Answer:
See below.
Step-by-step explanation:
-32 3/5
= [(-32* 5) + 3] / 5
= -163/5 is one expression.
Another is -32.6 ( because 3/5 = 0.6).
Answer:
D. F(x) = 2(x-3)^2 + 3
Step-by-step explanation:
We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)
We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.
The graph of F(x) shown is facing up, so we know that it is multiplied by a <em>positive</em> number. This means we can eliminate A and C because they are both multiplied by -2.
Our two equations left are:
B. F(x) = 2(x+3)^2 + 3
D. F(x) = 2(x-3)^2 + 3
Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.
y = 2(3+3)^2 + 3 =
2(6)^2 + 3 =
2·36 + 3 =
72 + 3 =
75
That one didn't give us a y value of 3.
y = 2(3-3)^2 + 3 =
2(0)^2 + 3 =
2·0 + 3 =
0 + 3 =
3
This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:
D. F(x) = 2(x-3)^2 + 3
Hopefully this helps you to understand parabolas better.
Answer:
a) Red marble: 6/17
b) Green marble: 11/17
c) Purple marble : 0/17 = 0
d) a red or a green marble: 1
Step-by-step explanation:
Number of marbles: 17
Probability to pick one red marble: (# successes) / (# total) = 6/17
Probability to pick a green marble: (# successes) / (# total) = 11/17
Probability to pick a purple marble: (# successes) / (# total) = 0/17 = 0
Probability to pick a green marble or a red marble: Prob one green + prob one red = 11/17 + 6/17 = 17/17 = 1
Answer:
Number of 2-point shots taken = 12
Number of 3-point shots taken = 6
Step-by-step explanation:
Total number of points scored by Gladys = 42
Only 2-point and 3-point shots are taken by Gladys.
Let number of 2-point shots taken = 
Let number of 3-point shots taken = 
Total number of shots taken = 18
Therefore, first equation can be written as:
Total points scored = 42
Therefore, second equation can be written as:
System of equations is:
Using elimination method to solve the system of equations.
Multiplying equation by 2 then subtracting it from equation (2):
By equation (1):
Therefore, Number of 2-point shots taken = 12
Number of 3-point shots taken = 6
Answer:
The shortest side has length 24 ft
Step-by-step explanation:
Try this: 3x + 4x + 5x =96 ft, or
12x = 96 ft
Then x = (96 ft) / 12, or x = 8
Multiplying this factor 8 by 3, we get 24. The shortest side has length 24 ft.
The middle-length side is 4(8), or 32.
The longest side is 5(8), or 40.
Check: Do 40 and 32 and 24 add up to 96 ft?
do 72 and 24 add up to 96 ft?
Yes.
