Answer:
(4, 5)
Step-by-step explanation:
Dilation by factor d about point (a, b) effects the transformation ...
(x, y) ⇒ d((x, y) -(a, b)) +(a, b)
⇒ (d(x-a) +a, d(y-b) +b)
(x, y) ⇒ (dx +a(1-d), dy +b(1-d))
We have (x, y) = (3, 4) and (a, b) = (1, 2) and d=3/2. Filling in these numbers, we get ...
(3, 4) ⇒ ((3/2)(3)+1(1-3/2), (3/2)(4)+2(1-3/2)) = (9/2 -1/2, 6 -1) = (4, 5)
Point E' is (4, 5).
_____
If you look at the graph, you realize that E is (2, 2) from (1, 2). Dilation by a factor of 3/2 moves it to (3/2)(2, 2) = (3, 3) from (1, 2). So ...
E' = (3+1, 3+2)
E' = (4, 5)
Answer:
1. 2(3x−2)(2x−3)
2. 3(3x+1)(2x+5)
3. 2(4x+1)(2x−5)
4. 4(2x+1)(2x+7)
5. 5(3x+1)(2x−5)
6. 3(3x−7)(2x+1)
7. 3(5x+3)(3x−2)
8. 2(7x−2)(2x−5)
9. 2(7x−3)(2x−3)
10. 4(5x−11)(2x+1)
11. 5(x−2)(x+12)
12. (x−1)(x−8)
15. x=1 or x=4
Step-by-step explanation:
1. Factor 12x2−26x+12
12x2−26x+12
=2(3x−2)(2x−3)
2. 3(3x+1)(2x+5)
3. Factor 16x2−36x−10
16x2−36x−10
=2(4x+1)(2x−5)
4. Factor 16x2+64x+28
16x2+64x+28
=4(2x+1)(2x+7)
5. Factor 30x2−65x−25
30x2−65x−25
=5(3x+1)(2x−5)
6. Factor 18x2−33x−21
18x2−33x−21
=3(3x−7)(2x+1)
7. Factor 45x2−3x−18
45x2−3x−18
=3(5x+3)(3x−2)
8. Factor 28x2−78x+20
28x2−78x+20
=2(7x−2)(2x−5)
9. Factor 28x2−54x+18
28x2−54x+18
=2(7x−3)(2x−3)
10. Factor 40x2−68x−44
40x2−68x−44
=4(5x−11)(2x+1)
11. Factor 5x2+50x−120
5x2+50x−120
=5(x−2)(x+12)
12. Let's factor x2−9x+8
x2−9x+8
The middle number is -9 and the last number is 8.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -9
Multiply together to get 8
Can you think of the two numbers?
Try -1 and -8:
-1+-8 = -9
-1*-8 = 8
Fill in the blanks in
(x+_)(x+_)
with -1 and -8 to get...
(x-1)(x-8)
15. Let's solve your equation step-by-step.
(x−2)(x−3)=2
Step 1: Simplify both sides of the equation.
x2−5x+6=2
Step 2: Subtract 2 from both sides.
x2−5x+6−2=2−2
x2−5x+4=0
Step 3: Factor left side of equation.
(x−1)(x−4)=0
Step 4: Set factors equal to 0.
x−1=0 or x−4=0
x=1 or x=4
Sorry I wasn't able to do 13 and 14 but hope this helps! :)
Answer:
There are 5 solutions
Step-by-step explanation:
Answer:
Step-by-step explanation:
P(0 personality in common) = 39/375 = 0.104
P(1 personality in common) = 69/375 = 0.184
P(2 personality in common) = 110/375 = 0.2933
P(3 personality in common) = 122/375 = 0.325
3
P(4 personality in common) = 35/375 = 0.093
3
b) No the probability did not add up to 1 because they do not cover the entire sample space
c) Sample space is 0, 1, 2, 3, 4 personality preferences in common
A translation and dilation