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Olin [163]
3 years ago
14

Honors algebra!! Plz help #22

Mathematics
1 answer:
ollegr [7]3 years ago
7 0

Answer:

8

Step-by-step explanation:

12 times x (the first square) is equal to 16 times x-2 (the second square)

12x = 16(x-2)

Distributed

12x = 16x-32

Simplified (divided by 16)

0.75x = x-2

Subtract x from both side of the equation

-0.25x = -2

Both negatives cancel each other out

0.25x = 2

0.25 times what equals 2,...

x = 8

Hope it help,... and I'll see you in life,... well not really, but you get the idea,... Chow,...!

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1.6 liters of drink were equally distributed into 20 cups how many liters of drink would be in each cup
zimovet [89]

Answer:

0.08

Step-by-step explanation:

1.6 liters of the drink was distributed in 20 cups

The litres of drink in each cup can be calculated as follows

= 1.6/20

= 0.08

Hence 0.08 liters of drink would be in each cup

6 0
2 years ago
Write the equation for the line that goes through the point (5, 12) with a slope m = 10​
Iteru [2.4K]

Answer:

<u>Point-slope form</u>:  y - 12 = 10 (x - 5)

<u>Slope-Intercept form</u>:  y= 10x - 38

Step-by-step explanation:

 im not fully sure which equation ur looking for but i think thats right lol. hopefully this helps ! :)

3 0
2 years ago
9.5 less than a number n equals 27
LuckyWell [14K]

Answer:

convert 9.5

n-9=27

Step-by-step explanation:

I converted it for you.

7 0
2 years ago
Someone plz help! thx
timurjin [86]
Convert each mixed number to an improper fraction

--------------------------------------------
Convert 6&1/2 to an improper fraction

6&1/2 = (6*2+1)/2
6&1/2 = (12+1)/2
6&1/2 = 13/2
--------------------------------------------
Do the same for 9&1/4

9&1/4 = (9*4+1)/4
9&1/4 = (36+1)/4
9&1/4 = 37/4
--------------------------------------------
Now multiply the improper fractions 13/2 and 37/4. Multiply straight across

(13/2)*(37/4) = (13*37)/(2*4)
(13/2)*(37/4) = 481/8
--------------------------------------------
The last step is to use long division to find the mixed number equivalent of 481/8

Or we an say 
60*8 = 480
So 60*8+1 = 480+1
which means 
481/8 = (480+1)/8 = 480/8+1/8 = 60&1/8

Making the final answer to be choice C

Another way to get the answer is to convert 481/8 into a decimal to get 60.125 and then convert that back to a mixed number. You should get 60&1/8
6 0
2 years ago
If the sum of the even integers between 1 and k, inclusive, is equal to 2k, what is the value of k?
Alisiya [41]
If k is odd, then

\displaystyle\sum_{n=1}^{\lfloor k/2\rfloor}2n=2\dfrac{\left\lfloor\frac k2\right\rfloor\left(\left\lfloor\frac k2\right\rfloor+1\right)}2=\left\lfloor\dfrac k2\right\rfloor^2+\left\lfloor\dfrac k2\right\rfloor

while if k is even, then the sum would be

\displaystyle\sum_{n=1}^{k/2}2n=2\dfrac{\frac k2\left(\frac k2+1\right)}2=\dfrac{k^2+2k}4

The latter case is easier to solve:

\dfrac{k^2+2k}4=2k\implies k^2-6k=k(k-6)=0

which means k=6.

In the odd case, instead of considering the above equation we can consider the partial sums. If k is odd, then the sum of the even integers between 1 and k would be

S=2+4+6+\cdots+(k-5)+(k-3)+(k-1)

Now consider the partial sum up to the second-to-last term,

S^*=2+4+6+\cdots+(k-5)+(k-3)

Subtracting this from the previous partial sum, we have

S-S^*=k-1

We're given that the sums must add to 2k, which means

S=2k
S^*=2(k-2)

But taking the differences now yields

S-S^*=2k-2(k-2)=4

and there is only one k for which k-1=4; namely, k=5. However, the sum of the even integers between 1 and 5 is 2+4=6, whereas 2k=10\neq6. So there are no solutions to this over the odd integers.
5 0
3 years ago
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