Answer:
m∠ABC = 119° and DC = 105 feet
Step-by-step explanation:
For better understanding of the solution see the attached figure of the trapezium ABCD :
m∠BCD = 61°
By using the property, Sum of interior opposite angles in a trapezium is supplementary ⇒ m∠BCD + m∠ABC = 180°
⇒ m∠ABC = 180° - 61°
⇒ m∠ABC = 119°
Now, to find length of DC,
Draw a perpendicular BE on CD ⇒ CD = DE + EC
AB = DE
⇒ DE = 80 feet
In ΔBEC, By using Pythagoras theorem
EC² = BC² - BE²
⇒ EC² = 65² - 60²
⇒ EC = 25 feet
Hence, DC = 80 + 25
= 105 feet
Step-by-step explanation:
let's look at the last line :
x³ + 8x - 3 = Ax³ +5Ax + Bx² + 5B + Cx + D
since we find A, B, C, and D by simply comparing the factors of the various terms in x (or constants) in both sides of the equation, we need to combine a few terms on the right hand side (so that we have one term per x exponent grade).
x³ + 8x - 3 = Ax³ + (5A + C)x + Bx² + (5B + D)
by comparing now both sides, to make both sides truly equal, the factors have to be equal.
A = 1 (the same as for x³ on the left hand side).
B = 0 (a we have no x² on the left side).
5A + C = 8 (a 8 is the factor of x in the left side).
5×1 + C = 8
5 + C = 8
C = 3
5B + D = -3 (as the constant term is -3 on the left side).
5×0 + D = -3
D = -3
so, the 4th answer option is correct.
Raw material for 500 units per week = 500 x $10 = $5000
Cost of hiring 20 workers per week = 20 x 40 x 25 = $12000
Rental = $2250
Total = 5000 + 12000 + 2250 = $19 250
I am not sure about b cut I think C is 10
Answer:
x = 0 or x = 5/2
Step-by-step explanation:
Solve for x over the real numbers:
x^2 sqrt(2 x - 5) = 0
Split into two equations:
x^2 = 0 or sqrt(2 x - 5) = 0
Take the square root of both sides:
x = 0 or sqrt(2 x - 5) = 0
Square both sides:
x = 0 or 2 x - 5 = 0
Add 5 to both sides:
x = 0 or 2 x = 5
Divide both sides by 2:
Answer: x = 0 or x = 5/2
