Answer:
9 hours
Step-by-step explanation:
Set up the equations: x is the amount of hours Amber worked and y is the hours Jake worked
8x + 8y = 120
y = 3 + x
Substitute the second equation into the first
8x + 8(3+x) = 120
Distribute
8x + 24 + 8x = 120
Combine like-terms
16x + 24 = 120
Subtract 24 on both sides
16x = 96
Divide 16 on both sides
x = 6 (hours Amber worked)
Plug in this x-value into on of the two equations. I will use the second
y = 3 + 6
y = 9
Answer:
- a rotation, followed by a translation
- a translation, followed by two reflections
Step-by-step explanation:
The rigid motions are the transformations that produce congruent images.
There are three main kinds of rigid motions :
- Reflections : Flips a figure across a line of reflection.
- Rotations : Rotates a figure about some degrees around a center point.
- Translations : Moves figure on a plane about some distance in a certain direction.
But dilation is not a rigid transformation because it may change the size of the image. It is usually used to shrink or enlarge a shape.
So, the options having dilation and term "stretch" cannot produce congruent figures.
Hence, the correct options are :
- a rotation, followed by a translation
- a translation, followed by two reflections
Answer:
yes
Step-by-step explanation:
To solve this we are going to use formula for the future value of an ordinary annuity:
![FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3DP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where

is the future value

is the periodic payment

is the interest rate in decimal form

is the number of times the interest is compounded per year

is the number of years
We know from our problem that the periodic payment is $50 and the number of years is 3, so

and

. To convert the interest rate to decimal form, we are going to divide the rate by 100%


Since the interest is compounded monthly, it is compounded 12 times per year; therefore,

.
Lets replace the values in our formula:
![FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3DP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
![FV=50[ \frac{(1+ \frac{0.04}{12} )^{(12)(3)} -1}{ \frac{0.04}{12} } ]](https://tex.z-dn.net/?f=FV%3D50%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.04%7D%7B12%7D%20%29%5E%7B%2812%29%283%29%7D%20-1%7D%7B%20%5Cfrac%7B0.04%7D%7B12%7D%20%7D%20%5D)

We can conclude that after 3 years you will have $1909.08 in your account.
Answer:
150 kids
Step-by-step explanation:
If 60 kids is 40% of the total kids, we can add another 60 to get 80% and then half of 60 (30) to bring the total up to 100% of the kids.