3x+33=10x+47 -> -14=7x so x=-2
Answer:
m = 3
Step-by-step explanation:
5m + 1 = 3m + 7
2m = 6
m = 3
Answer:
There are 59,049 different ways of answering the exam.
Step-by-step explanation:
The first thing we need to count is the total number of selections, then we need to count the number of options for each one of these selections. The total number of combinations will be equal to the product between all the numbers of options.
Here, the selections are each one of the 10 questions, so we have 10 selections.
And each one of these selections has 3 options (true, false, blank)
So, we have 10 selections with 3 options each, then the total number of combinations will be:
C = 3*3*3*3*3*3*3*3*3*3 = 3^10
C = 59,049
There are 59,049 different ways of answering the exam.
This is the volume of any generic box. Length times width times height
So volume = 7 x 5 x 6
Answer:
Step-by-step explanation:
The Law of Sines is
![\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}](https://tex.z-dn.net/?f=%5Cfrac%7BsinA%7D%7Ba%7D%3D%5Cfrac%7BsinB%7D%7Bb%7D%3D%5Cfrac%7BsinC%7D%7Bc%7D)
Filling in what we are given:
![\frac{sin(110.8)}{25.3}=\frac{sin(18.2)}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28110.8%29%7D%7B25.3%7D%3D%5Cfrac%7Bsin%2818.2%29%7D%7Bc%7D)
Cross multiply to get
and divide to solve for side c:
which gives you that
c = 8.45
We know that angle B has to be the difference between 180 and angle A and angle C, so
angle B = 51
Now we can solve for side b:
and
and
b = 21.03