Answer:
Option A.
Step-by-step explanation:
The length of the hypotenuse of a right angle 145 units.
The length of one leg of the triangle can be measured by Pythagoras theorem.
other leg = ![\sqrt{(Hypotenuse)^{2}-(oneleg)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28Hypotenuse%29%5E%7B2%7D-%28oneleg%29%5E%7B2%7D%7D)
=
= ![\sqrt{21025-20736}](https://tex.z-dn.net/?f=%5Csqrt%7B21025-20736%7D)
= ![\sqrt{289}](https://tex.z-dn.net/?f=%5Csqrt%7B289%7D)
Therefore, option A is the correct option because the other leg should be
.
Answer:
x = 41.81°, 138.19°, 210°, 330°
Explanation:
3cos(2x) + sin(x) = 1
subtract one from both sides
→ 3cos(2x) + sin(x) − 1 = 0
rewrite using trigonometry identities
→ 2 + sin(x) − 6sin²(x) = 0
solve x by substitution
f(x) = 2 + sin(x) − 6sin²(x)
= 2 + 4sin(x) - 3sin(x) − 6sin²(x)
= −2sinx(3sinx −2) − (3sinx−2)
= (3sinx −2)(−2sinx−1)
= −(3sinx −2)(2sinx+1)
f(x) = 2 + sin(x) − 6sin²(x) = 0
= −(3sinx −2)(2sinx+1) = 0
(3sinx −2) = 0 (2sinx+1) = 0
→sinx = 2/3 →sinx = −1/2
x = 41.81°, 138.19° x = 210°, 330°
(Please heart the answer if you find it helpful, it's a motivation for me to help more people)
Answer:
D
Step-by-step explanation:
To write an expression and equation, define the variables.
Taylor purchased three types of items:
x = number of bags of candy
y = number of picture frames
z = number of stickers.
We know she bought 9 items.
So x+y+z = 9.
X - 8 = -10...add 8 to both sides
x = -10 + 8
x = -2 <==
let's firstly convert the mixed fraction to improper fraction, and divide, so we can see how many times 1/6 goes into 2⅔
![\bf \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{8}{3}\div \cfrac{1}{6}\implies \cfrac{8}{3}\cdot \cfrac{6}{1}\implies \cfrac{8}{1}\cdot \cfrac{6}{3}\implies 8\cdot 2\implies 16](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B2%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%203%2B2%7D%7B3%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B8%7D%7B3%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B8%7D%7B3%7D%5Cdiv%20%5Ccfrac%7B1%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B8%7D%7B3%7D%5Ccdot%20%5Ccfrac%7B6%7D%7B1%7D%5Cimplies%20%5Ccfrac%7B8%7D%7B1%7D%5Ccdot%20%5Ccfrac%7B6%7D%7B3%7D%5Cimplies%208%5Ccdot%202%5Cimplies%2016)