Answer:
r = 10 or -10
Step-by-step explanation:
Answer:
Step-by-step explanation:
This is good! The length of the metal is 20 inches longer than the width. But we fold up 4-inch flaps on each side, so the height of the box is 4 inches, and the length and width will each decrease by 8 inches (4 inches on each side). Since the length and width decrease by the same amount, the length will still be 20 inches longer than the width. So the equations would be:
l = w + 20
vol = l x w x h = 1716 in3
1716 = (w + 20)(w)(4)
1716 = 4w2 + 80w
4w2 + 80w - 1716 = 0
4(w2 + 20w - 429) = 0
4(w + 33)(w - 13) = 0
w + 33 = 0, so w = -33
w - 13 = 0, so w = 13
Since the width can't be negative, the width of the box is 13 and the length is 33 (13 + 20).
But remember, the length and width of the piece of metal are each 8 inches longer than the box, so it was 41 inches by 21 inches.
Answer:
1,620
Step-by-step explanation:
Volume = bh
the base is 15x9 which gives you 135
know you must multiply the base x height
135x12= 1,620
for future length and width = base
Answer:
Step-by-step explanation:
A 45 degree angle in a right triangle produces 2 equal sides. In this case z and the perpendicular line are equal. So that's were we'll start. Then you move on to the 60 degree angle to get x and y.
Finding z
z^2 + z^2 = (24√2) Combine the left
2z^2 = 24^2 * 2 Divide both sides by 2
2z^2/2 = 24^2/2
z^2 = 24^2 Take the square root of both sides
√z^2 = √24^2
z = 24
Finding x and y
The perpendicular = 24. Because it is a 60 degree angle that's given, we can do this without a calculator.
Tan 60 = opposite over adjacent
sqrt(3) = Perpendicular / z Multiply both sides by z
z*sqrt(3) = perpendicular
The above calculation tells us the perpendicular is 24
z*sqrt(3) = 24 Divide by sqrt 3
z = 24/√3
z = 24/1.73
z = 8√3
Finding x
Use Pythagoras to determine x
Perpendicular^2 + (8√3)^2 = x^2
24^2 + 8^2*3 = x^2
576 + 192 = x^2
768 = x^2
√x^2 = √768
x = 27.71
Answer:
5
Step-by-step explanation:
The equation looks like 4x=20
Divide each side by 4 to get x=5
Thus x+5
