Carolyn was asked to solve the following system of equations. Her work is shown.




Correctly find the solution to the system of inequalities. Show your work for credit.

Carolyn Was Asked To Solve The Following System Of Equations. Her Work Is Shown.Correctly Find The Solution

Answers

Answer 1

Answer:

(11, 13)

Step-by-step explanation:

Given,

3x - 2y = 7 => (eqn. 1)

y = x + 2 => (eqn. 2)

Substitute y = (x + 2) in eqn. 1.

3x - 2(x + 2) = 7

Use -2 to multiply each term you have in the parentheses. (This is where Carolyn got it wrong)

3x - 2x - 4 = 7 (-2*4 = -4 not +4)

x - 4 = 7

Add 4 to both sides

x = 7 + 4

x = 11

Substitute x = 11 in eqn. 2.

y = x + 2

y = 11 + 2

y = 13

Solution: (11, 13)


Related Questions

Marissa bought 4 cans of corn and 8 cans of green beans for a total of $7.00. Bob bought 8 cans of corn and 7 cans of green beans for a total of $8.60. Determine how much each can green beans cost.

Answers

Step-by-step explanation:

1 can of corn = c

1 can of green beans = b

Marissa-> 4c+8b=7

Bob-> 8c+7b=8.60

form a simultaneous equation:

4c+8b=7

8c+7b=8.60

find a common coefficient, e.g. make the number of cans of corn that Marissa has, equal to the number of cans of corn that Bob has, so you would multiply the top equation by 2, so both people have 8 cans of corn

8c+16b=14

8c+7b=8.60

now you can cancel out the cans of corn, and subtract the second equation from the first one, so you would get:

16b-7b=9b

14-8.60= 5.4

so, 9b=5.4, and b= 0.6

so 1 can of green beans would cost $0.60

what is f(x) = 0,5 (x-3)( x-5) in general form??​

Answers

Answer:

[tex]f(x)=0.5x^2-4x+7.5[/tex]

Step-by-step explanation:

The general form of a quadratic function is:

[tex]y=ax^2+bx+c[/tex]

We'll find the general form of the function:

[tex]f(x)=0.5(x-3)(x-5)[/tex]

Multiplying the expressions in parentheses:

[tex]f(x)=0.5(x^2-5x-3x+15)[/tex]

Simplifying:

[tex]f(x)=0.5(x^2-8x+15)[/tex]

Operating:

[tex]\mathbf{f(x)=0.5x^2-4x+7.5}[/tex]

What is the value of ?

Answers

Answer:

65

Step-by-step explanation:

What is the equation of the line shown in the coordinate plane below?
Identify if the following relations are functions (yes or no)? Identify the domain and range for each.
{(-6, 5), (-4, 3), (-1, 0), (4, 3)}

Answers

Answer:

Step-by-step explanation:

domains:-6,-4,-1,4

Range:5,3,0,3

will you include the image of the line so i can answer the rest of the question?

what is the equation of the line in slope intercept form

Answers

Answer:

y=-3/2+1

Step-by-step explanation:

IM GIVING BRAINLIEST AND 50PTS TO SOMEONE THAT CAN ANSWER THE FOLLOWING QUESTION CORRECTLY
given the following linear function sketch the graph of the function and find the domain and range

f(x) = 2/7x - 2

i am giving brainliest to the first person that answers this and follows all the directions

Answers

Tell us the value of the variable to solve

The graph is attached btw

Answer:

Bet.

Step-by-step explanation:

(5i-3)(9i+1)
Answer must be in standard form

Answers

Answer:

-48-22i

Step-by-step explanation:

How would I create a graph for this equation? The equation is c=4.95+3.99b

Answers

Answer:

C is your y intercept 3.99b is your slope

Step-by-step explanation:

You are given the following sequences: Sequence A: 5, 11, 17, 23... Sequence B: 4000, 1000, 250, 62.5... Part A: Determine whether each sequence is arithmetic, geometric (2 pts) Part B: Write an explicit formula for each sequence (6 pts) Part C: Find the 6th term of each sequence (2 pts)

Answers

Answer:

I believe the first is arithmetic because it has a difference Of 6 between each number. The second is geometric because each number is divided by 4 to get the next number

Step-by-step explanation:

5, 11, 17, 23, 29, 35. (Difference of 6)

4000, 1000, 250, 62.5, 15.62, 3.90 (divide by 4)

As for the formulas I’m not sure, but I I would guess something like

an=6n-1

an=n/4

I am not sure about the formulas though

What is -19 equal to

Answers

Answer:

-19

Step-by-step explanation:

I need help plz answer this

Answers

Answer: A. (5)(5x+2y)

Step-by-step explanation:

I NEED HELP ON THIS TOOO!!! IMPORTANT!!!! EMERGENCY!!!!!

Answers

Answer:

$ 2188

Step-by-step explanation:

12.5%*17500=(12.5/100)*17500=12.5*175=2188

i need help with the group 1 and group 2, what do i write in the boxes :((

Answers

I don’t see anything it’s a black screen

The volume of a solid cube is 1700m3.
Work out the surface area.
Give your answer rounded to 1 DP.

Answers

Answer:

849.7m2

Step-by-step explanation:

L= length

SA = surface area

volume = L x L x L

1700= L x L x L

find cube root

=11.93m

round off to 1 dp

=11.9m

SA= 6( L x L)

     = 6( 11.9 x 11.9)

       =6(141.61)

       =849.66m2

round off to 1 dp

=849.7m2

-6 5 4 3 2 1
1 2 3 4 5 6
1
1-2
-3
Water Slide
Restrooms
-5

Answers

Answer:

I am sorry what are you showing

What is the factored form of the expression 24x + 64y?

Answers

Answer:

8(3x+8y)

Step-by-step explanation:

Answer:

24x + 64y

Step-by-step explanation:

6 divided by 2/3 = tell me thee answer in fraction form

Answers

Answer:

There wouldn't be a fraction form because its a whole number which is 9

Solve 3x2 + 4x = 2. ??​

Answers

Answer: Answer: The answer should be x = -1. Hope this helps!

A.
B.
C.
D.

Help me please!!

Answers

It's B!!!           ik cuz i ggogled it lol

Answer:

I think the answer is B. $92

Step-by-step explanation:

$80 time (115 on calculator will give you 9200

what is the value of x?

Answers

Answer:

I honestly have no clue.

Step-by-step explanation:

I honestly have no clue.

A business recently upgraded a conference TV they had in their conference room. Originally the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches. The new TV is 70 inches across the diagonal. Since the new TV will be recessed in the wall, it will need trim put on the border. What is the perimeter of the new TV? Round your answer to two decimal places.

Answers

Answer:

The perimeter of the new TV is approximately  95.32 inches

Step-by-step explanation:

The diagonal dimension of the original TV = 32 inches

The perimeter of the original TV = 87.16 inches

The diagonal dimension of the new TV = 70 inches

The perimeter of the new TV = 87.16 inches

For the original TV, we have;

Let w be the width of the original TV and l be the length of the original TV, we have;

2·w + 2·l = 87.16

√(w² + l²) = 32

Therefore, we have;

32² = w² + l²

w = (87.16 - 2·l)/2

w = 43.58 - l

32² = l² + (43.58 - l)²

l² + (43.58 - l)² - 32² = 0

l² + 43.58² - 2 × 43.85 × l + l² - 32² = 0

2·l² - 87.16·l + 875.2164 = 0

By the quadratic formula, we have;

l = (87.16 ± √((-87.16)² - 4×2 × 875.2164))/(2 × 2)

Therefore, l = 27.89 inches or l = 15.69

Therefore, w = (87.16 - 2·l)/2 = (87.16 - 2× 27.89)/2 = 15.69

or w = (87.16 - 2× 15.69)/2 = 27.89

Whereby the ratio of the width to the length of the original TV and the new TV are the same, we have;

15.69/27.89

w₂/l₂ for the new TV = 15.69/27.89

∴ w₂ = l₂ × 15.69/27.89

w₂² + l₂² = 70²

∴ (l₂ × 15.69/27.89)² + l₂² = 70²

l₂² × (15.69/27.89)² + l₂² = 70²

l₂²((15.69/27.89)² + 1) = 70²

l₂² = 70²/((15.69/27.89)² + 1) = 3722.04

l₂ = √(3722.04) ≈ 61.0

w₂ = l₂ × 15.69/27.89 = 61 × 15.69/27.89 ≈ 34.32

Therefore;

The perimeter of the new TV = 34.32 + 61 = 95.32 inches.

In this exercise we have to use the knowledge and information given to calculate the perimeter that will correspond to:

The perimeter of the new TV is approximately  95.32 inches

So the data for this exercise is from:

The diagonal dimension of the original TV = 32 inches The perimeter of the original TV = 87.16 inches The diagonal dimension of the new TV = 70 inches The perimeter of the new TV = 87.16 inches

Let w be the width of the original TV and l be the length of the original TV, we have;

[tex]2*(w) + 2*(l) = 87.16\\\sqrt{(w^2 + l^2)} = 32[/tex]

Therefore, we have:

[tex]32^2 = w^2 + l^2\\w = (87.16 - 2*l)/2\\w = 43.58 - l\\32^2 = l^2 + (43.58 - l)^2\\l^2 + (43.58 - l)^2 - 32^2 = 0\\l^2 + 43.58^2 - (2 * 43.85 * l)+ l^2 - 32^2 = 0\\(2)*(l)^2 - 87.16*l + 875.2164 = 0[/tex]

By the quadratic formula, we have;

[tex]l = (87.16 +/- \sqrt{((-87.16)^2 - 4*2 * 875.2164))/(2 * 2)} )[/tex]

Therefore:

[tex]w = (87.16 - (2)*(l))/2 = (87.16 - 2* 27.89)/2 = 15.69\\w = (87.16 - 2* 15.69)/2 = 27.89[/tex]

Whereby the ratio of the width to the length of the original TV and the new TV are the same, we have;

w₂/l₂ for the new TV = [tex]15.69/27.89[/tex]

[tex]w_2 = (l_2)* (15.69/27.89)\\w_2^2 + l_2^2 = 70^2\\(l_2 *15.69/27.89)^2 + l^2_2 = 70^2\\l^2_2 * (15.69/27.89)^2 + l^2_2 = 70^2\\l^2_2((15.69/27.89)^2 + 1) = 70^2\\l^2_2 = 70^2/((15.69/27.89)^2 + 1) = 3722.04\\l_2 = \sqrt{(3722.04)} = 61.0\\w_2= l_2 * 15.69/27.89 = 61 * 15.69/27.89 = 34.32\\[/tex]  

The perimeter of the new TV :

[tex]P = 34.32 + 61 = 95.32[/tex]

See more about perimeter at brainly.com/question/6465134

Ok now these are my very last points please help

Answers

Answer:

wait what grade are you in ?

what is the value of x that satisfies the following equation
1 over 3 ( x - 9) = 2 over 3 (2x + 6)​

Answers

Answer:

x=-7

Step-by-step explanation:

BRAINLIEST PLS

Fill in the blank so that the relation is NOT A FUNCTION. Type a number only in the blank. The blank represents the x-value of the last ordered pair. {(4.5),(0, -1), (-7,0). (-3,8). ( type your answer .. -1)​

Answers

Can you provide a photo question ?

on saturday keisha ran 2.175 kilometers. on sunday she ran 1.88 kilometers. how much farther did she run on saturday than on sunday?
Pls help fast I don't know what to do

Answers

Answer:

0.295

Step-by-step explanation:

you needed to subtract 2.175-1.88=0.295

Keesha will mow grass for $8 per hour write in standard form

Answers

Answer: y = 8x

Step-by-step explanation:

Evaluate the expression for 1/2(2x+8)+6x and explain your process

Answers

Answer:

7x+4

Step-by-step explanation:

1/2(2x+8)

=x+4

x+4+6x

=7x+4

PLS GIVE BRAINLIEST

Answer:

7x+4

Step-by-step explanation:

1/2(2x+8)+6x

divide by 2 or multiply 1/2 it equals the same anyway

x+4+6x

add like terms

7x+4

I am doing a science project and need a fun or short title. The project is on whether filtered water affects plant growth. Any creative title ideas?

Answers

Answer: Water: The battle between the clean vs the dirty :P

Step-by-step explanation:

The sum of four times a number and negative three is twelve. What is the number?

2 1/4
3 3/4
-2 1/4
6

Answers

The second one because, 3 3/4 x 4 equals 15 which is the sum of 3 3/4 x 4, minus 3 equals 12.

Answer:

Dgfyb

Step-by-step explanation:

The difference between two same side interior angles of two parallel lines is 35 degrees. Find the measures of these two angles.

Answers

Answer:

  107.5° and 72.5°

Step-by-step explanation:

  x + y = 180          same side interior angles of two parallel lines add up to 180

  x - y = 35            

___________

     2x = 215                           add above two equations

       x = 107.5°                       divide by 2 to isolate x

Substitution to find y:

  x + y = 180

  107.5 + y = 180

              y = 72.5°

The measure of these two angles is 107.5° and 72.5°.

Given that,

The difference between two same-side interior angles of two parallel lines is 35 degrees.We need to find the measure of the two angles. Here we assume the two angles be x and y.

Based on the above information, the calculation is as follows:

x + y = 180          

And,

x - y = 35            

So, after solving it, it comes

2x = 215                            

x = 107.5°                  

So, y = 180 - 107.50 = 72.5

Therefore we can conclude that the measure of these two angles is 107.5° and 72.5°.

Learn more: brainly.com/question/13549064

Therefore we can conclude that

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