Let S be the sum,
S = 2 + 4 + 6 + ... + 2 (n - 2) + 2 (n - 1) + 2n
Reverse the order of terms:
S = 2n + 2 (n - 1) + 2 (n - 2) + ... + 6 + 4 + 2
Add up terms in the same positions, so that twice the sum is
2S = (2n + 2) + (2n + 2) + (2n + 2) + ... + (2n + 2)
or
2S = n (2n + 2)
Divide both sides by 2 to solve for S :
S = n (n + 1)
The correct answers are B and C.
Since the mixture requires 5 mL of black wax and 6 mL of white wax, we want multiples of these numbers; specifically, we need multiples that are the same number of times away.
A does not work; 10 is 5*2 and 24 is 6*4. These won't be in the same ratio.
B works; 15 is 5*3 and 18 is 6*3. These have the same ratio.
C works; 35 is 5*7 and 42 is 6*7. These have the same ratio.
D does not work; 26 is not a multiple of 6.
E does not work; 45 is 5*9 and 48 is 6*8. These will not have the same ratio.
Answer:
Dilation
Step-by-step explanation:
Dilation is when a shape is made bigger but the form of the shape does not change. So its enlarged.
Figure out slope by using:
(y2-y1)/(x2-x1)
Plug in values:
29.98-15.49/50-25
Simplify:
14.49/25 = 0.5796
Then, use this ratio for the 40 lbs bag. So, then:
40*0.5796 = 23.184
So, your price for the 40 lbs bag should be $23.18 because cents only go up to 2 decimal places (otherwise, it would be $23.184).
Answer:
x= −7/5
Step-by-step explanation:
Step 1: Distribute and combine like terms
3(x−6)−8x=−2+5(2x+1)
(3)(x)+(3)(−6)+−8x=−2+(5)(2x)+(5)(1)(Distribute)
3x+−18+−8x=−2+10x+5
(3x+−8x)+(−18)=(10x)+(−2+5)(Combine Like Terms)
−5x+−18=10x+3
−5x−18=10x+3
Step 2: Subtract 10x from both sides.
−5x−18−10x=10x+3−10x
−15x−18=3
Step 3: Add 18 to both sides.
−15x−18+18=3+18
−15x=21
Step 4: Divide both sides by -15.
Hope this helps! :)
