X is equal to 50 in this equation.
Answer:q = - 9 and r = - 10
Step-by-step explanation:
since g(x) is divided by (x - 1) with remainder - 12, then (1) = 4(1)³ + q(1)² + r + 3 = - 12, that is 4 + q + r + 3 = - 12
q + r + 7 = - 12 ( subtract 7 from both sides )
q + r = - 19 → (1)
Since (x - 3) is a factor of g(x), then
g(3) = 4(3)³ + q(3)² + 3r + 3 = 0, that is
108 + 9q + 3r + 3 = 0
9q + 3r + 111 = 0 ( subtract 111 from both sides )
9q + 3r = - 111 → (2)
The 2 equations to be solved simultaneously are (1) and (2)
Multiply (1) by - 3
- 3q - 3r = 57 → (3)
Add (2) and (3) term by term to eliminate r
6q = - 54 ( divide both sides by 6 )
q = - 9
Substitute q = - 9 into (1)
- 9 + r = - 19 ( add 9 to both sides )
r = - 10
Hope the helps!!! ❤️
Q) <span>If 365 work days are split among 12 employees evenly
Part A: To understand this question, you need to read carefully and pick out key words that tells you what to do. All math word / puzzle problems have key words that tell you what you need to do.
For instance, the key word split tells us we need to divide. So, we know we have 365 work days that need to be split among 12 employees. So for Part A:
365 / 12
For Part B it wants to know what this represents. It represent the number of days each of the 12 employees will get if split evenly among each employee. </span>
Answer:
(x²-10x+33)/(-8) = y
Step-by-step explanation:
The distance between any point on a parabola from both its focus and directrix are the same.
Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,
is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.
Equating the two equations given, we have
square both sides to get
(x-5)²+(y+3)²=(y-1)²
expand the y components
(x-5)² + y²+6y+9 = y²-2y+1
subtract y²+6y+9 from both sides
(x-5)² = -8y - 8
expand the x components
x²-10x+25 = -8y - 8
add 8 to both sides to isolate the -8y
x²-10x+33 = -8y
divide both sides by -8 to isolate y
(x²-10x+33)/(-8) = y
