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lidiya [134]
3 years ago
7

CAN SOMEONE HELP ME WITH QUESTION 3. PLEASE SHOW YOUR WORK

Mathematics
1 answer:
oee [108]3 years ago
8 0
Let 
x = number of liters of the 40% salt solution 
y = number of liters of the 20% salt solution 

The two amounts (x and y) must combine to 1500 liters, so 
x+y = 1500
we can solve for y to get
y = 1500-x
after subtracting x from both sides

---------------------------------------------------

If we have x liters of the 40% salt solution (composed of pure salt plus other stuff) then we have exactly 0.40*x liters of pure salt. Simply multiply the decimal form of the percentage with the amount of solution. 

Similarly, if we have y liters of the 20% solution, then we have 0.20*y liters of pure salt

Combined, we have 0.40*x + 0.20*y liters of pure salt all together. 

We want 1500 liters of a 28% solution, so we want 1500*0.28 = 420 liters of pure salt

Equate the two expressions (0.40*x + 0.20*y and 420) to get
0.40*x + 0.20*y = 420

---------------------------------------------------

We have the equation 0.40*x + 0.20*y = 420 and we also know that y = 1500-x

Let's use the substitution property now

0.40*x + 0.20*y = 420
0.40*x + 0.20*( y ) = 420
0.40*x + 0.20*( 1500 - x ) = 420 ... note how y is replaced with 1500-x

Now we can solve for x
0.40*x + 0.20*( 1500 - x ) = 420
0.40*x + 0.20*(1500) + 0.20*(-x) = 420
0.40*x + 300 - 0.20x = 420
0.40*x - 0.20x + 300 = 420
0.20x + 300 = 420
0.20x + 300 - 300 = 420 - 300
0.20x = 120
0.20x/0.20 = 120/0.20
x = 600

Now that we know x, use this to find y
y = 1500-x
y = 1500-600 ... plug in x = 600 (ie replace x with 600)
y = 900
---------------------------------------------------
---------------------------------------------------

Answers:

We need 600 liters of the 40% solution
We need 900 liters of the 20% solution

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romanna [79]
10.
Answer: 42° and 138°
Steps: First find value of x by adding both equations and setting them equal to 180°:
3x + 12x - 30 = 180
15x - 30 = 180
15x = 210
x = 14

Next, put value of x into equations to find the angle:
3x
3(14)
42°

12x - 30
12(14) - 30
168 - 30
138°


11. Answer: 28°
Steps: Complementary angles add up to 90°, so subtract 62° from 90° to find its complementary angle.
90 - 62 = 28


12. Answer: Corresponding angles are congruent.
7 0
3 years ago
Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and
Alika [10]

Answer:

3 spoons were sold last April

Step-by-step explanation:

Let x represent the total number of forks that they made last month.

Let y represent the total number of spoons that they made last month.

It costs the store $1.70 to buy the supplies to make a fork. This means that the cost of making x spoons will be 1.70×x = 1.7x

It costs the store $1.30 to buy the supplies to make a spoon. This means that the cost of making y spoons will be 1.30×y = 1.3y.

Total cost of making x forks and y spoons is 1.7x + 1.3y

Last April Molly's Custom Kitchen Supplies spent $37.90. This means that

1.7x + 1.3y = 37.90 - - - - - - - - - - 1

The store sells forks for $5.60. This means that the total amount for x forks will be 5.60×x = 5.6x

The store sells spoons for $5.40. This means that the total amount for y spoons will be 5.40×y= 5.4y.

Total amount made from selling x forks and y spoons is 5.6x + 5.4y. They sold the finished products for a total of $147.20. This means that

5.6x + 5.4y = 147.20 - - - - - - - -2

Multiplying equation 1 by 5.6 and equation 2 by 1.7, it becomes

9.52x + 7.28y = 212.24

9.52x + 9.18y = 250.24

Subtracting

- 1.9x = - 38

x = - 38/- 1.9

x = 20

Substituting x = 20 into equation 1, it becomes

1.7×20 + 1.3y = 37.90

34 + 1.3y = 37.90

1.3y = 37.90- 34 = 3.9

y = 3.9/1.3

y = 3

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3 years ago
Each pair of figure is similar. Find the missing length
ExtremeBDS [4]

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7 0
2 years ago
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Slope of KL:-

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2 years ago
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Since we have a cubic root, we're interested in factoring cubes inside the root, so that we can take them out. If we factor 648, we have

648=2^3\times 3^4=2^3\times 3^3\times 3 = (2\times 3)^3\times 3 = 3\times 6^3

So, we have

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