Mathematics Middle School

x + y = 12
3x = 2y + 6


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Answers

Answer 1
[tex]X + y = 12[/tex]
[tex]3x = 2y + 6[/tex]

In the first equation, multiply the first equation by 2.
In the second equation, move the 2y to the left.

[tex]2x+2y=24[/tex]
[tex]3x-2y=6[/tex]

Add the two equations to eliminate y and solve for x:
[tex]5x+0=30[/tex]
[tex]x=6[/tex]

Plug-in the the value of x in the either original equation to solve for x. 
I will use the first original equation because it is simpler than the second.
[tex]X + y = 12[/tex]

[tex]y=6;x=6[/tex]

Related Questions

without dividing or listing multiples how can you tell if 61 is a multiple of 6

Answers

It's not even. And every multiple if 6 is even.
It isn't even it is odd

If x = 15 units, y = 18 units, z = 9 units, and h = 12 units, then what is the surface area of the triangular prism shown above?
A. 432 units2 B. 972 units2 C. 864 units2 D. 648 units2


Answers

15*9=135+135=270
18*12=216+216=432
9*18=162
270+432+162=864

C.864 is the answer

The surface area of a triangular prism is 648 square units.

What is the surface area of a triangular prism?

The surface area of a triangular prism is

= (perimeter of the base triangle × length) + (2 × base area of the triangle)

Given, the area of the base triangle is

= (1/2) × y × h square units

= (1/2) × 18 × 12 square units

= (1/2) × 216 square units

The perimeter of the base triangle is

= (x + x + y) units

= (15 + 15 + 18) units

= 48 units

Length = z = 9 units

Therefore, the surface area of the triangular prism is

= [(48 × 9) + 2 × (1/2) × 216] square units

= 648 square units

Learn more about the surface area of the triangular prism here: https://brainly.com/question/23137171

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Solve the perimeter formula for an isosceles triangle, p=2a+b, solve for b.

Answers

minus 2a from both sides
p-2a=b

Answer:

b= (p)/(2a)

Step-by-step explanation:

When someone donated 14 gallons of paint to Rosendale Elementary School, the fifth grade decided to paint a mural. They split the gallons equally among the four classes. How much did each class have to paint their mural?

Answers

3.5 gallons is your answer. I hope this helped!
3.5  each class have to paint 

Writing. To. Explain Lola. Does. Dog. Sitting. For. 18hours. Per. Week. In the summer. About how much. Is her. Hourly. Rate. If she earns. $205.50. Per. Week

Answers

Her hourly rate would be $11.42
205.50 divided by 7 is 11.42

what is 4c squared + 6c - 3c squared - 2c -3

Answers

Your answer to your problem is c squared + 4c -3.
4c^2 + 6c - 3c^2 - 2c - 3

Answer: c^2 + 4c - 3

Television Videl watched 6 times as many hours of television over the weekend as Dineen. Together they watched a total of 14 hours of television. How many hours of television did each person watch over the weekend

Answers

We can make this into an equation. 6 times as many means Videl watched 6 times as many as Dineen, and Dineen watched x hours.
Thus, 6x+x=14. Isolate and solve for x.
7x=14
Divide by 7 on both sides.
x=2.
Videl watched 6*2 hours, or 12 hours of TV.
Dinnen watched 2 hours of TV.

The number of hours of television that they both watched will be 2 hours and 12 hours respectively.

Let the number of hours used by Dineen be x.

Therefore, the number of hours that Videl watched will be 6 × x = 6x

Therefore, based on the information given, the number of hours of television watched will be:

6x + x = 14.

7x = 14.

x = 14/7 = 2 hours.

Therefore, 6x = 6 × 2 = 12 hours

Learn more about division on:

https://brainly.com/question/885563

A number divided by 3.Then 14 is added to the quotient. The result is 33.What is the original number? I did x/3 + 14 = 33. Then i multiplied the 3 on both sides but didn't get the right answer .Help!!

Answers

i think the original number is 19

Answer:57


Step-by-step explanation: If you do in calculator 57÷3+14 it equals 33


What are the slope and y-intercept for the the graph of y - 7x = 10

Answers

y-7x=10
y-7x=10
y=10+7x
y=10+7x, x€r
The finished equation should be y=7x+10

Therefore the slope is 7x and the y-intercept is 10

(7/8+1/12)- 1/2=
please help me with this

Answers

0.45833333333 this is the answer i think and sorry if it is the wrong one

How do you solve equations using multiplication and division

Answers

In order to move a number that is multiplied or divided by the variable, you must do the inverse to both sides. That means, if the number is multiplied, you must divide it by both sides. If it's divided, you must multiply it by both side. steps so that you can apply them to more complex problems.

Hope This Helps
To properly answer this I would need to know what the problem is.

However, to multiply you must figure out how many times you add one number to itself. For example, 3 x 4 is three added to itself four times. 3 x 4 = 12 and 3 + 3 + 3 + 3 = 12.

To divide you must figure out how many times one number can go into another. For example, 15 divided by 3 is seeing how many times 3 must be added to itself to equal 15. 15 divided by 3 = 5 and 3 + 3 + 3 + 3 + 3 = 15. (There are five threes added together to get 15, which is how we know the answer to the equation is 5.)

I'm not entirely sure if this is what you wanted or not, again, I would need to see the entire problem to figure this out.

Find the percent change from the first value to the second.

Answers

25%

Or 69 is 75% of 92

Ellen walks dogs on weekends she gets paid $ 8.50 per hour each day she works 5 hours and 45 minutes does she earn more or less than $85 in one weekend? how much more or less explain.

Answers

$8.50 * 5 = $42.50
45 mins -> $8.50 / 60 * 45 = $6.37

She will earn less than $84 in one weekend because $42.50 + $6.37 = $48.87

Answer:

Ellen earns $159.375 more than $85.

Step-by-step explanation:

We have been given that Ellen walks dogs on weekends she gets paid $ 8.50 per hour. Each day she works 5 hours and 45 minutes.

[tex]\text{45 minutes}=\frac{45}{60}\text{ hour}[/tex]

[tex]\text{45 minutes}=0.75\text{ hour}[/tex]

We know that each week has 5 working days.

[tex]\text{Hours worked each week}=5\times 5.75\text{ hours}[/tex]

[tex]\text{Hours worked each week}=28.75\text{ hours}[/tex]

[tex]\text{Earnings each week}=\$8.50\times 28.75[/tex]

[tex]\text{Earnings each week}=\$244.375[/tex]

Since $244.375 is greater than $85, therefore, Ellen earns $159.375 more than $85.

if a 14 karat gold necklace weighs 1.8 ounces how many ounces of pure gold does it contain

Answers

it contains three 3 pure gold
Three 3 pure gold (: hope this helps

What is 0.003 one tenth of ?

Answers

0.003 is one tenth of .03
0.03 is the correct answer

Which linear inequality is represented by the graph?

Answers

for this one, all you have to do is test out those points and see if you get a valid answer!! it's easier than it looks.

y < 0.5x + 2

then, you can either find these points on your graph to check them (easier for most), but some people prefer the other method which is just taking your answer choices and plugging them in:
(-3, -2)
-2 < 0.5(-3) + 2
-2 < -1.5 + 2
-2 < 0.5
then, you just ask yourself "is that true?" is -2 less than 0.5? and the answer is yes, that's true, so this point is a solution.

the same process repeats with the rest of them, but:
(-3, 2) is a solution.
(-2, 1) is not a solution.
(-1, -2) is a solution.
(-1, 2) is not a solution.
(1, 2) is a solution.
(1, -2) is not a solution.
(1, 2) is a solution.

Answer:

The correct options are 1, 3, 5 and 6.

Step-by-step explanation:

The given inequality is

[tex]y<0.5x+2[/tex]

A point is the solution of a linear inequality, if it satisfy the inequality.

The given point is (-3,-2). Check whether this is a solution or not.

[tex](-2)<0.5(-3)+2[/tex]

[tex]-2<0.5[/tex]

This statement is true. Therefore (-3,-2) is a solution.

The given point is (-2,1). Check whether this is a solution or not.

[tex](1)<0.5(-2)+2[/tex]

[tex]1<1[/tex]

This statement is false. Therefore (-2,1) is not a solution.

The given point is (-1,-2). Check whether this is a solution or not.

[tex](-2)<0.5(-1)+2[/tex]

[tex]-2<1.5[/tex]

This statement is true. Therefore (-1,-2) is a solution.

The given point is (-1,2). Check whether this is a solution or not.

[tex](2)<0.5(-1)+2[/tex]

[tex]2<1.5[/tex]

This statement is false. Therefore (-1,2) is not a solution.

The given point is (1,-2). Check whether this is a solution or not.

[tex](-2)<0.5(1)+2[/tex]

[tex]-2<2.5[/tex]

This statement is true. Therefore (1,-2) is a solution.

The given point is (1,2). Check whether this is a solution or not.

[tex](2)<0.5(1)+2[/tex]

[tex]2<2.5[/tex]

This statement is true. Therefore (1,2) is a solution.

Thus the correct options are 1, 3, 5 and 6.

True or False: 5a + 6b = 11ab? Can you think of a way you can prove it using a and b?

Answers

False unless they are either both 1 or both 0.
11ab=11(a+b) not 5a+6b

Hope this helps :)

Jeanette ' s sister charges $5.50 per hour before 9:00 P.M for babysitting and $8 per hour after 9:00 P.M .She finished babysitting at 11:00 P.M and earned $38 . At what time did she begin babysitting ?

Answers

9:00-11:00 she earned $16. 38-16=22 22/5.50=4 9 minus four equals 5, so she started babysitting at 5:00.

what percent of 2000 is 204

Answers

204 is 10.2% of 2000

Working Out 

204/2000 x 100 = 10.2%

what is the quotient of -4/5 divided by 2

Answers

The answer is -2/5; hope this helps

What is the ratio 18 to 27 written as a fraction in lowest terms?

Answers

The answer would be 2/3 because 18:27 converted to fraction would have been 18/27 but simplify and now 2/3.

Answer:

2/3

Step-by-step explanation:

I took the quiz

How do I show work for 5- (a-4) = 3 (a+2)

Answers

Here is how I would show the work for this problem

5- (a-4) = 3 (a+2)
5-a+4 = 3*a+3*2
5-a+4 = 3a+6
-a+9 = 3a+6
-a+9+a = 3a+6+a
9 = 4a+6
9-6 = 4a+6-6
3 = 4a
4a = 3
4a/4 = 3/4
a = 3/4

So the solution is the fraction a = 3/4 (in decimal form 0.75)

Let me know if you have any questions or issues with any of the steps shown above. It's a lot to take in so feel free to ask about anything really. 
5-(a-4)=3+(a+2)
distribute invible -1
5-a+4=4+a+1
9-a=a+5
add a to both sides
9=2a+5
minus 5 both sides
4=2a
divide by 2 both sides
2=a

60% of what number is 360? 10% of what number is 30?

Answers

.6X=360
X=600

.3X=30
X=100
60% of 600 is 360.
      360/.60=600
            check: 0.60*600=360

do the same to get this answer, simply change to the different numbers.
10% of 300 is 30.

Hope this helps!

512+270 is the same as 500 + ______

Answers

is the same as 500 plus 282

4x7x25=find the product tell which strategy used

Answers

700 would be the answer
Since it is just multiplication, you just multiply the numbers in any order.
For example:
1. 4x7=28x25=700
2. 25x4=100×7= 700
325 × 7= 175 x 4= 700

when a number x is multiplied by 4 the result is 2/5 what is the vaule of x

Answers

2/5 as a decimal is 0.4 
4*0.1=0.4 
meaning x is 0.1
4x=2/5
x=(2/5)/4
x=(2/5)/(4/1)
x=2/5*1/4
x=2/20
x=1/10
x=0.1

Hope this helps :)

what is the square root of 92/207

Answers

.6666666666. Because you divide 92 and 207.

What is 9/4 divided by 3/4 and make a model to support it

Answers

The answer would be 3/1. Hope that helps.

what is the least common multiple of 5 and 10

Answers

The least common multiple of 5 and 10 is 5. I hope this helps you.
To find out what the LCM is, list the multiples of each number:

5, 10, 15 ...
10, 20, 30...

The number that is not only common but also is a multiple of both 5 and 10 would be 10.

What does a variable mean in an addition expression

Answers

In addition or subtraction, a variable represents an unknown number.

Example(s):
1. 20 - x = 17; the variable is 'x'
2. 5 + d = 25; the variable is 'd'

Therefore, you can use any letter to represent a variable. If you don't know what the unknown number is, just pretend that the variable is either a 1 or 0.
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