Mathematics Middle School

Solve the system of equations: 12x + 6y = 60 and 3y = -6x + 30

a) (10,0)
b) (0,10)
c) Infinite Solutions
d) No solutions

Answers

Answer 1
Hello there!

12x + 6y = 60
3y = -6x + 30

Ok so we need to solve 12x + 6y = 60 for x

Let's start by adding -6y to both sides

12x + 6y - 6y = 60 - 6y

12x = -6y + 60

Since we are looking for x, we need to divide both sides by 12

12x/12 = (-6y + 60)/12

x = -1/2 y + 5

We are not done yet, now we need to substitute -1/2 y + 5 for x in 3y = -6x + 30

3y= -6x + 30

3y = -6(-1/2 y + 5)+ 30

3y = 3y

Finally subtracting 3y from both sides

3y - 3y = 3y - 3y

0 = 0

Thus, Infinite Solutions

Related Questions

A girl weighs 5/8 as much as her brother does. If the girl weighs 110 lb, how much does her brother weigh?

Answers

176 is the brothers weight.
Her brother weighs 68.75 pounds or 69 pounds if you round

Samantha has $200 to spend on school clothes. She can buy two designer blouses that all of her friends have, or she can buy four generic blouses for the same amount. She decides to buy the designer blouses. What is Samantha’s motivation behind buying the designer blouses?
conspicuous consumption
consideration for the future
confusion of needs and wants
desire to get the best deal

Answers

the answer would be conspicuous consumption because she wanted to be like her friends.

Answer: A. conspicuous consumption

Step-by-step explanation:

Explain how to estimate the length of the whale using compensation

Answers

Answer:

Assuming that the longest blue whale on record  was about 18 scuba divers in length and a scuba diver is 6 feet length, we want to estimate the length of the whale.

Length of the whale = 18*6

You can multiply mentally by  using compensation. Substitute a number for 18 that is easy  to multiply.

20*6 = 120

Now adjust. Subtract 2 groups of 6, or 12.

120 - 12 = 108

and that is the length of the whale in feet

Is 32,643 divisible by both 3 And 9 why or why not

Answers

Yes, 32,643 divided by 3=10,881 
        32,643 divided by 9=  3,627
Both can be divided and result in whole numbers, no remainders.

In the number 0.561 which is the hundredths place

Answers

Hello There!

After the decimal point it goes: tenths, hundredths, thousandths, tens thousandths etc...
In the hundredths place is the '6'

Hope This Helps You!
Good Luck :) 

- Hannah ❤
56.1

you move the decimal two places to the right.

Can someone help me on this??

Answers

To find the sale price, subtract the discount price from the original price.

17) 11.99 × .53 = 6.3547

11.99 - 6.3547 = 5.6353

Round to the nearest cent.

The sale price is $5.64.


19) 56.5 × 0.16 = 9.04

56.50 - 9.04 = 47.46

The sale price is $47.46.

20) 219.95 × 0.15 = 32.9925

219.95 - 32.9925 = 186.9575

Round to the nearest cent.

The sake price is $186.96.


21) 40.95 × 0.38 = 15.561

40.95 - 15.561 = 25.389

Round to the nearest cent.

The sale price is $25.39


23) 33.99 × 0.08 = 2.7192

33.99 - 2.7192 = 31.2708

Round to the nearest cent.

The sale price is $31.27.

24) 174.99 × 0.23 = 40.2477

174.99 - 40.2477 = 139.7423

Round to the nearest cent.

The sale price is $138.74.


25) 50,000 × 0.3 = 15,000

50,000 - 15,000 = 35,000.

The sale price is $35,000.

26) 31.95 × 0.2 = 6.39

31.95 - 6.39 = 25.56

The sale price is $25.56

Simplify 1/5(-22.38-10.12)

Answers

Your answer should be -6.5. Hope it helps.
1/5(-22.38-10.12)
1/5(-32.5)
1/5(-65/2)
-13/2 = -6 1/2 = -6.5

Shaun collects coins. He has 24 quarters and 32 pennies in a jar. What is the ratio of quarters to pennies in the jar?

Answers

The ratio of quarters to pennies in Shaun's jar is 3:4, with 24 quarters and 32 pennies.

To find the ratio of quarters to pennies in the jar, we need to divide the number of quarters by the number of pennies.

Given:

Number of quarters = 24

Number of pennies = 32

The ratio of quarters to pennies can be expressed as:

[tex]\[ \text{Ratio} = \frac{\text{Number of quarters}}{\text{Number of pennies}} \][/tex]

Substitute the given values:

[tex]\[ \text{Ratio} = \frac{24}{32} \][/tex]

Now, simplify the fraction:

[tex]\[ \text{Ratio} = \frac{3}{4} \][/tex]

So, the ratio of quarters to pennies in the jar is  3:4 .

Gym class of 30 boys and 45 girls is divided into groups each group has the same number of students each group has only boys or girls which is the greatest possible group sizes if every student participates

Answers

The greatest number of groups is 15. This is because 15 is a common multiple of 30 and 45

Out of the 25 students in Mrs. Green's class, 10 have a pet. What percent of the students in Mrs. Green's class have a pet?

Answers

40% of Mrs. Green's student has a pet.

In order to calculate this you:

First, you divide the low number by the high number. In this case that would be 10 / 25= 0.4.

Lastly, you will multiple the answer from your division (0.4) by 100. This would be 0.4 x 100= 40.



What system of linear inequalities is shown in the graph?   Enter your answers in the boxes. there should be two, I have an idea but still a little confused XP

Answers

In order to determine the system of inequalities that have been graphed, we need to find the equations of the two lines. We can then use the equations to write the corresponding inequalities.

[tex]<b><u>Equation of the dashed line</u></b>[/tex]

The equation of this line is given by the formula,

[tex]y = mx + c[/tex]
where m is the slope and c is the y -intercept.

From the graph,

[tex]m = \frac{rise}{run} = \frac{ + 4}{ - 1} = - 4[/tex]
and
[tex]c = 1[/tex]
Hence the equation of this line is
[tex]y = - 4x + 1[/tex]
Since the line is not solid it means the possible inequalities are

[tex]y < - 4x + 1 \: or \: y > - 4x + 1[/tex]

From the graph one of the solution sets is the origin, which has coordinates,
[tex](0,0) [/tex]
We can test the two inequalities with this point to determine the right one. That is,

[tex]0< - 4(0)+ 1 \: or \: 0> - 4(0)+ 1[/tex]

[tex]0< 0+ 1 \: or \: 0 > 0+ 1[/tex]

[tex]0< 1 \: or \: 0 > 1[/tex]

We can see that the first statement is true but the second is false.

This implies that the right inequality is;

[tex]y < - 4x + 1[/tex]

[tex]<b><u>Equation of the solid line</u></b>[/tex]

With the solid line,the slope is
[tex]m=\frac{1}{2}[/tex] and

[tex]c=-1[/tex]

Hence the equation is,
[tex]y=\frac{1}{2}x-1[/tex]

Since this line is solid, the possible inequalities are;

[tex]y\ge \frac{1}{2}x-1 \:or\:y\le \frac{1}{2}x-1[/tex]

Testing with the origin again, we have;
[tex]0\ge \frac{1}{2}(0)-1 \:or\:y\le \frac{1}{2}(0)-1[/tex]

[tex]0\ge -1 \:or\:y\le -1[/tex]

The second statement is true.

Hence the inequaliy of the solid line is,

[tex]y \geqslant \frac{1}{2} x - 1[/tex]

Therefore the system of inequalities are;

[tex]y < - 4x + 1[/tex]

and

[tex]y \geqslant \frac{1}{2} x - 1[/tex]

Answer:

the correct answer is in the image

Step-by-step explanation:

Sharon buys 14 folders for 0.75 dollars each how much change she will
receive if she pays for $15

Answers

0.75 x 14 = 10.50
15 - 10.50 = 4.50
your answer is : Sharon will receive $4.50 change

What is the least common multiple (​ LCM ​) of 4 and 9?

Answers

36 will be the LCM for 4 and 9. 
36 is your answer because 4x9=36 4x8=32 9x3=27.

A home improvement store advertises 60 square feet of flooring for $287.00 including an $80.00 installation fee. Write in equation to represent the cost of one square foot of flooring.

Answers

Hello there,
60 square feet= $287.00 + $80.00
                       = $367
1 square feet= $367 / 60
                     = $6.116666667
                     = $6.12 (to 2dp)

Hope this helps :))

~Top

The cost of one square foot of flooring (excluding the installation fee) can be calculated by subtracting the installation fee from the total cost and then dividing by the total square feet. The equation for this would be c = ($287 - $80) / 60. Solving this equation yields a cost of $3.45 per square foot.

The total cost for a flooring, including the installation fee, is $287. This cost is for 60 square feet of flooring.  Therefore the cost c for one square foot of flooring can be calculated using the equation c = (Total Cost - Installation Fee) / Total Square Feet. To find this, subtract the installation fee from the total cost and then divide the remainder by the total square feet. This gives us the equation c = ($287 - $80) / 60. Solving this equation, we find that c = $3.45. So, the cost per square foot of flooring, excluding the installation fee, is $3.45.

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Helppppppppppppppppppppppppppppppppp

Answers

i believe answer is grin
hope it helps
im 100% sure its b) Grin

The equation y = 5x represents the amount of miles Fran runs in x days. When a graph of this situation is drawn, what does the point (1, 5) on the graph represent? (asap if possible)

Answers

so y=5x on a graph is going to look like a 5/1 slope. X represents days and Y represents miles. So (1,5) means in 1 day Fran runs 5 miles.

Answer:

The answer is "in one day, Fran runs 5 miles"

Step-by-step explanation:

In order to determine the answer, I have attached an image that shows the graph of the equation. We know that "x" represents days and "y" represents miles that Fran runs.

In any function, the pairs of coordinates are represented by (x,y) that belong to the function.

So in this case, the pair (1,5) represents:

x=1

y=5

It means, in one day Fran runs 5 miles.

What is the quotient of 15p^-4 q^-6/-20p^-12 q^-3 in simplifed form?

Answers

In this question, you have two variable p and q. To simplify it, you need to divide each variable which will result in subtracting the power/exponent. Since all the exponent is a minus, it will be easier to switch the position first. The calculation should be: 

15 * p^-4 * q^-6  / -20 * p^-12 * q^-3=
15 * p^12 * q^3 / -20 * p^4 * q^6=
15 /-20 * p^(12-4) * q^(3-6)=
-3 /4 * p^8 * q *-3=
-3 * p^8/ q^3

∠E and ∠F are vertical angles with m∠E=8x+8 and m∠F=2x+38 .

What is the value of x?

Answers

We know that ∠E = ∠F because of the vertical angle theorem.

Using substitution we get 8x + 8 = 2x + 38

Solve for x.

8x + 8 = 2x + 38
8x = 2x = 30 <-- Subtract 8 from each side
6x = 30 <-- Subtract 2x from each side
x = 5 <-- Divide both sides by 6

So, x is equal to 5.

Tommy packed 8 coolers. Each cooler has 14 bottles of water and 12 bottles of juice.

Answers

112 waters 96 bottles of juice
112 waters and 96 bottles of juice

At the zoo there were 3 times as many monkeys as lions. Tom counted a total of 24 monkeys and lions. How many monkeys were there

Answers

lions = x

 monkeys = 3x ( 3 times as many )

3x +x = 24

4x = 24

x = 24/4

x = 6

6 lions

6*3 = 18 monkeys

ten times the square of a non-zero number is equal to seventy times the number

Answers

it is 1000 because you multiple

The number will be 7.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is given as;

'ten times the square of a non-zero number is equal to seventy times the number'

Now, Let a number = x

Then, By the given condition;

10x² = 70x

Solve the expression as;

10x² - 70x = 0

10x (x - 7) = 0

This given two condition,

10x = 0

x = 0

But the number is non zero, so x = 0 is not true.

Then, x - 7 = 0

x = 7

Thus, The number will be 7.

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list a characteristic of univariate data

Answers

Frequency Distribution Tables.Bar Charts.Histograms.Frequency Polygons.Pie Charts.

Hilary wants to fill a mini cake pan with batter to make a mini cake for Phillip's party. The cake pan is 4.0 inches long, 9.0 inches wide, and 2.2 inches deep. What is the volume of the cake pan?  

Answers


You would just have to multiply 4.0 * 9.0 * 2.2 = 79.2 thx :P
79.2 i think

hope i helped

what is the value of x

Answers

131 + 108 +107 +110 = 456


180*3 = 540

540 -456 = 84

x = 84 degrees

Fifty students are trying to raise at least $12,500 for a class trip. They have already raised $1,250. How much should each student raise, on average, in order to meet the goal? Write and solve the two-step inequality for this problem.
_________________________________________________________________________________________

Answers

12 500- 1 250= 11 250
11 250 (divided by) 50= 225
Each student should raise 225 dollars

check my answers please solve the following equation. 2(h - 8) - h = h - 16 h = 8 h = -8 infinitely many solutions no solution

Answers

sorry that is wrong, you distribute the 2 to the h and the 8 so it would be 2h-16-h. that would be h-16 on the left side,

Round 16.748 to the place named tenths

Answers

16.48 probably cuz the 4 is not a 5 but check
16.75 the tenth place is the second one but it is determined on id the hundredth place (the third one) is five or above you round up and drop the last number if it is below you keep it the same and drop the last number, If that makes sense lol :p

The price of an antique book is $91,which is two-fifth more then the cost to the book dealer.Find the cost.

Answers

Let the price of book x. That's the cost the book dealer.

He wants to earn some money while selling it, so he listed the book by a new price, 91 $

He added two-fifth (2/5) price to its initial price. In other words, its new price is 40 % more expensive. (2/5 = x /100)

Here is the equation in words,
initial price + 2/5 of the initial price = 91

by equation: x + 2/5 x =91 

multiply both sides by 5, to eliminate the denominator:

5x +2x = 91.5 ; 7x = 455

divide both sides by 7 to simply coefficient of x: x= 65

The answer is 65$.



Answer:

The cost to book dealer is $65

Step-by-step explanation:

Given : The price of an antique book is $91.

           The price is two - fifth more than the cost to book dealer.

To Find : Cost.

Solution :

Let the cost to book dealer be x

The price of an antique book is $91.

Two - fifth of the dealer cost  :  [tex]\frac{2}{5}x[/tex]

Since we are given that  price is two - fifth more than the cost to book dealer.

⇒[tex]x+\frac{2}{5}x=91[/tex]

⇒[tex]\frac{7}{5}x=91[/tex]

⇒[tex]x=\frac{91*5}{7}[/tex]

⇒[tex]x=\frac{455}{7}[/tex]

⇒[tex]x=65[/tex]

Hence , The cost to book dealer is $65



Randy walks 1/2 mile in each 1/5 hour. How far did randy walk in 1 hour in decimal

Answers

there are 5 1/5 in an hour

 so multiply 1/2 by 5

1/2 = 0.5

0.5 *5 = 2.5 miles in 1 hour

The area of a circular pool cover is 314 square feet. Write and solve an equation to find the diameter of the pool cover. Use 3.14 for pie.

Answers

Step-by-step explanation:

First you need to know that A=πr^2

And the equation to find the diameter is d=2r

So, the equation is d=2√A/3.14

A is 314, so 314 divided by 3.14 is 10

So all that's left is d=2*10

And the diameter is 20 feet.

The diameter of the circular pool is 20 feet.

What is the diameter of the pool?

A circle is a bounded figure which points from its center to its circumference is equidistant. The diameter is two times the value of the radius.

The first step is to determine the radius of the pool; Radius = √Area of a circle /π

Where :

π = pi = 22/7R = radius

√314/3.14 = 10feet

Diameter 10 x 2 = 20 feet

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