Answer: Choice B) 
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Work Shown:
This shows why choice B is the answer.
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Explanation:
- In the second step, I multiplied top and bottom by
- This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
- In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.
So in general, if the denominator is 
and you want to rationalize the denominator, then you should multiply top and bottom by 
. The same applies in reverse as well.
This leads to the denominator becoming 
Keep in mind that 
and 
The difference between the exponents = - 4 ( x - 6 - (x - 2) = -4)
A shift of 4 units to the right (Choice )
Slope intercept form is: y=mx+b
So you take the first equation: 2x-3y=6 and you subtract the 2x from both sides and get: -3y= 2x+6
Then you take that equation: -3y= 2x+6 and divide -3 from both sides and get: y= -2/3x -2
So the equation 2x-3y=6 in slope intercept from is
y = -2/3x -2
Can you do the next one your self based on the one i did...?
(Scroll and check ⬇️ )
Here ya go ;)
5x + 2y = 3 okay same steps as above you want to get the x on the other side so you subtract the 5x from both sides and get:
2y = 5x + 3
Then you want to get the y by its self so you divide the 2 from both sides so you get:
y = 5/2x +2/3
Now idk if your allowed to leave it like that (based on your teacher's preferance really) but if not you can simplfy your fractions and get:
y = 2.5x + 0.66
( i would leave the 2/3 and just leave it as y = 2.5x + 2/3 ) but you do you and i hope that helped you :)
Represent these consecutive numbers (assuming that they are all integers):
x
x+1
x+2
x+3
x+4
x+5
and so on
x+8
x+9 is the tenth number. x+9 = 10, so x = 9.
Think of it this way: there are 10 consecutive numbers, and the last one is 10.
Working backwards, we get the sequence 10, 9, ... 3, 2, 1.
The sum of such an arith sequence is equal to the count of the numbers times the average of the first and last terms:
sum here = 10(1+10)/2 = 5(11) = 55 (answer)
Answer:
13 cents, 17 cents, Brand A
Step-by-step explanation:
The unit price is the price of a single pencil. You can find that by dividing the total price by the number of pencils.
Brand A= $2.36/18= $0.13
Band B= $4.09/24= $0.17
0.13 < 0.17
Brand A is cheaper because the price per pencil is less.
