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Sloan [31]
3 years ago
6

Factor 3M^2+11MN+6N^2

Mathematics
1 answer:
antoniya [11.8K]3 years ago
8 0
3M^2 + 11MN + 6N^2 = 3M^2 + 2MN + 9MN + 6N^2

= M(3M + 2N) + 3N(3M + 2N) = (3M + 2N)(M + 3N)

Answer: 3M^2 + 11MN + 6N^2 = (3M + 2N)(M + 3N)
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A pharmacist has 30% and 60% iodine solutions on hand. How many liters of each iodine solution will be required to produce 6 lit
kkurt [141]

Answer:

4 liters of 60% solution; 2 liters of 30% solution

Step-by-step explanation:

I like to use a simple, but effective, tool for most mixture problems. It is a kind of "X" diagram as in the attachment.

The ratios of solution concentrations are 3:6:5, so I've used those numbers in the diagram. The constituent solutions are on the left; the desired mixture is in the middle, and the numbers on the other legs of the X are the differences along the diagonals: 6 - 5 = 1; 5 - 3 = 2. This tells you the ratio of 60% solution to 30% solution is 2 : 1.

These ratio units (2, 1) add to 3. We want 6 liters of mixture, so we need to multiply these ratio units by 2 liters to get the amounts of constituents needed. The result is 4 liters of 60% solution and 2 liters of 30% solution.

_____

If you're writing equations, it often works well to let the variable represent the quantity of the greatest contributor—the 60% solution. Let the volume of that (in liters) be represented by v. Then the total volume of iodine in the mixture is ...

... 0.60·v + 0.30·(6 -v) = 0.50·6

... 0.30v = 0.20·6 . . . . subtract 0.30·6, collect terms

... v = 6·(0.20/0.30) = 4 . . . . divide by the coefficient of v

4 liters of 60% solution are needed. The other 2 liters are 30% solution.

6 0
3 years ago
Leah has two savings accounts with balances totaling $8,000. She withdrew 15% from one and
DedPeter [7]

Answer:930 Hope this Helps :D

Step-by-step explanation:

For the given problem:

Let the balances of the saving accounts be (x) and (y)

Leah has two savings accounts with balances totaling $8,000

so,

x+y=8000 (1)

She withdrew 15% from one and 40% from the other. If she has $6,350 remaining in the accounts

So, The remaining from the accounts will be (1 - 15%) and ( 1 - 40%)

that will give the decimals: 0.85 and 0.6

so, we can write the following equation:

0.85x+0.6y=6350 (2)

Now, solve the equations (1) and (2) to find (x) and (y)

From equation (1)

y=8000-x (3)

Substitute with (y) from equation (3) into equation (2)

0.85x+0.6*(8000)-x =6350

Now solve the equation

0.85x+0.6*8000-0.6x=6350

0.85x-0.6+4800+6350

0.25x=6350-4800

0.25x=1550

x=6200

Substitute with (x) into equation (3) to find (y)

y=8000-6200=1800

So, the larger account = x = 6200

and the smaller account = y = 1800



Now, we will answer the question, how much money did she withdraw from the account with the larger balance?

so, the answer will be: 15% of x = 0.15 * 6200 = 930



So, the answer will be $930

6 0
2 years ago
What is 862,840 rounded to
aliya0001 [1]
862,840 is rounded to 900,000
3 0
3 years ago
20 years ago, father's age was 5 times his son's age. Now his age is 10 years more than twice his son's present age. Find their
Montano1993 [528]

Step-by-step explanation:

x = father's age now

y = son's age now

x = 2y + 10

x - 20 = 5(y - 20) = 5y - 100

using the first in the second equation :

2y + 10 - 20 = 5y - 100

-10 = 3y - 100

90 = 3y

y = 30

x = 2y + 10 = 2×30 + 10 = 60 + 10 = 70

the father is now 70 years old, the son now 30 years old.

6 0
2 years ago
PLEASE SHOW WORK ILL GIVE BRAINLIEST DUE TODAY!!!
Vanyuwa [196]

Answers:

14 + 18 ÷ 2 x 18 – 7 = 169

  • 14 + 9 * 18 - 7
  • 14 + 162 - 7
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60 – 9 x 8 ÷ 8 x 6 = 6

  • 60 - 72 / 8 * 6
  • 60 + -216/4
  • 60 - 54
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15 x 10 + 12 ÷ 3 + 9 = 163

  • 150 + 12 / 3 + 9
  • 150 + 4 + 9
  • 163

(10 ÷ 5)3 + 100 – 9 x 11 = 7

  • 2 * 3 + 100 - 9 * 11
  • 6 + 100 - 99
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8 x 4 + 9 – 9 + 18 = 50

  • 32 + 9 - 9 + 18
  • 41 - 9 + 18
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3 x 8 x 2 – 42 + 5 = 11

  • 24 * 2 - 42 + 5
  • 48 - 42 + 5
  • 11

<em>i hope this helps, good luck :)</em>

3 0
3 years ago
Read 2 more answers
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