Answer:
x^3 - 3x^2 - 3x + 9 + (-36/(x+3))
OR
x^3 - 3x^2 - 3x + 9 - (36/(x+3))
Step-by-step explanation:
First set the divisor equal to 0:
x + 3 = 0
Subtract 3 from both sides
x = -3
This is what you'll divide the dividend by in synthetic division.
Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:
x^4 + 0x^3 - 12x^2 + 0x -9
Coefficents: 1. 0. -12. 0 -9.
Please see the image for the next steps.
The remainder is -36. Put the remainder over the divisor and add it to the polynomial (shown in image)
-36/(x+3)
6x-8y=48
to find the x intercept set y=0
6x - 8*0 = 48
6x = 48
divide by 6 on each side
x =48/6
x=8
(8,0)
to find the y intercept set x=0
6(0) - 8y = 48
0 - 8y = 48
-8y = 48
divide by -8 on each side
y = -6
(0,-8)
Answer:
<em>The voltage at the middle source is</em> 
Step-by-step explanation:
<u>Voltage Sources in Series</u>
When two or more voltage sources are connected in series, the total voltage is the sum of the individual voltages of each source.
The figure shown has three voltage sources of values:
The sum of these voltages is:
Operating:
We know the total voltage is 
, thus:
Equating the real parts and the imaginary parts independently:
4+a=6
1+b=-3
Solving each equation:
a = 2
b = -4
The voltage at the middle source is
Answer: He can predict that 420 students will be in support of the purchase.
Step-by-step explanation:
Since Randy surveyed one student out of every 5 he came across in the cafeteria, it means that if he came across five people, he will survey one, if he came across ten students, he will survey 2 and so on.
If then he surveyed a total of 140 students, then we can actually multiply the number by 5 to know the exact number of students he possibly came across in the cafeteria:
= 140 × 5
= Total of 700 students
If 84 out of the surveyed students supported the purchase, we can find what that figure represents in the total number of students in the cafeteria:
84/140 = x/700
We cross multiply
140 × X = 84 × 700
140X = 58,800
X = 58,800/140
X = 420 students
Therefore, he can predict that 420 students out of a total of 700 students in the cafeteria will be in support of the purchase of the P.E equipment
Answer:
The solution of given equation 5(x - 6) = 2(x + 3) is given by,
x = 12
Step-by-step explanation:
It is given that,
5(x - 6) = 2(x + 3)
<u>To find the solution of given equation</u>
5(x - 6) = 2(x + 3)
5x - (5 * 6) = 2x + (2 * 3)
5x - 30 = 2x + 6
5x - 2x = 6 + 30
3x = 36
x = 36/3
x = 12
Therefore the solution of given equation is,
x = 12
