to double-check to see if my answer is correct)
> Last year the ratio of the number of middle school students
> to the number of high school students was 1:8.
1/9 x + 8/9 x = makeup of middle and high school students
> this year the ratio ... changed to 2:7
2/9 x + 7/9 x = x (again)
> there are 18 middle school students in the band this year
2/9 x = 18
2x = 9 * 18 → x = 81
Total = 81 in band ...
Last year:
1/9 and 8/9 = 9 and 72
This year
2/9 and 7/9 = 18 and 63
And from there you can figure out the changes:
+9 for middle school (which is increase from 1/9 to 2/9)
--9 for high school (which is decrease from 8/9 to 7/9)
The values of the trigonometry ratios are:
- cos α = - 5/13 and cot α = 5/12
- cot α = -5/12 and sec α = 13/5
<h3>How to solve the
trigonometry ratios?</h3>
<u>1: sin α = -12/13 and tan α > 0, find cos α and cot α</u>
Because tan α > 0, then it means that cos α and sin α are negative
So, we have:
sin²α + cos²α = 1
Substitute sin α = -12/13
(-12/13)² + cos²α = 1
This gives
cos²α = 1 - (-12/13)²
Evaluate the squares
cos²α = 1 - 144/169
Evaluate the difference
cos²α = 25/169
Take the square root of both sides
cos α = - 5/13
The cotangent ratio is represented as:
cot α = cos α/sin α
This gives
cot α = (-5/13)/(-12/13)
Evaluate
cot α = 5/12
Hence, cos α = - 5/13 and cot α = 5/12
<u>2: tan α = -12/5 for α in quadrant IV, find sec α and cot α</u>
Because α is in quadrant IV, then it means that sec α is positive
cot α = 1/tan α
This gives
cot α = 1/(-12/5)
Evaluate
cot α = -5/12
Also, we have:
sec²α = 1 + tan²α
Substitute tan α = -12/5
sec²α = 1 + (-12/5)²
Evaluate the squares
sec²α = 1 + 144/25
Evaluate the sum
sec²α = 169/25
Take the square root of both sides
sec α = 13/5
Hence, cot α = -5/12 and sec α = 13/5
Read more about trigonometry ratios at:
brainly.com/question/11967894
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Answer:
Step-by-step explanation:
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