Answer:
see below
Step-by-step explanation:
Usually, we're concerned about the relationship of y to x. Here, the question is asking you to consider the relationship of x to y.
The easiest way to find the answer to this one is to check the given explanations to see which is true. You can pretty much ignore the first row of the table and just look at the second row where x=5 and y=15.
- it is NOT TRUE that x is 3 times y (5 is not 3 times 15)
- it is TRUE that x is 1/3 of y (5 is 1/3 of 15)
- it is NOT TRUE that x is 5 times y (5 is not 5 times 15)
- it is NOT TRUE that x is 1/5 of y (5 is not 1/5 of 15)
_____
If you know your multiplication tables, you know that 15 = 3×5, so ...
5 = 15/3
5 = (1/3) × 15
The relationship of these numbers should not be a mystery.
Answer:
The answer is B - 288
To get this answer all you need to do is
First, subtract 316 - 28 to get your answer :)
Hope this helps!
-sofia~
9514 1404 393
Answer:
$125 per year
Step-by-step explanation:
In the 2 years from 2015 to 2017, the spending on lunches increased by ...
$800 -550 = $250
That is an average per year of ...
$250/(2 yr) = $125/yr . . . . average dollar increase per year
_____
<em>Additional comment</em>
For costs, it is often true that they follow an exponential curve, not a linear one. Ed's spending increased by a factor of 800/550 = 16/11 in the two years, so an average percentage increase of √(16/11) -1 = 20.6% per year.
Answer:
x = 9, Angles are 54°
Step-by-step explanation:
First, we need to find x:
7x-9 = 5x+9
+9 +9
7x = 5x+18
-5x -5x
2x = 18
x = 9
Now, we plug our x value in to find our angles.
5(9) + 9 = 54
Angle B = 54°
7(9) - 9 = 54°
Angle E = 54°
(angles are the same due to AAA property)
Answer:
a. closed under addition and multiplication
b. not closed under addition but closed under multiplication.
c. not closed under addition and multiplication
d. closed under addition and multiplication
e. not closed under addition but closed under multiplication
Step-by-step explanation:
a.
Let A be a set of all integers divisible by 5.
Let
∈A such that ![x=5m\,,\,y=5n](https://tex.z-dn.net/?f=x%3D5m%5C%2C%2C%5C%2Cy%3D5n)
Find ![x+y,xy](https://tex.z-dn.net/?f=x%2By%2Cxy)
![x+y=5m+5n=5(m+n)](https://tex.z-dn.net/?f=x%2By%3D5m%2B5n%3D5%28m%2Bn%29)
So,
is divisible by 5.
![xy=(5m)(5n)=25mn=5(5mn)](https://tex.z-dn.net/?f=xy%3D%285m%29%285n%29%3D25mn%3D5%285mn%29)
So,
is divisible by 5.
Therefore, A is closed under addition and multiplication.
b.
Let A = { 2n +1 | n ∈ Z}
Let
∈A such that
where m, n ∈ Z.
Find ![x+y,xy](https://tex.z-dn.net/?f=x%2By%2Cxy)
![x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)](https://tex.z-dn.net/?f=x%2By%3D2m%2B1%2B2n%2B1%3D2m%2B2n%2B2%3D2%28m%2Bn%2B1%29)
So,
∉ A
![xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1](https://tex.z-dn.net/?f=xy%3D%282m%2B1%29%282n%2B1%29%3D4mn%2B2m%2B2n%2B1%3D2%282mn%2Bm%2Bn%29%2B1)
So,
∈ A
Therefore, A is not closed under addition but A is closed under multiplication.
c.
![Let A=\{2,5,8,11,14,...\}](https://tex.z-dn.net/?f=Let%20A%3D%5C%7B2%2C5%2C8%2C11%2C14%2C...%5C%7D)
Let
but
∉A
Also,
∉A
Therefore, A is not closed under addition and multiplication.
d.
Let A = { 17n: n∈Z}
Let
∈ A such that ![x=17n,y=17m](https://tex.z-dn.net/?f=x%3D17n%2Cy%3D17m)
Find x + y and xy
![x+y=17n+17m=17(n+m)](https://tex.z-dn.net/?f=x%2By%3D17n%2B17m%3D17%28n%2Bm%29)
![xy=(17m)(17n)=289mn=17(17mn)](https://tex.z-dn.net/?f=xy%3D%2817m%29%2817n%29%3D289mn%3D17%2817mn%29)
So,
∈ A
Therefore, A is closed under addition and multiplication.
e.
Let A be the set of nonzero real numbers.
Let
∈ A such that ![x=-1,y=1](https://tex.z-dn.net/?f=x%3D-1%2Cy%3D1)
Find x + y
![x+y=-1+1=0](https://tex.z-dn.net/?f=x%2By%3D-1%2B1%3D0)
So,
∈ A
Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.
Therefore, A is not closed under addition but A is closed under multiplication.