Answer:
(i) p = -7, q = -3
(ii) (-3/2, 0), (2, 0), (3, 0)
Step-by-step explanation:
Use long division (see picture).
When we divide by x − 1, we get a remainder of q + p + 20.
When we divide by x + 1, we get a remainder of 16 − q + p.
We know the first remainder is equal to 10 and the second remainder is equal to 12. Solving the system of equations:
10 = q + p + 20
12 = 16 − q + p
0 = q + p + 10
0 = 4 − q + p
0 = 14 + 2p
p = -7
q = -3
Therefore:
f(x) = 2x³ − 7x² − 3x + 18
Finding the zeros:
f(x) = 2x³ − 6x² − x² − 3x + 18
f(x) = 2x² (x − 3) − (x² + 3x − 18)
f(x) = 2x² (x − 3) − (x − 3) (x + 6)
f(x) = (x − 3) (2x² − (x + 6))
f(x) = (x − 3) (2x² − x − 6)
f(x) = (x − 3) (x − 2) (2x + 3)
The zeros are at x = -3/2, x = 2, and x = 3.
Answer:
1
Step-by-step explanation:
The denominator in 9 is one. This also applies for all numbers without a denominator.
Hope this helps :)
Answer:
80
Step-by-step explanation:
<u><em>A = Area of First Rectangle </em></u>
<u><em>B = Area of Second Rectangle </em></u>
<u><em>w = Width</em></u>
<u></u>
12(w)=320+B (1st Equation)
8(w) = B (2nd Equation)
w=B/8 <em><u>(Plug this value of w into the first equation)</u></em>
12B/8 = 320 +B <u><em>(you get this)</em></u>
12B= 2560 + 8B <u><em>(Simplify)</em></u>
4B = 2560
B =640 <em><u>plug this value into the 2nd equation</u></em>
8(w) = 640
w = 80
<em>To Test This</em>
12x80 = 960
8x80 = 640
<h3>960 - 640 = 320
<u><em>Therefore the answer is correct the width is 80</em></u></h3>
<h3 />
Answer:
2 radical 14
Step-by-step
square root of 7(7-3)(7-5)(7-6)
which is the square root of 56
which is about 7.5 or 2 radical 14
Answer: 6x+18/(-x²+6x-5)
Step-by-step explanation:
• f is not defined at 1
• f(−3) = 0
• f(3) = 9
• lim x→5+ f(x) = −[infinity]
• lim x→5− f(x) = [infinity]
• f is not defined at 1
we need to have a denominator 0 for x = 1
so, 1/(x-1)
• lim x→5+ f(x) = −[infinity]
• lim x→5− f(x) = [infinity]
For the limits, we need to have
1/(-x+5)
this way, lim x→5+ f(x) = −[infinity] and lim x→5− f(x) = [infinity]
So far we have
1/(x-1)(-x+5)
• f(−3) = 0
the nominator has to be 0 when x = -3
this way, x+3
so, (x+3)/(x-1)(-x+5)
• f(3) = 9
All we need to do is multiply (x+3)/(x-1)(-x+5) by 6, so
6(x+3)/(x-1)(-x+5) = 6x+18/(-x²+6x-5)