Answer:
If I am correct, I think the surface area is 448.
Step-by-step explanation:
First start by finding the area of all the sides
Front side. 12 x 10 = 120
2 triangle sides: 8 x 10 = 80, 80 x 2 = 160
Bottom side: 6 x 12 = 72
Back side: 8 x 12 = 96
Then add up the surface area
120 + 160 + 72 + 96 = 448
Btw I don't know if I am correct, but I think this is the way you find surface area.
Answer:
x = 33.8°
Step-by-step explanation:
The resulting diagram we have is a right triangle. To find x, apply trigonometric function.
Reference angle = x
Opposite = 116
Adjacent = 173
Apply TOA:
Tan x = Opp/Adj
x = 33.8° (nearest tenth)
Answer:
see explanation
Step-by-step explanation:
The hypotenuse is the longest side thus is (4x + 1)
The legs are 2x and (4x - 1)
Using Pythagoras' theorem, then
(4x + 1)² = (2x)² + (4x - 1)² ← expanding factors
16x² + 8x + 1 = 4x² + 16x² - 8x + 1 , that is
16x² + 8x + 1 = 20x² - 8x + 1 ( subtract 20x² - 8x + 1 from both sides )
- 4x² + 16x = 0 ( multiply through by - 1 )
4x² - 16x = 0 ← factor out 4x from each term
4x(x - 4) = 0
Equate each factor to zero and solve for x
4x = 0 ⇒ x = 0
x - 4 = 0 ⇒ x = 4
Now x > 0, thus x = 4
2x = 2(4) = 8
4x - 1 = 4(4) - 1 = 16 - 1 = 15
4x + 1 = 4(4) + 1 = 16 + 1 = 17
Thus
perimeter = 8 + 15 + 17 = 40 cm
Answer:
- 39 quarters and 41 nickels
Step-by-step explanation:
Let the number of quarters be x and nickels be y.
<u>Given:</u>
- Quarter is 25 cents
- Nickel is 5 cents
- Number of coins is 80
- Total amount is $11.80 = 1180 cents
<u>We have equations:</u>
- x + y = 80
- 25x + 5y = 1180
<u>Solve the system by elimination, subtract 5 times the first equation from the second one:</u>
- 25x + 5y - 5x - 5y = 1180 - 80*5
- 20x = 780
- x = 780/20
- x = 39
<u>Find the value of y:</u>
- 39 + y = 80
- y = 80 - 39y = 41
<u>Verify:</u>
- 25*39 + 5*41 = 975 + 205 = 1180
