Answer:
Step-by-step explanation:
The given polynomial is :
p(x) = 5-10x
We need to find the zeros of the above polynomial. To find it, put p(x) = 0
5-10x = 0
Subtract 5 from both sides
5-10x-5=0-5
-10x=-5
or
10x=5
Divide both sides by 10.
x = 0.5 = 1/2
Hence, the zeros of the polynomial is 1/2.
3:18 is the only equivalent ratio
Answer: the cost per unit of gas is $0.28
Step-by-step explanation:
Let x represent the cost per unit of electricity.
Let y represent the cost per unit of gas.
During one month, a homeowner used 500 units of electricity and 100 units of gas for a total cost of $333. This is expressed as
500x + 100y = 333 - - - -- - -- - -- -1
The next month, 400 units of electricity and 150 units of gas were used for a total cost of $286. This is expressed as
400x + 150y = 286 - - - - - - - - - --2
Multiplying equation 1 by 400 and equation 2 by 500, it becomes
200000x + 40000y = 133200
200000x + 75000y = 143000
Subtracting, it becomes
- 35000y = - 9800
y = - 9800/- 35000
y = 0.28
Substituting y = 0.28 into equation 2, it becomes
400x + 150 × 0.28 = 286
400x = 286 - 42 = 244
x = 244/400 = 0.61
When they work together, it takes John 1/x hours and it takes Brian 1/(x+15) hours to complete 1/4 of the model.
1/x + 1/( x+15 ) = 1/4 / · x ( x+15 )
x+15 + x = x ( x+15 ) /4 / · 4
8 x + 60 = x² + 15 x
x² + 15 x - 8 x - 60 = 0
x² + 7 x - 60 = 0
x² + 12 x - 5 x - 60 = 0
x · ( x + 12 ) - 5 ·( x+ 12 ) = 0
( x + 12 ) · ( x - 5 ) =0
x = - 12 ( not accepted ) or x = 5
The time taken by Brian: 5 + 15 = 20 hours
Answer:
5x^7 + 4x^4 - 2x^2 - 4x - 10.
Step-by-step explanation:
(x^4 - 9x + 5x^7) + (5x - 10 + 3x^4 - 2x^2)
= x^4 - 9x + 5x^7 + 5x - 10 + 3x^4 - 2x^2
Combine like terms:
= 4x^4 - 4x - 2x^2 + 5x^7 - 10
Now rearrange to standard form ( in decreasing degree):
= 5x^7 + 4x^4 - 2x^2 - 4x - 10.
