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1 year ago

Solve the system using elimination.5x-9y=12x-9y=-12

Mathematics

1 answer:

NemiM [27]1 year ago

4 0

Answer:

x = 6

y = 2

Explanation:

To solve the system using elimination, we need to multiply the second equation by -1, so the second equation is equivalent to:

x - 9y = -12

-1 (x - 9y) = -1 (-12)

-x + 9y = 12

Then, we can sum this equation and the first equation. So:

5x - 9y = 12

-x + 9y = 12

4x + 0 = 24

So, we can solve for x, as:

4x = 24

4x/4 = 24/4

x = 6

Then, we can replace x by 6 on the first equation and solve for y, so:

5x - 9y = 12

5(6) - 9y = 12

30 - 9y = 12

30 - 9y - 30 = 12 - 30

-9y = -18

-9y/(-9) = -18/(-9)

y = 2

Therefore, the solution of the system is x = 6 and y = 2

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Kay has 28 coins which includes nickels and dimes if the total is 2.35$, how many of each coin does Kay have?

BaLLatris [955]

Answer:

19 dimes and 9 nickels

Step-by-step explanation:

Model the situation using two equations, then solve the system.

let n be number of nickels and d be number of dimes.

n + d = 28 <= This equation is about the number of coins.

0.05n + 0.10d = 2.35 <=This equation is about the worth in dollars.

Rearrange n + d = 28.

n = 28 - d

Now we can substitute this equation into the other one.

Sub n =28-d at the "d" variable for the equation 0.05n + 0.10d = 2.35

0.05n + 0.10d = 2.35

Now there is only one variable.

0.05(28 - d) + 0.10d = 2.35 <=distribute this

0.05(28 - d) + 0.10d = 2.35

1.4 - 0.05d + 0.10d = 2.35 <=combine like terms

1.4 + 0.05d = 2.35 <= begin to isolate d

0.05d = 2.35 - 1.4

0.05d = 0.95

d = 0.95/0.05

d = 19

Now that we know d=19, we can substitute it into any equation.

Choose the equation n + d = 28 because the numbers are easier.

n + d = 28

n + 19 = 28 <=isolate n

n = 28 - 19

n = 9

Since n=9 and d=19, Kay has 9 nickels and 19 dimes.

8 0

3 years ago

Read 2 more answers

What is 35% of 98? I need Help with this problem?

elena55 [62]

35% of 98 is 34.3

Change the percentage (35) into a decimal by dividing over 100:

35 / 100 = 0.3

Multiply the decimal and 98:

0.35 × 98 = 34.3

8 0

3 years ago

A container is filled with 100 grams of bird feed that is 80% seed. Tom and Sally want to mix the 100 grams with bird feed that

marta [7]

Answer:

Initially, we had:

100 grams of a mixture that is 80% seed, (or 0.8 in decimal form)

This means that the quotient between the mass of seeds and the total mass of the mixture is equal to 0.8

Then the mass of seeds, x, can be calculated as:

x/100g = 0.8

x = 0.8*100g

x = 80g

We also have another mixture, that is 5% seed (or 0.05 in decimal form)

This means that in X grams of this mixture, there will be y grams of seeds, such that:

y/X = 0.05

y = 0.05*X grams

Now, we want to create a mixture that is 40% seeds (or 0.4 in decimal form).

Let's do this.

If we add X grams of the 5% mixture, the total mass will be:

M = 100g + X.

The total mass of seeds will be:

m = 80g + X*0.05

and we want that the quotient between the mass of seeds and the total mass to be exactly 0.4

m/M = 0.4

(80g + X*0.05)/(100g + X) = 0.4

Let's solve this for X.

(80g + X*0.05) = 0.4*(100g + X)

80g + X*0.05 = 40g + X*0.4

80g - 40g = X*0.4 - X*0.05

40g = X*0.35

40g/0.35 = X = 114.2g

If we want the mixture to be exactly 40% seeds, we need to add 114.2g of the 5% mixture. (We already can see that Tom is closer to the exact result than Sally)

If we add 114g, like Tom wants, we will have:

M = 100g + 114g = 214g

m = 80g + 0.05*114g = 85.7g

m/M = 85.7g/214g = 0.4005

This is a really good aproximation, if we write this in percentage form this would be:

0.4005*100% = 40.05%

8 0

3 years ago

Tom's's garden has 9 tomato plants, 5 pepper plants, 3 squash plants, and 6 pumpkin plants.

Marianna [84]

Answer:

Squash plant.

Step-by-step explanation:

I'm not sure how to explain, but if you divide 9 by 3, you get 3. There are 3 squash plants, so that's the answer. You could also write it as a ratio...

9:3

3:1

I'm not exactly sure how to explain the ratio part either, but I hope it helped at least a little bit...have an amazing day :3

6 0

3 years ago

ANSWER BOTH!!!

brilliants [131]

Answer:

A = $52.00
B = $6.30

Step-by-step explanation:

<h3>A. How much Bill paid AFTER the discount.</h3>

Step 1: Convert the discounted percent to decimal

20% = 0.2

Step 2: Multiply the discount to the item regularly priced

0.2(65.00) = 13

So, Bill received a $13 discount, therefore, the amount he paid AFTER his discount is:

Step 3: Subtract the result (the discount Bill received) from the regular price

$65.00 - $13.00= $52.00

Therefore, Bill paid $52.00

<h3>B. The price of the pillow in the department store.</h3>

Step 1: Multiply the wholesale price for a pillow by the marked-up the wholesale price

$4.50 × 40% = 1.8

Set up a fraction

$\frac{4.50}{x}=\frac{100\%}{40\%}$

The reciprocal of both sides gives

$\frac{x}{4.50}=\frac{40}{100}$

x = 1.8

Step 2: Add the result to the wholesale price for the pillow

4.50 + 1.8 = $6.3

Step 3: Round to the nearest cent

Add a zero behind the result = 6.30

Therefore, the price of the pillow in the department store is $6.30

7 0

2 years ago