Answer:
-5
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
45−(5+8y−3(y+3))=−3(3y−5)−(5(y−1)−2y+6)
45+−1(5+8y−3(y+3))=−3(3y−5)+−1(5(y−1)−2y+6)(Distribute the Negative Sign)
45+(−1)(5)+−1(8y)+−1(−3(y+3))=−3(3y−5)+−1(5(y−1))+−1(−2y)+(−1)(6)
45+−5+−8y+3y+9=−3(3y−5)+−5y+5+2y+−6
45+−5+−8y+3y+9=(−3)(3y)+(−3)(−5)+−5y+5+2y+−6(Distribute)
45+−5+−8y+3y+9=−9y+15+−5y+5+2y+−6
(−8y+3y)+(45+−5+9)=(−9y+−5y+2y)+(15+5+−6)(Combine Like Terms)
−5y+49=−12y+14
−5y+49=−12y+14
Step 2: Add 12y to both sides.
−5y+49+12y=−12y+14+12y
7y+49=14
Step 3: Subtract 49 from both sides.
7y+49−49=14−49
7y=−35
Step 4: Divide both sides by 7.
7y
7
=
−35
7
y=−5
Answer:
Part I: cot(15 degrees) = cot(45 - 30)
Part II: Evaluation is below
Step-by-step explanation:
<em>Everything is done in degrees</em>
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Two angles that differ by 15 degrees that is easy to evaluate is 30 degrees and 45 degrees. The cot(15 degrees) = cot(45 - 30) = 1/tan(45-30) = (1+tan45tan30)/(tan30 - tan45) = (1+ sqrt(3))/(sqrt(3) - 1)
We rationalize this by multiplying 1+ sqrt(3) in the top and bottom, getting:
(4 + 2sqrt(3))/2 = 2 + sqrt(3)
I hope this helps! :)
The rate of the airplane is 300mph per hour.
Answer:
She will use the ratio shortening to flour as 4 : 15
Step-by-step explanation:
When Mrs. Stewart makes pie dough, she uses 
cups of shortening for every 
cups of flour.
So, for each cup of shortening she uses 
cups of flour.
Then, the ratio of shortening to flour in the mixture of pie dough will be
i.e. 4 : 15.
Therefore, she will use the ratio shortening to flour as 4 : 15 to find the amount of flour she needs when she uses 5 cups of shortening. (Answer)
