solving systems of linear equations by graphing 2x+3y=-12 and 10x+3y=12

Answers

Answer 1

Answer:

  (x, y) = (3, -6)

Step-by-step explanation:

I like a good graphing calculator for solving systems of equations by graphing.

__

If you're solving these by hand, you need to graph the equations. It can be convenient to put the equations into "intercept form" so you can use the x- and y-intercepts to draw your graph.

That form is ...

  x/(x-intercept) +y/(y-intercept) = 1

Dividing a standard-form equation by the constant on the right will put it in this form.

  x/(-12/2) +y/(-12/3) = 1 . . . . . . divide the first equation by -12

  x/(-6) +y/(-4) = 1 . . . . . . . . . . . the x-intercept is -6; the y-intercept is -4

__

  x/(12/10) +y/(12/3) = 1 . . . . . . divide the second equation by 12

  x/1.2 +y/4 = 1 . . . . . . . . . . . . . the x-intercept is 1.2*; the y-intercept is 4

__

The locations of these intercepts and the slopes of the lines tell you that the solution will be in the fourth quadrant. The lines intersect at (x, y) = (3, -6).

_____

* It can be difficult to draw an accurate graph using an intercept point that is not on a grid line. It may be desirable to put the second equation into slope-intercept form, so you can see the rise/run values that let you choose grid points on the line. That equation is y =-10/3x +4. A "rise" of -10 for a "run" of +3 will get you to (3, -6) starting from the y-intercept of (0, 4).

Solving Systems Of Linear Equations By Graphing 2x+3y=-12 And 10x+3y=12

Related Questions

What is the denominator of zero

Answers

Answer:Any number

Step-by-step explanation:

The drama club is selling tickets to a play for each ticket they sell the school receives x dollars and the drama club receives the remaining amount the drama club sells 96 tickets for a total of (96x + 672) how much money does the drama club receive for each ticket that they sell

Answers

The drama club receives $7 for each ticket that they sell.

Step-by-step explanation:

Given,

Amount received by school = x dollars

Amount received by school for 96 tickets = 96x

Amount received by drama club = remaining amount after school

Total amount of 96 tickets = 96x+672

Here,

96x is the share of school

672 is the share of drama club for 96 tickets.

Therefore;

96 tickets = dollars

1 ticket = [tex]\frac{672}{96}[/tex]

1 ticket = 7 dollars

The drama club receives $7 for each ticket that they sell.

Keywords: division, addition

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The volume, V, of gas varies inversely with the pressure, P, on it. If the volume is 320 cm^3 under pressure of 40 kg/cm^2, what pressure has to be applied to have a volume of 200 cm^3?



Fill in the blank:

Answer: _________ kg/cm^2

Answers

The pressure [tex]64kg/cm^{2}[/tex] has to be applied to have a volume of [tex]200cm^{3}[/tex]

Explanation:

According to Boyle's law, for a fixed amount of gas, the volume and pressure are inversely proportional.

[tex]P_{1} \cdot V_{1}=P_{2} \cdot V_{2}[/tex]

Substituting the values, we get,

[tex]40 \times 320=P_{2} \times 200[/tex]

Dividing both sides by 200,

[tex]\frac{40 \times 320}{200}=P_{2}[/tex]

Simplifying the terms, we get,

[tex]\begin{aligned}\frac{12800}{200} &=P_{2} \\64 &=P_{2}\end{aligned}[/tex]

Thus, the pressure [tex]64kg/cm^{2}[/tex] has to be applied to have a volume of [tex]200cm^{3}[/tex]

Four tomatoes cost $3.40. What is the unit rate?

Answers

Answer:

$0.85 per tomato

Step-by-step explanation:

A unit rate is the cost for one item. Like $0.99 for this one bag of skittles.

So $3.40 divided by four is $0.85.

The unit rate would be 0.85. If you divide 3.40 by 4 you 0.85

Find the unit rate. Three medium apples have about 285 calories.

Answers

Answer:A “unit rate” is the average rate for a single unit. This is found by dividing the total amount of an item by the number of units in the group. In this case we have the ratio of (3285) Applescalories .

Step-by-step explanation:

Is a rectangle always a parallelogram?

Yes or No

Answers

Yes, a rectangle is always a parallelogram.

The answer is yes.

Rectangles are quadrilaterals with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal.

Another one! This is so annoying! thank u all who are actually helping me

Answers

Answer:

10cm

Step-by-step explanation:

find the diameter of the circumference of 5cm:

d= c÷3.14

=5cm÷3.14

=1.6cm

Double 1.6cm:

1.6×2= 3.2

Find the new cicumference:

c= 3.14×d

= 3.14×3.2

= 10cm

My work to your question

Add 8 to h, then add 5 to the result

Answers

Answer:

(h+8)+5

Step-by-step explanation:

First, you need to add 8 to h, which is h+8 and then you need to add 5 to the result, which means you need to put parentheses around h+8 because you need to do that first. then your answer becomes (h+8)+5.

After adding 8 to h and then 5 to the result, the final value will be h + 13.

To perform the specified operations, you first need to add 8 to the value of h and then add 5 to the result. This can be expressed as a mathematical expression:

Result = (h + 8) + 5

Start with the value of h.

Add 8 to it, which gives you (h + 8).

Now, take the result from step 2 and add 5 to it, yielding the final result.

This process essentially means you're increasing the original value of h by 8, and then further increasing the updated value by 5. The final result will be h + 8 + 5, or simply h + 13.

So, the answer is that you will end up with a value equal to h + 13 after performing these operations.

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An exotic dancer pole is 16 feet tall. How tall would the pole be if 2 more poles were added on top?​

Answers

Answer:48 feet

Step-by-step explanation:

16x3=48

Answer:38 feet tall

Step-by-step explanation:

The point (-2,5) satisfies the inequality y + 2x2 -7.

Answers

Answer:

false?

Step-by-step explanation:

do u mean equals? and the x is x not multiply?

Sergio has 10 leftover cookies and that he wants to share equally with four students from his class. How many cookies will each other four students get?

Answers

Answer:

2

Step-by-step explanation:

There is 5 people since there are 4 students then you. So you would do 10 divided by 5 which is 2.

4. Write an equation represented by this tape diagram using these operations.

a. addition

b. subtraction

c. multiplication

d. division


Please answer a-d pleaseeee I need help :(

Answers

a. 9+9+9=27
b. 27-9-9-9=0 ?
c. 9*3=27
d. 27/3=9. or 27/9=3

if angles of a triangle are 2 is to 3 is to 4 is to .find the value of each angle​

Answers

Answer:

Angles of triangle are 40°,60° and 80°.

Step-by-step explanation:

Given:

if angles of a triangle are 2 is to 3 is to 4.

Let the common factor between the angles be 'x'.

So we can say that;

Angle 1 = [tex]2x[/tex]

Angle 2 = [tex]3x[/tex]

Angle 3 = [tex]4x[/tex]

We need to find the value of each angle.

Solution:

Now we know that;

"Sum of all angles of triangle is 180°."

framing in equation form we get;

[tex]Angle \ 1+Angle\ 2+Angle \ 3 =180[/tex]

Substituting the values we get;

[tex]2x+3x+4x=180\\\\9x=180[/tex]

Dividing both side by 9 we get;

[tex]\frac{9x}{9}=\frac{180}{9}\\\\x=20[/tex]

Angle 1 = [tex]2x=2\times20=40\°[/tex].

Angle 2 = [tex]3x=3\times20=60\°[/tex]

Angle 3 = [tex]4x=4\times20=80\°[/tex]

Hence Angles of triangle are 40°,60° and 80°.

4. Determine if the equation is a linear equation:
8x + 9y = -19
yes
no

Answers

Answer: it is linear

Step-by-step explanation:

It is linear because the highest power of the unknown variable is 1

5. The average of 4, -8, 6, 14, -3 is

Answers

Add all together then divide by the amount of inputs. 2.6

What is 2 times one fourth

Answers

Answer:

0.5

Step-by-step explanation:

2 times 1/4 equals 0.5 or 1/2.

we can solve this equation by turning 2 into 2/1.

2/1 x 1/4 equals 1/2 or 0.5

word problem for 456 divided by 6

Answers

Answer:

76

Step-by-step explanation:

456 divided by 6 equals 76. Hope that helps.

Answer

Emma made 456 cookies and she wanted to divid them to 6 friends. how manny cookies will each friend get?

Step-by-step explanation:

Describe a Whats a real-life example that you can represent by -1200

Answers

Answer:

Step-by-step explanation:

well you could say a person lost a $1200 bet on anything and go from their.

Or someone payed a bill for his Car payment of $1200

ordan has 168 inches of string. He cuts the string into 6 equal pieces. He cuts another 8 inches from each piece.

How long is each piece of string?

Answers

Each piece is 20 inches long.

Step-by-step explanation:

The length pieces of the ribbon can be obtained by dividing the total length of ribbon by total number of pieces

Given

String length = 168 inches

Number of pieces = 6

So the length of each piece will be:

[tex]Length\ of\ each\ piece = \frac{Length\ of\ string}{Number\ of\ pieces}\\= \frac{168}{6}\\= 28\ inches[/tex]

Cutting 8 inches from each piece means that the length will be reduced 8 inches

[tex]Length\ after\ cutting\ 8\ inches = \ length\ of\ each\ piece - 8\\= 28-8\\=20\ inches[/tex]

Hence,

Each piece is 20 inches long.

Keywords: Division, length

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Answer:

20

Step-by-step explanation:

i have no idea

                                       

a+12/3=8 what is the answer to this math problem

Answers

Answer:

4

Step-by-step explanation:

a + 12/3 = 8

a + 4 = 8

a = 8 - 4

a = 4

Answer:

a=4

Step-by-step explanation:

a+12/3=8

a+4=8

a=8-4

a=4

Martha invested a principal amount of $15,000 into a savings account that earns simple interest at a rate of 4.5% per year. How much money will she earn in interest over 6 years?

A.

$4,050

B.

$1,500

C.

$3,845

D.
4,500

Answers

Option A

The simple interest earned over 6 years is $ 4050

Solution:

Martha invested a principal amount of $15,000 into a savings account that earns simple interest at a rate of 4.5% per year

The formula for simple interest is given as:

[tex]Simple\ Interest = \frac{p \times n \times r}{100}[/tex]

Where, "p" is the principal and "n" is the number of years and "r" is the rate of interest

From given,

p = 15000

r = 4.5 %

n = 6 years

Substituting the values we get,

[tex]Simple\ Interest = \frac{15000 \times 4.5 \times 6}{100}\\\\Simple\ Interest = 150 \times 4.5 \times 6\\\\Simple\ Interest = 4050[/tex]

Thus simple interest earned over 6 years is $ 4050

Final answer:

Martha will earn $4,050 in simple interest over 6 years on her $15,000 savings account at a 4.5% annual rate. This is calculated using the simple interest formula, Interest = Principal × Rate × Time.

Explanation:

To calculate the simple interest that Martha will earn over a period of 6 years, we will use the formula for simple interest: Interest = Principal × Rate × Time. Here, the principal amount is $15,000, the annual interest rate is 4.5% (which is 0.045 in decimal form), and the time is 6 years.

Let's plug these values into the formula:

Interest = $15,000 × 0.045 × 6

Interest = $15,000 × 0.27

Interest = $4,050

Therefore, the total amount of interest Martha will earn over 6 years is $4,050, which matches option A.

Write 6,219 in expanded form.​

Answers

Answer:

6.219*10^3

Step-by-step explanation:

LN is tangent to circle O at point M and QM is a diameter. Determine the measure of the following angles.

Answers

Answer:

Step-by-step explanation:

Alright, lets get started.

QM is the diameter given.

NL is the tangent given.

The tangent makes 90 degree angle with diameter.

hence the angle QML will be : 90°   ...............   Answer

Similarly, QMN will also be 90°

The angle PMQ is given as 27°

Hence the angle PMN will be = [tex]90-27[/tex]

Hence the angle PMN will be = [tex]63[/tex]°   .....................   Answer

Hope it will help :)

What is six minus negative two x?

Answers

Answer:

Therefore the Expression will be.

[tex]6-(-2x)[/tex]

[tex]6+2x[/tex] ...As minus - minus sign becomes plus.

Step-by-step explanation:

What is six minus negative two x?

Solution:

It is the Algebraic Expression in Statement form.

Algebraic Expression is given in the form numbers and variables with the operands such as

' + ' Plus Sign' - ' Minus Sign ' × ' Multiplication Sign ' ÷ ' Division Sign, etc.

Hence Our Statement is " six minus negative two x "

i.e. Number 6 minus sign then again a minus sign of 2x.

Therefore the Expression will be.

[tex]6-(-2x)[/tex]

Also equals

[tex]6+2x[/tex] ...As minus - minus sign becomes plus.

Which expression is equivalent to 0.18?

A. 1/9

B. 2/11

C. 1/11

D. 11/2


Side note I can do this my self but im too lazy. plus, if anyone wants some easy points just answer this question. I dont feel like dividing.

Answers

Final answer:

Among the options given, 2/11 is most similar to 0.18 when we convert these fractions to their decimal format. Remember that this is an approximation since 2/11 results in a repeating decimal.

Explanation:

The given expression is equivalent to 0.18. To find out which among the provided options this is equivalent to, we need to convert these fractions to decimal format. Let's start with A.
A. 1/9 is equal 0.111 repeating.
B. 2/11 equals approximately 0.1818 repeating.
C. 1/11 equals approximately 0.0909 repeating.
D. 11/2 equals 5.5.

Comparing these to our given expression of 0.18, we find that Option B (2/11) is most closely equivalent after rounding. It's worth noting the repeating decimal in 2/11, which is why it is an approximation rather than an exact equivalent.

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Use the values in the table to determine the slope

Answers

Answer:

sorry where is the table? i dont see the picture... mabye it isnt loading for some-reason

Step-by-step explanation:

sorry wish i could help :(

Answer:

I don't know which table you need help with, so.. Yeah, this may or may not be what you need help with.

But the answer to the table I put is -3/2

Step-by-step explanation:

Sorry if this wasn't what you were looking for!

right triangle ABC has to legs of lengths 9 cm (AB) and 12 cm (AC). what is the length of the third side (BC)?
a. 6 cm
b. 8 cm
c. 14 cm
d. 15 cm

Answers

Answer:

D. 15 cm

Step-by-step explanation:

9² + 12² = x²

81 + 144 = x²

225 = x²

√225 = x

15 = x

D is the correct answer

21+x=26 what is the answer I need it done step by step

Answers

Answer: x=5

Step-by-step explanation:

21+x=26 (you need to isolate x)

-21    -21 (inverse operation to isolate x)

(subtract 21 from 26)

x=5

Answer: x = 5

Step-by-step explanation: In this problem, we want to get x by itself on one side of the equation. Since we have 21 + x, in order to get x by itself, we must subtract 21 from the left side of the equation and when we subtract 21 from the left side of the equation, we must also subtract 21 from the right side of the equation in order to keep our equation balanced.

So on the left, +25 and -25 cancel eachother out and on the right, 26 - 21 simplifies to 5 so x = 5. To check our answer, we plug 5 back in for x in the original equation and we get 21 + (5) = 26 or 26 = 26 which is a true statement  so we know our answer is correct.

Can someone help? Maria, a color specialist, mixes 2 parts of white and 13 parts of red to develop a particular shade. If she creates 150 liters of the shade, what volume of white color did she use? a. 20 L c. 75 L b. 22 L d. 130 L

Answers

The volume of white color used by Maria is 20 liter

Solution:

Maria, a color specialist, mixes 2 parts of white and 13 parts of red to develop a particular shade

She creates 150 liters of the shade

Given ratio is:

2 parts of white and 13 parts of red

white : red = 2 : 13

Let the white mixed be 2x

Let the red mixed be 13x

Total shade = 150 liters

Therefore,

2x + 13x = 150

15x = 150

x = 10

Therefore, volume of white color used = 2x = 2(10) = 20

Thus, volume of white color used by Maria is 20 liter

If 1once of toppings costs. .50 how much would 11onces be

Answers

Answer:

If one ounce of toppings cost $0.50, then you would need to take $0.50*11

.5*11= 5.5

11 ounces would be $5.50

hope this helps ;)

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