Answer:
see explanation
Step-by-step explanation:
(a)
Under a rotation of 180° about the origin
a point (x, y ) → (- x, - y)
the coordinates of P, Q and R are
P(1, -1 ), Q(3, - 2 ), R(3, - 4 )
Hence under the given rotation
P(1, - 1 ) → P'(- 1, 1 )
Q(3, - 2 ) → Q'(- 3, 2 )
R(3, - 4 ) → R'(- 3, 4 )
(b)
Under a reflection in the x-axis
a point (x, y ) → (x, - y ), hence
P(1, - 1 ) → P''(1, 1 )
Q(3, - 2 ) → Q''(3, 2 )
R(3, - 4 ) → R''(3, 4 )
Answer:
Step-by-step explanation:
<u>Multiply the number of containers by the amount in each to find the total amount of sugar:</u>
- 2 4/5 * 2 3/7 =
- 14/5 * 17/7 =
- 2*17/5 =
- 34/5 =
- 6 4/5
Answer:
63% of students
Step-by-step explanation:
Z = (X - μ) / σ
Z = 520 - 500 / 60
Z = 0.33
ON THE Z-TABLE
0.33 = 0.6293
<em>62.93% = 63% of students answer</em>
Function is p(x)=(x-4)^5(x^2-16)(x^2-5x+4)(x^3-64)
first factor into (x-r1)(x-r2)... form
p(x)=(x-4)^5(x-4)(x+4)(x-4)(x-1)(x-4)(x^2+4x+16)
group the like ones
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
multiplicity is how many times the root repeats in the function
for a root r₁, the root r₁ multiplicity 1 would be (x-r₁)^1, multility 2 would be (x-r₁)^2
so
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
(x^2+4x+16) is not on the real plane, but the roots are -2+2i√3 and -2-2i√3, each multiplicity 1 (but don't count them because they aren't real
baseically
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
