Answer:
∠a = 10°
Step-by-step explanation:
The measure of ∠a = x
The measure of ∠b = 4x-30
It is also mentioned that the measure a and measure b are vertical angles. We need to find the value of a.
For vertically opposite angles,
∠a = ∠b
x = 4x-30
or
4x-30=x
Taking like terms together,
4x-x= 30
3x = 30
x = 10
So, the meausre of ∠a is equal to 10°.
Answer:
C. 2:5
Step-by-step explanation:
Find perimeter of each...
a. 10+25+21.5=56.5
b. 4+10+8.6=22.6
b:a
22.6:56.6
simplify
11.3 will go into both for..
2:5
To find the probability of picking a five dollar bill and then another five dollar bill, you will find the chance of picking a five dollar bill the first time, and multiply by the probability of picking another one the second time.
There is a 3 out of 9 chance the first time because there are 3 - $5 dollar bills, and 9 total bills.
The second time there will be a 2 out of 8 chance, because if you picked a $5 dollar bill the first time, there should be 2 - $5 bills left and 8 total bills.
3/9 x 2/8 or 1/3 x 1/4 = 1/12 chance.
Answer:
Step-by-step explanation:
Given functions:
![\sf f(x) \cdot g(x) = \left(\sqrt{x^2+12x+36}\right)\times (x^3 - 12) \\\\\ \textsf{[rewrite the radicand using the perfect square trinomial rule: $a^2+2ab+b=(a+b)^2$]}\\\\](https://tex.z-dn.net/?f=%5Csf%20f%28x%29%20%5Ccdot%20g%28x%29%20%3D%20%5Cleft%28%5Csqrt%7Bx%5E2%2B12x%2B36%7D%5Cright%29%5Ctimes%20%28x%5E3%20-%2012%29%20%5C%5C%5C%5C%5C%20%5Ctextsf%7B%5Brewrite%20the%20radicand%20using%20the%20perfect%20square%20trinomial%20rule%3A%20%24a%5E2%2B2ab%2Bb%3D%28a%2Bb%29%5E2%24%5D%7D%5C%5C%5C%5C)
![\sf f(x) \times g(x) = \left(\sqrt{(x+6)^2}\right) \times \left(x^3 - 12\right)\textsf{[take the square root of the perfect square trinomial]}\\\\\sf f(x) \cdot g(x) = \left(x+6}\right) \times \left(x^3 - 12\right) \textsf{[multiply]}\\\\f(x) \cdot g(x) = x\left(x^3 - 12\right) + 6 \left(x^3 - 12\right) \textsf{[simplify]}\\\\f(x) \cdot g(x) = x^4 - 12x + 6x^3 - 76 \textsf{ [rewrite in descending order]}\\\\f(x) \cdot g(x) = x^4 + 6x^3 - 12x - 76](https://tex.z-dn.net/?f=%5Csf%20f%28x%29%20%5Ctimes%20g%28x%29%20%3D%20%5Cleft%28%5Csqrt%7B%28x%2B6%29%5E2%7D%5Cright%29%20%5Ctimes%20%5Cleft%28x%5E3%20-%2012%5Cright%29%5Ctextsf%7B%5Btake%20the%20square%20root%20of%20the%20perfect%20square%20trinomial%5D%7D%5C%5C%5C%5C%5Csf%20f%28x%29%20%5Ccdot%20g%28x%29%20%3D%20%5Cleft%28x%2B6%7D%5Cright%29%20%5Ctimes%20%5Cleft%28x%5E3%20-%2012%5Cright%29%20%5Ctextsf%7B%5Bmultiply%5D%7D%5C%5C%5C%5Cf%28x%29%20%5Ccdot%20g%28x%29%20%3D%20x%5Cleft%28x%5E3%20-%2012%5Cright%29%20%2B%206%20%5Cleft%28x%5E3%20-%2012%5Cright%29%20%5Ctextsf%7B%5Bsimplify%5D%7D%5C%5C%5C%5Cf%28x%29%20%5Ccdot%20g%28x%29%20%3D%20x%5E4%20-%2012x%20%2B%206x%5E3%20-%2076%20%5Ctextsf%7B%20%5Brewrite%20in%20descending%20order%5D%7D%5C%5C%5C%5Cf%28x%29%20%5Ccdot%20g%28x%29%20%3D%20x%5E4%20%2B%206x%5E3%20-%2012x%20%20-%2076)
