Answer:
See the attached figure which represents the problem.
As shown, AA₁ and BB₁ are the altitudes in acute △ABC.
△AA₁C is a right triangle at A₁
So, Cos x = adjacent/hypotenuse = A₁C/AC ⇒(1)
△BB₁C is a right triangle at B₁
So, Cos x = adjacent/hypotenuse = B₁C/BC ⇒(2)
From (1) and (2)
∴ A₁C/AC = B₁C/BC
using scissors method
∴ A₁C · BC = B₁C · AC
Answer:
7. D
8. A
9. D
10. B
11 A)
11 B)
Step-by-step explanation:
7.
Let Emmet work for "m" minutes
Since, Cal worked 4times as this, we can say Cal worked for "4m" minutes
Now, the total time (CAL + EMMET) is 720, so we SUM UP their individual times' expression and equate to 720. Shown below:
4m + m = 720
This is Answer choice D
8.
Let s be the price of each shirt
Each shirt costs "s" each, so 4 shirts cost "4s" in total.
4 shirts costs 60 AFTER 10 dollar discount, so before discount, it was:
60 + 10 = 70 dollars
Hence, 4 shirts cost 70 dollars BEFORE discount, so we can say:
4s = 70
But none of the choices are this, we need to simply manipulate this equation to get our answer (from choices).
<em>How did we get 70? We added 60 and 10. So we can put "60" on the right hand side and "-10" on the left hand side to get:</em>
<em>4s - 10 = 60</em>
<em />
<em>This is ultimatley 4s = 70</em>
<em>So the correct answer choice is A</em>
9.
Let Tony's age be "y"
We know grandmother is "3 years MORE than 6 times TONY (y)", thus we can write:
Grandmother is "6y + 3"
Total sum of them both is 87. Thus we can SUM both these expressions and equate to 87. Thus,
y + 6y + 3 = 87
D is the correct choice.
10.
THe total length is "f"
Each piece cut is 3/4
So the number of pieces is the total by each piece, so that is
All these "number of pieces" makes 6 shelves (since he used all), so we equate this expression to "6". Now we have:
That is answer choice B
11 A)
Let Jocelyn's computer's price be "j",
Adrian's is 640, which is 20% LESS THAN Jocelyn's (j), so we can say:
640 is 20% less than "j"
or
"20% less than j" would be:
j - 0.2j = 0.8j
Now, we can write:
640 = 0.8j
11 B)
We can say:
Adrian is 15% more than Corbin
or
A = 0.15C + C
A = 1.15C
[note: let adrian's computer price be A and Corbin's computer price be C]
Also we know
0.8j = Adrian
We can put this in to get:
A = 1.15C
C = A/1.15
C = 0.8j/1.15
THis is an expression for Corbin's computer price in terms of j:
