Find the value of x. *

Step-by-step explanation:

To find - How can you determine the number of solutions of a system

              of linear equations by inspecting its equations?

Proof -

There exists three types of solution for a system of linear equations.

1. No solution.

2. Unique solution.

3. Infinite many solutions.

Now,

Let the 2 linear equations are as follows :

y = ax + b

y = cx + d

1. For no solution -

a = c and b ≠d

For example-

y = -2x + 5

y = -2x  - 1

Subtract first equation from second , we get

y - y = -2x - 1 - ( -2x + 5)

⇒0 = -2x - 1 + 2x - 5

⇒0 = -6

Not possible

So, There exist no solution.

2. For unique solution -

a ≠ c and b , d can be any value

For example -

If b and d are same ,

y = 2x - 4

y = -3x - 4

Subtract equation 1st from 2nd , we get

y - y = -3x - 4 - ( 2x - 4)

⇒0 = -3x - 4 - 2x + 4

⇒0 = -5x

⇒x = 0

⇒y = 2(0) - 4 = -4

∴ we get

x = 0, y = -4

If b and d are different

y = 2x - 4

y = -3x + 5

Subtract equation 1st from second

y - y = -3x + 5 - 2x + 4

⇒0 = -5x + 9

⇒-5x = -9

⇒x = [tex]\frac{9}{5}[/tex]

⇒y =2([tex]\frac{9}{5}[/tex]) - 4 = [tex]\frac{18}{5} - 4 = \frac{18 - 20}{5} = -\frac{2}{5}[/tex]

∴ we get

x = [tex]\frac{9}{5}[/tex] , y = [tex]-\frac{2}{5}[/tex]

3. Infinitely many solution -

a = c and b = d

For example -

y = -4x + 1

y = -4x + 1

Subtract equation first from equation second

y - y = -4x + 1 - ( -4x + 1)

⇒0 = -4x + 1 + 4x - 1

⇒0 = 0

Satisfied

So, Infinite many solution possible.

Answer:

D

Step-by-step explanation:

use math wwwway , it gives ypu the answer and explenation

Answer:

The ordered pair works for the first equation on the top, but not the second equation on the bottom.

Step-by-step explanation:

You have to plug in the x and y values into the equations:

x - 2y = -6

2 - 2(4) = -6  

That equation works.

...now for the next one...

3x + 2y = 12

3(2) + 2(4) = 12

That equation doesn't work.

Hope this helps!

Answer:

Step-by-step explanation:

Let the merchandise she sold = x

Her commission is 15% of that, so 15% of x or 0.15x

We know her commission was $40, so 0.15x = $40

0.15x = $40

Divide by 0.15

x = $266.67

We can check our answer by substituting $266.67 back into the equation.

0.15(266.67) = 40

40 = 40 ✅

Alyson sold $266.67 worth of merchandise.

Answer: 75

Step-by-step explanation:

Answer:

$6.50

Step-by-step explanation:

43.50-24=19.5

19.5/3=6.5

Answer: Each snack costs $6.50

Step-by-step explanation:

Subtract 43.50 by 24

Then divide

Answer:

If it is direct proportionality, then y = kx where k is a constant.  Use the given information to find k:

8 = k(12) ⇒ k = 8/12 = 2/3

y = (2/3) x

For y = 12,

12 = (2/3) x ⇒ x = (3/2)*12 = 18

x = 18 when y = 12

I hope this helps a little bit.

Answer:

Step-by-step explanation:

[tex]6a^2-13ab-5b^2\\ \\ 6a^2+2ab-15ab-5b^2\\ \\ 2a(3a+b)-5b(3a+b)\\ \\ (2a-5b)(3a+b)[/tex]

Answer:

the median is the middle set of data.

Step-by-step explanation:

Answer:

6*15 = 5(x+5)

90 = 5x + 25

65 = 5x

x = 13

Step-by-step explanation:

I've gone ahead and labeled some points.

There is a formula that says PA*PB = PC*PD, this is what you use.  If you would like me to show why this works I would be happy to.

So what we have is PA = 6, PB = 9+6 = 15, PC = 5 PD = 5+x so let;s writ ethe formula with these values

6*15 = 5(x+5)

90 = 5x + 25

65 = 5x

x = 13

EDIT: Here is the explanation for the formula

If you form triangles PCB and PAD you can find angle D and angle B are the same, because they are inscribed angles that intersect the same arc of the circle.  Also angle P is the same on both triangles since they are the same angle, so this means both triangles are similar.

This means DA is similar to BC, AP is similar to CP and PD is similar to PB. Similar sides means if you can multiply one side by a number to get to its similar side, then you can multiply all sides by that value to get all sides of that similar triangle.  

This also means if you divide one side by its similar side you get the scale value, so this means if you do it to two different sets of similar sides you get the same number

[tex]\frac{PA}{PC}=\frac{PD}{PB}\\PA*PB = PC*PD[/tex]

Answer:

5

Step-by-step explanation:

The greatest common factor of 435 and 100 is 5, so if you make 5 groups, each group will have 87 representatives and 20 senators.

Answer:

25

Step-by-step explanation:

Answer:$5.00

Step-by-step explanation:

Let c = the cost of each candy bar

3 + 8c = 43

8c = 40

c = $5.00

Answer:

each candy bar costs 5 dollars

Step-by-step explanation:

43-3=50 and 40÷8=5

Answer:

Not sure

Step-by-step explanation:

Answer:3

Step-by-step explanation:

7x3=21 4x3=12 21÷12=9 3x3=9

Answer:

Step-by-step explanation:

7 × 3 = (3 × 3) + (4 × 3)

Answer:

$15 in interest

Step-by-step explanation:

sorry if it is wrong. I found 5% of 300 which is 15.

$15  money will tameka pay in interest.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

Here, we have,

formula: I = Prt.

here, we get,

given that,

Tameka borrowed $300 to buy a digital music player she will pay the money back in 1 year at 5%simple interest.

P=$300

r=5%

t=1year

so, I =$300*5%*1

       =$15

Hence, $15  money will tameka pay in interest.

To learn more on interest click:

brainly.com/question/29335425

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Answer:

A

Step-by-step explanation:

We want to find the equation of the line in slope-intercept form.

From the graph, we are given the two points (-5, 1) and (0, -3).

We can find the slope between them. The slope formula is given by:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We will let (-5, 1) be (x₁, y₁) and (0, -3) be (x₂, y₂). Substitute:

[tex]\displaystyle m=\frac{(-3)-(1)}{(0)-(-5)}[/tex]

And evaluate:

[tex]\displaystyle m=\frac{-4}{5}=-\frac{4}{5}[/tex]

Next, notice that the point (0, -3) is already the y-intercept, so we do not need to find it.

Slope-intercept form is given by:

[tex]\displaystyle y=mx+b[/tex]

Therefore, our equation is:

[tex]\displaystyle y=-\frac{4}{5}x-3[/tex]

Our answer is A.

Answer: The answer is 13.5

Step-by-step explanation:

Answer:

1. YES  2. NO

Step-by-step explanation:

1. Since x=0.121212... and the question is asking for 100x, we need to multiply each side by 100. 0.121212... multiplied by 100 is 12.1212... So YES, 100x is still a repeating decimal.

2. 12.121212... minus 0.121212... would just be 12. This is because if we know that all the numbers behind the decimal point is 0.121212 and so on, 12.121212... minus 0.121212... the numbers behind the decimal would cancel out. So we are left with 12. So NO, the answer for 99x is NOT a repeating decimal.

Answer:

8 visits

Step-by-step explanation:

Create an equation, where x is the number of visits to the theater.

Since she gets 12.5 points for each visit, the number of points from visits will be represented by 12.5x.

85 will be added to this, since she gets 85 points for signing up. Then, this will be set equal to 185, since she needs 185 points for the free ticket.

12.5x + 85 = 185

Solve for x:

12.5x = 100

x = 8

So, Aria needs to make 8 visits to earn a free movie ticket

Aria must make 8 visits to earn a free movie ticket when She needs 185 points for a free movie ticket.

By given she has  85 rewards points just for signing up.

She earns 12.5 points for each visit to the movie theater.

She needs 185 points for a free movie ticket.

We must find how many visits does aria has to make to earn a free movie ticket

If two expressions with equal sign is called as equation.

Let  x is the number of visits to the theater.

Since she gets 12.5 points for each visit, the number of points from visits will be represented by 12.5x.

85 will be added to this, since she gets 85 points for signing up. Then, this will be set equal to 185, since she needs 185 points for the free ticket.

12.5x + 85 = 185

12.5x = 100

x = 8

So, Aria needs to make 8 visits to earn a free movie ticket

To learn more about solving equation click here:https://brainly.com/question/19297665

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A

Because of 3 adults bought 3 tickets, 9 x 3. 9(3)

4 students bought 4 tickets, 4 x 5, 4(3)

Step-by-step explanation:

hope this helps you

,..............

Answer:

(5x + 5) ( 2x - 3)

5x (2x-3) +5(2x-3)

10x^2 - 15x + 10x -15

10x^2 -5x -15

Answer:

$1.25

Step-by-step explanation:

Given data

let the movie ticket be x and the candy bar be y

x+y= 5-------------1

also

2x+y= 8.75--------2

solve 1 and 2

x+y= 5

2x+y= 8.75

from 1

x= 5-y

put this inplace of x in 2

2(5-y)+y=8.75

10-2y+y= 8.75

10-y= 8.75

10-8.75=y

y= 1.25

Hence candy bar is $1.25

Question:

Alfie tossed a paper cup in the air 150 times and recorded the side it landed on.

     Right side up = 60         Upside down = 53             Side = 37

If Alfie tosses the paper cup 100 more times what is the expected number of times the cup will land on its side?

Answer:

The expected number of times the cup will land on its side is 25 times

Step-by-step explanation:

Given

[tex]Right = 60[/tex]

[tex]Upside\ down = 53[/tex]

[tex]Side = 37[/tex]

Required

First, we calculate the probability of landing on side

[tex]P(Side) = \frac{n(Side)}{Total}[/tex]

[tex]P(Side) = \frac{37}{150}[/tex]

[tex]P(Side) = 0.247[/tex]

Next, we calculate the expected value; E(x) using:

[tex]E(x) = n * P(x)[/tex]

When tossed 100  more times:

n = 100 and P(x) = P(Side) = 0.247

So:

[tex]E(x) = 100 * 0.247[/tex]

[tex]E(x) = 24.7[/tex]

[tex]E(x) = 25[/tex] --- approximated

Hence, it is expected that it will land on its side 25 times

Answer:

I see nothing tho

Step-by-step explanation:

Answer:

1/3 times 9 so just do that math and there's your answer ;)

Answer: do the math kid 1/3 times 9 theres your answer

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Answer: She had 22 incorrect answers

Step-by-step explanation: You divide 44 by 2.