They got paid the same amount. If you divide 417.96 and 27, you get 15.48. And if you divide 495.36 and 32 you get 15.48.

I hope that helped you.

**Answer:**

tan theta = 2 sqrt(5) /15

**Step-by-step explanation:**

sin theta = opp / hypotenuse

sin theta = 2/7

We can use the Pythagorean theorem to find the length of the adjacent side

a^2 + b^2 = c^2

2^2 +adj^2 = 7^2

4 + adj^2 = 49

adj ^2 = 49-4

adj^2 = 45

Taking the square root of each side

adj = sqrt(45) = sqrt(9*5) =sqrt(9) sqrt(5) = 3 sqrt(5)

The tan theta = opp/ adj

tan theta = 2 / 3 sqrt(5)

Multiply by sqrt(5) / sqrt(5)

= 2 sqrt(5) / 3 *5

= 2 sqrt(5) /15

Coolio

lw=1000

lets assume that the aluminum sides are the legnth

2 sides

2*15=30

30l=cost of aluminum

steel=10w

wood=(w-10)5=5w-50

we can eliminate the w by solving for w in first relation

lw=1000

divide both sides by l

w=1000/l

sub that for w

10(1000/l)=steel

5(1000/l)-50=wood

wood cost+steel+aluminum cost=total cost

10(1000/l)+5(1000/l)-50+30l=1525

(10000/l)+(5000/l)-50+30l=1525

(15000/l)-50+30l=1525

add 50 to both sides

(15000/l)+30l=1575

times both sides by l

15000+30l²=1575l

minus 1575l from both sides

30l²-1575l+15000=0

factor

(15)(l-40)(2l-25)=0

set each equal to 0

l-40=0

l=40

2l-25=0

2l=25

l=12.5

the there are 2 possible combinations

aluminum=40yd and steel=25yd or

aluminum=12.5yd and steel=80ft

both yield 1000yd² and cost $1525

**Answer:**

True

**Step-by-step explanation:**

If you simplify an expression you divide for example:

4 x 6 - 10 would be dividing each number by 2, 2 x 3 - 5.

I'm not a genius so hopefully this is right and helps!

The answer would be 100/250, but simplified it would be 2/5. Jus divide both numbers by a common factor, in this case, 50.

Hopefully this helps!