Answer: the answer is -3
Step-by-step explanation:
-3y-7=2 you add 7 to both side that make -3y=9
then you divide by -3 in both side and the answer will be -3
Tan(angle) = opposite leg / adjacent leg.
Tan(64) = x /30
x = 30 * tan(64)
x = 61.51
What is the least common denominator for fractions that have denominators of 5x+10 and 25x^2-100
21 and 7/8-8 and 5/12
remember that 21 and 7/8=21+7/8 and 8 and 5/12=8+5/12 so
21+7/8-(8+5/12)
21+7/8-8-5/12
21-8+7/8-5/12
13+7/8-5/12
so 7/8 and 5/12
make bottom number the same
multiply 7/8 by 12/12 and multiply 5/12 by 8/8
7/8-5/12=84/96-40/96=(84-40)/96=44/96=11/24
so the answer is
13 and 11/24
By "which is an identity" they just mean "which trigonometric equation is true?"
What you have to do is take one of these and sort it out to an identity you know is true, or...
*FYI: You can always test identites like this:
Use the short angle of a 3-4-5 triangle, which would have these trig ratios:
sinx = 3/5 cscx = 5/3
cosx = 4/5 secx = 5/4
tanx = 4/3 cotx = 3/4
Then just plug them in and see if it works. If it doesn't, it can't be an identity!
Let's start with c, just because it seems obvious.
The Pythagorean identity states that sin²x + cos²x = 1, so this same statement with a minus is obviously not true.
Next would be d. csc²x + cot²x = 1 is not true because of a similar Pythagorean identity 1 + cot²x = csc²x. (if you need help remembering these identites, do yourslef a favor and search up the Magic Hexagon.)
Next is b. Here we have (cscx + cotx)² = 1. Let's take the square root of each side...cscx + cotx = 1. Now you should be able to see why this can't work as a Pythagorean Identity. There's always that test we can do for verification...5/3 + 3/4 ≠ 1, nor is (5/3 + 3/4)².
By process of elimination, a must be true. You can test w/ our example ratios:
sin²xsec²x+1 = tan²xcsc²x
(3/5)²(5/4)²+1 = (4/5)²(5/3)²
(9/25)(25/16)+1 = (16/25)(25/9)
(225/400)+1 = (400/225)
(9/16)+1 = (16/9)
(81/144)+1 = (256/144)
(81/144)+(144/144) = (256/144)
(256/144) = (256/144)
