Answer:
k = 7
Step-by-step explanation:
Vertical shift down by 7units, f(x) - 7
g(x) = (0.5)x - 7
g(x) = (0.5)x - k
Comparing both equations, k = 7
Answer:
Width = 15 inches Length = 20 inches
Step-by-step explanation:
The area of a rectangle is calculated using the following formula.
(1)
Where L is the length and x is the width of the rectangle
In this case we know that the length of the rectangle is 5 inches greater than its width. This means that:
(2)
Also The area of a rectangle can be represented by the equation 
so to find the width x we solve the equation
(3)
For an equation of the form
the quadratic formula is:

In this case note that:

Then:




→ 
→ 
We take the positive solution 
Now we use equation (2) to find L
Answer: She bought 68 books.
Step-by-step explanation:
Subtract 31 from 99 to find the difference! The difference tells us how many books she bought at the yard sale.
Answer:
10
30%
Step-by-step explanation:
In this case it would be the combination of 2 taken from 5.
That is, when n = 5 and r = 2
nCr = n! / r! * (n-r)!
replacing
5C2 = 5! / (2! * 3!)
5C2 = 10
Which means that the sample space is 10 possible combinations.
the probability that the card you draw is even is 3/5, since there are 3 even cards that exist and 5 is the total number of cards.
Now, so that both are for it would be the multiplication of the previous probability and 2/4 because an even card and a card in general have already been drawn:
(3/5) * (2/4) = 0.3
So the probability that both are even is 30%
The answer should be 2(2b+3)