<span>All the angles of a triangle add up to 180 degrees.
Since two of the angles are the same, we can write:
2A+B=180
Where 2A accounts for the two angles that are the same.
We are given the relation:
B=A+30
We can plug this into our first equation:
2A+A+30=180
</span><span>
Combine like terms and move the 30 to the other side:
3A=150
Divide both sides by 3:
A=50
We can solve for B by plugging A back into our relation:
B=50+30
B=80
To check: 80+50+50 so we are correct.</span>
Answer:
11*n
Step-by-step explanation:
11 is each bookshelf, n is an unknown number, try to imagine it as 2. You would multiply 11 by two to get total number of books.
Answer:
98
Step-by-step explanation:
An average score can be calculated by finding the sum of all scores and then dividing by the number of tests. So we can create an equation like this:
![\frac{(92+86+83+90+91+x)}{6}=90](https://tex.z-dn.net/?f=%5Cfrac%7B%2892%2B86%2B83%2B90%2B91%2Bx%29%7D%7B6%7D%3D90)
The numerator is the sum of her scores, where x represents the score of her next test (which is what we're trying to find).
The denominator is the total number of tests, which is 6 - this includes the 5 she has taken already and the next test that she hasn't taken yet.
Furthermore, we know all of this has to equal 90 because that's the average we're looking for.
Now we just solve for x.
Step 1) Multiply by 6:
![92+86+83+90+91+x=90 \times 6](https://tex.z-dn.net/?f=92%2B86%2B83%2B90%2B91%2Bx%3D90%20%5Ctimes%206)
Step 2) Simplify equation:
![442+x=540](https://tex.z-dn.net/?f=442%2Bx%3D540)
Step 3) Subtract 442:
![x=540-442=98](https://tex.z-dn.net/?f=x%3D540-442%3D98)
Therefore, x = 98, so Danielle must achieve a score of 98 to have an overall class average of 90.
Answer:
1008
Step-by-step explanation: