Answer:
yes
Step-by-step explanation:
Polynomial Long Division :
4.3 Polynomial Long Division
Dividing : x5-5x4+10x3-10x2+5x-1
("Dividend")
By : x-1 ("Divisor")
dividend x5 - 5x4 + 10x3 - 10x2 + 5x - 1
- divisor * x4 x5 - x4
remainder - 4x4 + 10x3 - 10x2 + 5x - 1
- divisor * -4x3 - 4x4 + 4x3
remainder 6x3 - 10x2 + 5x - 1
- divisor * 6x2 6x3 - 6x2
remainder - 4x2 + 5x - 1
- divisor * -4x1 - 4x2 + 4x
remainder x - 1
- divisor * x0 x - 1
remainder 0
Quotient : x4-4x3+6x2-4x+1 Remainder: 0
Answer:
75 cubic units
Step-by-step explanation:
Bottom layer of a rectangular prism is made up of 15 unit cubes.
Therefore, area of the 15 unit cubes = 15(area of the base of one unit cube)
= 15(1)²
= 15 unit²
Number of layers of unit cubes in the rectangular prism = 5
So the height of the prism = 5 units
Volume of the prism = (Area of the base) × Height
= 15 × 5
= 75 cubic unit
The standard form of the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle, (x,y) is a point of the circle, and r is the length of the radius of the circle. When the equation of a circle is written, h,k, and r are numbers, while x and y are still variables. (x-2)^2 + (y-k)^2 = 16 is an example of a circle. The problem gives us two of the three things that a circle has, a point (5,9) and the center (-2,3). We need to find the radius in order to write the equation. We substitute -2 for h, 3 for k, 5 for x, and 9 for y to get (5 - (-2))^2 + (9 - 3)^2 = r^2 We simplify: 49 + 36 = r^2, r^2 = 85. We only need to know r^2 because the equation of a circle has r^2. We now have all the information to write the equation of a circle. (x + 2)^2 + (y - 3)^2 = 85.
Answer:
two real, unequal roots
Step-by-step explanation:
y is definied as y = 3x - 1. Substitute 3x - 1 for y in xy = 9, obtaining:
x(3x - 1) = 9. Then:
3x^2 - x - 9 = 0. In this quadratic, the coefficients are a = 3, b = -1 and c = -9.
Calculating the discriminant b^2 - 4ac, we get (-1)^2 - 4(3)(-9), or 1 + 108, or 109. Because the discriminant is positive, we have two real, unequal roots.
Because there was a pay rise, we can write the equation as x+0.04x = 24.492 and solve for x.
x+0.04x = 24.492
1.04x = 24.492
x=23.55
His original pay was £23.55
