Answer:
1
Step-by-step explanation:
<IHG = 162
<IHK = 4x + 4
<KHG = 8x + 2
<IHG + <IHK + <KHG = 180° (sum of angles in a triangle is equal to 180°)
See attachment for better illustration of the triangle
162 + (4x + 4) + (8x + 2) = 180
162 + 4x + 4 + 8x + 2 = 180
168 + 12x = 180
Collect liketerms
12x = 180 - 168
12x = 12
x = 1
Answer:
Two angles of a quadrilateral : 220 and 90 deg.
The other two angles (x and y) are in ratio 2:3.
We have:
x + y = 360 - 220 - 90 = 50 (property of sum of 4 angles in quadrilateral)
x/y = 2/3 => x = 2y/3
=>2y/3 + y = 50
=> 5y/3 =50
=> 5y = 150
=> y = 30
=> x = 2 x 30/3 = 20
=> Two other angles are 20 and 30 deg
Hope this helps!
:)
g(x) = x - 3 = 0
g(x) = x = 3
f(x) = 2x^3 + x - 4
f(3) = 2(3)^3 + 3 - 4
f(3) = 2(27) - 1
f(3) = 54 - 1
f(3) = 53
The remainder when f(x) is divided by x - 3 is <u>53</u>.
Answer: Lee would make $25 on commission.
Step-by-step explanation: I found this by multiplying 500 by .05 or 5%. Lastly you can check this by taking 25 times 20, because 5% x 20 = 100%, so if 25 was really equal to 5% then it would equal the whole, or 500.
Hope this helps.
A) Diagram
Below is a sketch of the recctangular lawn (the inside rectangle) and the gravel border.
6 ft + 150 yards + 6 ft
-------------------------------
| |
| --------------------- |
| | | |
| | | | 6 ft + 80 yard + 6 ft
| | | |
| --------------------- |
| |
|------------------------------|
B) How many square feet of the gravel will surround the lawn?
Conversion: 1 yard = 3 feet
=> 80 yard = 80*3 feet = 240 feet
=> 150 yard = 150 * 3 feet = 450 feet
Area of the external rectangle = (6 ft + 240 ft + 6 ft) (6 ft + 450 ft + 6 ft) = 252 ft * 462 ft = 116,424 ft^2
Area of the internal rectangle = 240 ft * 450 ft = 108,000 ft^2
Area of the gravel border = 116,424 ft^2 - 108,000 ft^2 = 8424 ft^2
answer: 8424 ft^2
C) volume
volume = area of the base * depth
2 inches = 2/12 ft = 1/6 ft
=> volume = 8424 ft^2 * 1/6 ft = 1404 ft^3
answer: 1404 ft^3
C) cost
1 yard^3 = $ 30
1yard ^3 = (3 feet)^3 = 27 ft^3
=> cost = $ 30 / 27 ft^3
=> 1404 ft^3 * $30 / 27 ft^3 = $ 1560
answer: $ 1560
