Answer: 22 minutes
Step-by-step explanation: 500-170 means that he drained 330 gallons of water so 330 divided by 15 gallons a minute so you get 22 so it takes 22 minutes to have 170 gallons left in the pool
It is fine that you did not include the measure of angle XYZ in your posting.
This question is testing your knowledge of the four types of transformations.
1) Translations - an item is "slid" to a new location.
2) Reflections - an item is "flipped" (usually over the x-axis or y-axis)
3) Rotations - an item is rotated, usually around the origin (the point (0,0) is the center of most rotations, especially in high school math).
4) Dilations - an item is enlarged or reduced by a certain ratio.
It the first three, the image after the transformation is congruent to the pre-image. It has the same size and shape. It is simply flipped, rotated, slid...
But... in the fourth, dilation, the image now has a different size. It is still, however the same shape.
In geometry terms, after the first three transformations, the image is still "congruent" to the pre-image. After dilation, the image is "similar" but not "congruent."
So... all that to say that when you rotate an angle around the origin, the measure of the angle doesn't change.
So the first choice is correct. The measure of the image of the angle is the same as the measure of the angle.
<span>m∠X’Y’Z’ = m∠XYZ
</span>
7^2 +6 ^2= 85
Square root of 85 = 9.219544457
Answer : 9.2
Answer:
Step-by-step explanation:
Equation is t÷5=8
first you multiply 5 on each to cancel it out
t÷5*5=8*5
solve to get
t=40
Answer: it will take 14 years
Step-by-step explanation:
A savings account is started with an initial deposit of $600. This means that the principal P is
P = 600
It was compounded annually. This means that it was compounded once in a year. Therefore,
n = 1
The rate at which the principal was compounded is 2.1%. So
r = 2.1/100 = 0.021
The duration of time that for which the money stayed in the account is t years. So
Time = t
The formula for compound interest is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years. Therefore,
a) the equation to represent the amount of money in the account as a function of time in years would be
A = 600 (1+0.021/1)^1×t
A = 600 (1.021)^t
b) the amount of time it takes for the account balance to reach $800 would be
800 = 600 (1.021)^t
Dividing both sides of the equation by 600, it becomes
1.33 = (1.021)^t
t = 14
