Use the graph to find estimates for the solutions of
[tex]3x {}^{2} - 3x - 1 = x + 1[/tex]

Use The Graph To Find Estimates For The Solutions Of [tex]3x {}^{2} - 3x - 1 = X + 1[/tex]

Answers

Answer 1

Answer:

x = - 0.25, x = 1.25

Step-by-step explanation:

The solutions to the equation are the values of x where the graph crosses the x- axis, that is as an estimate

x ≈ - 0.25 and x ≈ 1.25

Answer 2

Answer:

[tex]x=-0.4[/tex]

[tex]x=1.7[/tex]

Hopefully the answers are accepted to the nearest tenths.

Step-by-step explanation:

Since the left hand side was already graphed, we just need to graph the right hand side which is [tex]x+1[/tex].

We are going to still let [tex]y[/tex] represent the outputs of [tex]x+1[/tex].

So we want to graph the equation [tex]y=x+1[/tex] on the same graph as the parabola, the almost U shaped graph.

You could make a table to plot the equation.

[tex]y=x+1[/tex]

[tex]x[/tex]     |      [tex]y[/tex]         |     ordered pair to graph [tex](x,y)[/tex]

-------------------------------------------------------------------------------------------------------

     -2                     -2+1=-1                          (-2,-1)

     -1                       -1+1=0                           (-1,0)

      0                       0+1=1                            (0,1)

      1                         1+1=2                           (1,2)

      2                        2+1=3                          (2,3)

The purple line I made is the line formed from these points which was generated from the equation [tex]y=x+1[/tex].

Now where the blue curve touches the purple line is our solutions. I put those in orange.

The solutions are approximately, [tex]x=-0.4[/tex] or [tex]x=1.7[/tex].

Hopefully, it accepts solutions to the nearest tenths.

We are trying to approximate where those orange dots are on the number line. Please see attachment 2.      

Use The Graph To Find Estimates For The Solutions Of [tex]3x {}^{2} - 3x - 1 = X + 1[/tex]
Use The Graph To Find Estimates For The Solutions Of [tex]3x {}^{2} - 3x - 1 = X + 1[/tex]

Related Questions

In which quadrant or on which axis would you find the point B(-8,0)?

Answers

Answer:

The x-axis, it would be between quadrant 2 and quadrant 3

Trevor Has $178 in his bank account at the start of the week. He makes one withdrawal during the week. At the end of the week, Trevor Gets a notice from the bank that he has a negative balance of -$62. Write and solve an equation to determine how much money Trevor Took out in his withdrawal.

the answer that is correct and shows work gets the crown! good luck and happy new year!

Answers

Answer:

Equation: 178 - x = - 62

Explanation:

Start of the wee: 178

One withdrawal: x

End of the week: -62

178 - x = -62

Simplify both sides of equation

178−x=−62

178+−x=−62

−x+178=−62

Subtract 178 from both sides

−x+178−178=−62−178

−x=−240

Divide both sides by -1

-x / -1 = -240 / -1

x=240

Trevor withdrew $240 from his bank account. This was calculated by setting up an equation with his initial positive balance and final negative balance, and solving for the withdrawal amount.

To determine how much money Trevor withdrew from his bank account, we can set up an equation representing the transactions in his account. Let x represent the amount of money withdrawn. We start with Trevor's initial balance, subtract the withdrawal, and set that equal to his final negative balance:

Initial balance - Withdrawal = Final balance

178 - x = -62

To solve for x, we add x to both sides to get the withdrawal amount on its own and then add 62 to both sides to isolate x:

178 - x + x = -62 + x

178 = x - 62

178 + 62 = x

240 = x

So, Trevor withdrew $240 from his bank account.

when is the following rational expression undefined? 6d-4
-------
d+2

Answers

Answer:

For [tex]d=-2[/tex] rational expression will be undefined.

Step-by-step explanation:

Given function is [tex]\frac{6d-4}{d+2}[/tex]

We need to find for what value of variable [tex]d[/tex] this rational expression will be undefined.

The rational expression will be undefined if the denominator of the expression will become zero.

So, let us plug denominator equal to zero.

[tex]d+2=0\\\\Subtracting\ both\ side\ 2\\\\d+2-2=-2\\\\d=-2[/tex]

Hence, this rational expression will be undefined if the value of variable [tex]d=-2[/tex].

can you help find the quotient for 4/5 ÷ 10

Answers

Answer:

2/25

Step-by-step explanation:

Answer:

0.08

Step-by-step explanation:

In which of the following functions would it be appropiate to use only positve integers for the domain?Select all that apply.

Answers

Complete Question:

As you may have unintentionally forgotten to add the answer choices in your question, but I was able to find the complete the question and answering your question based on this as it may surely clear your concepts. Here is the complete question.

In which of the following functions would it be appropriate to use only positive integers for the domain? Select all that apply.

The function c(p) represents The cost for P people to attend the movies. The function m(t) represents the miles driven over T hours. The function t(m) represents the average high temperature for a given number of months. The function p(w) represents the prophet of a farmer who sells whole watermelons. The function h(n) represents the number of person-hours it takes to assemble n engines in a factory.

Answer Explanation:

Domain is termed as all the input values on a certain interval that define the function.

Here are the appropriate function scenarios where it is appropriate to use only positive integers.

The function c(p) represents The cost for P people to attend the movies.

As the function c(p) contains people. And People are not counted as negative, although they can be zero. So, only positive integers should be appropriate to use in this scenario.

The function m(t) represents the miles driven over T hours

As the function m(t) contains miles. And miles are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.

The function t(m) represents the average high temperature for a given number of months.

As the function t(m) contains months. And months are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.

The function p(w) represents the prophet of a farmer who sells whole watermelons.

As the function p(w) contains the number of watermelons. And watermelons are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.

The function h(n) represents the number of person-hours it takes to assemble n engines in a factory.

As the function h(n) contains the number of engines. And engines are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.

Keywords: domain, function, positive integer

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Triangles ABC and DEF are similar.
I added in a photo...
Part 1: Find the lenght of segment DF (rounded to the nearest hundreth) _____ units.
Part 2: Find the lenght of segment EF (rounded to the nearest hundreth) _____units.

Answers

All I can really remember is find the scale factor and divide it by the segment

y=6x-7 and find the x intercept

Answers

Answer:

x-intercept

= 7/6

= 1.16667

A music player was marked down by 1/4 of the original price.
a. If the sales price is $128, what is the original price?
b. If the music player was marked up by 1/2 before it was placed on the sales floor, what was the price that the store paid for the player?
c. What is the difference between the discount price and the price that the store paid for the music player?

PLEASE SHOW ALL OF YOUR WORK! I NEED THIS ASAP! I WILL GIVE YOU BRAINLIEST! IF YOU SEND ME NONSENSE OR ANSWERS WITH NO WORK, I WILL REPORT YOU!!!! HAPPY NEW YEAR!!!!!!!!!!!

Answers

Answer:

A ) The Original price of music player before it was marked down by  [tex]\dfrac{1}{4}[/tex]  is $512

B ) The price that store paid for player is $256

C ) The difference between discount price and price paid by store is $128

Step-by-step explanation:

Given as :

A ) The sale price of music player = $128

The music player is marked down by [tex]\dfrac{1}{4}[/tex] of original price

Let The original price = $x

Now, According to question

[tex]\dfrac{1}{4}[/tex] of original price = $128

i.e [tex]\dfrac{1}{4}[/tex] × $x = $128

Or, x = 128 × 4

∴ x = $512

So, The Original price of music player before it was marked down by  [tex]\dfrac{1}{4}[/tex]  is $512

B ) The music player is marked up by [tex]\dfrac{1}{2}[/tex] before it was placed on sales floor .

Let The price that store paid for player = $y

Now, According to question

∵ The original price of player = $512

So, The price that store paid for player = [tex]\dfrac{1}{2}[/tex]  × original price of player

i.e y =  [tex]\dfrac{1}{2}[/tex]  × $512

Or , y = $256

So,The price that store paid for player = $256

C ) Let The difference between discount price and price paid by store = $z

So, According to question

z = y - discount price

Or , z = $256 - $128

∴  z = $128

So, The difference = $128

Hence, A ) The Original price of music player before it was marked down by  [tex]\dfrac{1}{4}[/tex]  is $512

B ) The price that store paid for player is $256

C ) The difference between discount price and price paid by store is $128

Answer

Use Order of Operations. (2/5 x 30) x 6 to the second power - 3 to the second power​

Answers

Answer:

Step-by-step explanation:

(2/5 * 30) * 6^2 - 3^2           Reduce 2/5 * 30

180 * 6^2 - 3^2                    Raise the bases of the power

180 *36 - 9                           Multiply 36 and 180

6480 - 9                               Subtract 9

6471

Please Help!!!! Give me your own real life scenarion using an inequality thanks so much :)

Answers

Scenario:

Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Write an inequality that would be used to solve for the least amount of money he needs to deposit to avoid a fee.

Equation:

727.29 − 248.50 + x ≥ 500

Answer:

x  ≥  21.21

if 3 popsicles cost $5.25. at this rate how much would 1 popsicle cost?

Answers

If 3 popsicles cost $5.25, 1 popsicle would cost $1.75. To find the unit rate/cost of 1 popsicle, you divide $5.25 by 3 and you get $1.75 per popsicle.

the local music activities coordinator sold 300 tickets to the orchestra concert. student tickets were $4 and the adult tickets were $6 if the total sales were $1600 how many student tickets were sold

Answers

There were 100 student tickets sold

Step-by-step explanation:

The given is:

The local music activities coordinator sold 300 tickets to the orchestra concertStudent tickets were $4The adult tickets were $6The total sales were $1600

We need to find how many student tickets were sold

Assume that the number of student tickets is x and the number of adult tickets is y

∵ The number of student tickets is x

∵ The number of adult tickets is y

∵ They sold 300 tickets

x + y = 300 ⇒ (1)

∵ The price of the student ticket = $4

∵ The price of the adult ticket = $6

∵ The total sales = $1600

- Add the prices of the students tickets and the adult tickets

  and equate the sum by the total sales

4x + 6y = 1600 ⇒ (2)

Now we have a system of equation to solve it

Multiply equation (1) by -6 to eliminate y

-6x - 6y = -1800 ⇒ (3)

- Add equations (2) and (3)

∴ -2x = -200

- Divide both sides by -2

x = 100

There were 100 student tickets sold

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What is 6 to the power of “h” equal to 126

Answers

Answer:

6^h=126

Step-by-step explanation:

6 to the power of h is just 6^h

Plug it into an equation with =126

Boom you have the equation 6^h=126

if an=5n-3 find the common difference​

Answers

Answer:

d = 5

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a₂ - a₁ = a₃ - a₂ = [tex]a_{n}[/tex] - [tex]a_{n-1}[/tex]

Given

[tex]a_{n}[/tex] = 5n - 3

Generate the first 2 terms of the sequence by substituting n = 1, n = 2

a₁ = 5(1) - 3 = 5 - 3 = 2

a₂ = 5(2) - 3 = 10 - 3 = 7

d = 7 - 2 = 5

Which coordinate grid shows Point A at (0.75, −1.50)?

Answers

Answer:

Very bottom graph

Step-by-step explanation:

Go .75 units right (positive x) then go 1.5 units down (negative y)

Answer:

Your answer will be D.

Step-by-step explanation:

Coordinate grid shown from negative 2 to positive 2 on the x-axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 3 grid lines to the right of the y-axis and 6 grid lines below the x-axis.

Tammi deposited $520 into a bank account that earned simple interest each year. After 5 years, she had earned $156 in interest.

If no money was deposited into or withdrawn from the account, what was the annual interest rate?

Enter your answer in the box.

% / new questoin Gloria deposited $500 into a bank account that earned 7.5% simple interest each year. She earned $225 in interest before closing the account.

If no money was deposited into or withdrawn from the account, for how many years was the money in the account?

Round your answer to the nearest whole year.

Enter your answer in the box.

years

Answers

Answer:

For Tammi it is 6% interest Rate.

For Gloria it is 6 Years.

Step-by-step explanation:

Tammi:

Principal = $520

Time = 5 Years

Interest = $156

Interest Rate = Interest / (Principal x Time)

Interest Rate = $156 / ($520 x 5)

Interest Rate = $156 / $2,600

Interest Rate = 0.06

Hence Interest Rate is 6%

Gloria:

Principal = $500

Interest Rate = 7.5%

Interest = $225

Time = Interest / (Principal x Interest Rate)

Time = $225 / ($500 x 0.075)

Time = $225 / $37.5

Time = 6 Years

Hence it will take 6 Years

Answer:

6%

Step-by-step explanation:

We did percent and converting problems in class and we've been doing it since yesterday.

I hope this helps!

3k-k+5k-7=7 solve for k

Answers

Answer:

k=2

Step-by-step explanation:

3k-k+5k-7=7

2k+5k=7+7

7k=14

k=14/7

k=2

Answer:

[tex] \: \: \: \: \: \: \: \: 3k - k + 5k - 7 = 7 \\ = > 8k - k = 7 + 7 \\ = > 7k = 14 \\ = > k = \frac{14}{7} \\ = > k = 2[/tex]

A.
discrete

B.
continuous

C.
linear

D.
nonlinear

E.
increasing

F.
decreasing

G.
both increasing and decreasing

H.
neither increasing nor decreasing

Answers

Answer(s): C (linear) and E (increasing)

E) This graph is positive, meaning that the values are increasing

C) this line is straight, and passes the vertical line test

Hope this helps comment below for more questions :)
linear, increasing, and continuous. it is continuous because it is linear, it is a straight line with no definite end. and it obviously is moving in the positive direction, so it is increasing

Which has the greatest value?

Answers

Answer:

f(6)

Step-by-step explanation:

Answer:

f(2)

Step-by-step explanation:

Karen bought a hat for $15.62,$15.62, which was 22%22% of her money. How much money did Karen have to start?

1) $71.00
2) $710.00
3) $343.64
4) $140.85

Answers

Option 1: $71.00 is the correct answer

Step-by-step explanation:

Let x be the money Karen started with:

Then

22% of x is $15.62

Mathematically writing

[tex]15.62 = 22\%\ of\ x\\15.62 = 0.22 * x\\x = \frac{15.62}{0.22}\\x = 71[/tex]

Hence,

Karen had $71.00 to start.

Option 1: $71.00 is the correct answer

Keywords: Percentage, percent

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Find the distance from the point (-6,8) to the line y=-3x+10. Round distance to nearest hundredths.

Answers

Final answer:

The distance from the point (-6,8) to the line y=-3x+10 is calculated using the distance formula which yields a value of approximately 6.32, when rounded to the nearest hundredths.

Explanation:

The subject of this question is mathematics, specifically it pertains to finding the distance between a point and a line. The distance between a point (x1, y1) and a line ax + by + c = 0 can be calculated using the formula: distance = |ax1 + by1 + c|/sqrt(a²+b²). In your case, the given point is (-6,8) and the line is y = -3x + 10, which can be rewritten as 3x + y - 10 = 0. Therefore, a = 3, b = 1, c = -10, x1 = -6, and y1 = 8.

Substituting these values into the distance formula: distance = |3*(-6) + 1*(8) - 10|/sqrt((3)² + (1)²) = |-18 + 8 - 10|/sqrt(10) = |-20|/sqrt(10) = 20/sqrt(10) = 6.32, rounded to the nearest hundredths.

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1. Simplify f(g(x)) in terms of x if f(x) = x² - 1 and g(x) = 2 x + 3.​

Answers

In this question, you're plugging in g(x) into f(x) to simplify.

You would plug the g(x) equation into the x variable in the f(x) equation.

Plug g(x) into f(x):

(2x+3)² - 1

Solve:

(2x+3)² - 1

Use FOIL:

F = First

O = Outsides

I = Insides

L = Last

4x² + 12x + 9 - 1

Combine like terms:

4x² + 12x + 8

Answer:

4x² + 12x + 8

B Jamal says that 18:12 and 3:4 are not equivalent ratios Margie says they are equivalent ratios who is correct

Answers

Answer:

Jamal  is correct.

Step-by-step explanation:

3:4 is equivalent to 9:12, not 18:12.

We can see that for 3:4, the left side is less than the right, but for 18:12, left side is greater than the right, which immediately tells us the ratios are not equivalent.

Jamal is correct. 18:12 and 3:4 are not equivalent ratios.

Equivalent ratios

To determine if two ratios are equivalent, you can simplify them to their simplest form or find a common factor that divides both terms. In this case:

18:12 can be simplified by dividing both terms by their greatest common factor, which is 6:

18 ÷ 6 = 3

12 ÷ 6 = 2

So, 18:12 simplifies to 3:2.

Now, compare it to 3:4. Since they have different values (3:2 vs. 3:4), Jamal's statement is incorrect, and Margie is right; they are not equivalent ratios.

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A sandbox has an area of 26 square feet . The length is 6 1/2 feet. What is the width of the sandbox

Answers

If the sandbox is a square then it would be 26/6.5 and that would equal 4 meaning all the sides are the same length

Answer:

The width of the sandbox is 4 feet

Step-by-step explanation:

Area = Length x Width

Fill in known values

26 sq ft = 6.5 ft x w

Divide by 6.5 on both sides

4 ft = w

Width = 4 ft

:)

identify the vertex for
f(x)=4x^2-8x-4

Answers

Answer:

Step-by-step explanation:

You could complete the square to do this, or you could just evaluate the h coordinate using the simple formula

[tex]h=-\frac{b}{2a}[/tex]

then find k by subbing that h value into the equation for x to find y which is the same as k.  In our quadratic, a = 4, b = -8, and c = -4.

[tex]h=\frac{-(-8)}{2(4)}=1[/tex]

Now sub that value into the quadratic to find y (k):

[tex]4(1)^2-8(1)-4=4-8-4=-8[/tex]

The vertex of the quadratic is (1, -8)

A set is _____ under an operation (such as addition, etc) if any elements of that set always generate element IN set, when the operation is performed on them help need this answer now

Answers

Answer:

Closed.

Step-by-step explanation:

2m- -3m + -15 =20 solve for m

Answers

Answer:

m=7

Step-by-step explanation:

2m-(-3m)+(-15)=20

2m+3m-15=20

5m-15=20

5m=20+15

5m=35

m=35/5

m=7

Sharon purchased a used car for $24,600. The car depreciates exponentially by 8% per
much will the car be worth after 5 years? Round your answer to the nearest penny.

Answers

Answer:

The value of car after 5 years of exponentially depreciation is $16,213.36  

Step-by-step explanation:

The initial amount of the car = i = $24,600

The depreciates rate of interest applied = r = 8%

Let The value of car after n years = A  

The number of years = n = 5 years

Now,According to question

The value of car after n years = initial price of car  × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The value of car after 5 years = i × [tex](1-\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or, $A = $24,600 × [tex](1-\dfrac{\textrm 8}{100})^{\textrm 5}[/tex]

Or, $A = $24,600 × [tex](0.92)^{5}[/tex]

Or, $A = $24,600 × 0.65908

Or, $A = $16,213.36

So, The value of car after 5 years = A = $16,213.36

Hence , The value of car after 5 years of exponentially depreciation is $16,213.36  . Answer

If (3, 5) is a solution of both y= 4x + 7 and y=5, what is the solution of 4x + 7=5?

Answers

Answer:

Step-by-step explanation:

X=-1/2

Hope this helps mark me as brainiest pls

Yes, -1/2 will be the x-coordinate for the solution. We can also find the y-coordinate by subbing in -1/2 for x in the equation y=4x+7.

y=4(-1/2)+7

y=-2+7

y=5

The intersection point would be (-1/2,5).

A survey was given to residents of all 50 states asking
if they had earned a bachelor's degree or higher
The results from 7 of the states are given in the table
above. The median percent of residents who earned
a bachelor's degree or higher for all 50 states was
26.95%. What is the difference between the median
percent of residents who carned a bachelor's degree
or higher for these 7 states and the median for al
50 states!​

Answers

Answer:

B.) 0.95%

Step-by-step explanation:

19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4

27.9 − 26.95 = 0.95

The difference is 0.95%

How to find the difference

The data is given as 19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4

Organize the Data:

Arrange the percentages in ascending order:

19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4

Find the Median of the 7 States:

Since there are 7 data points, the median will be the 4th value.

Median = 27.9

Calculate the Median for All 50 States:

The median for all 50 states is given as 26.95%.

Find the Difference:

Difference = Median for all 50 states - Median for 7 states

Difference = 26.95 - 27.9

Difference = 0.95

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What was the containment policy A woman at 36 weeks gestation is admitted to the hospital to receive a tocolytic medication in an attempt to stop labor. In addition, betamethasone (Celestone) is prescribed to enhance fetal lung maturity. The prescription reads: administer betamethasone 12 my IM daily for 3 days. The betamethasone comes in a vial labeled 6mg/mL. How many millimeters should the nurse administer each day? How many years didn take the United States to become involved in World War 112TwoFourThey never comes to the war, they only supplied money and weapons. you want to limit the amount of television you watch to an average of at most two hours per week do an eight week. How many hours acts of television must you watch in the eighth week to meet your goal. PLEASE SHOW YOUR WORK According to an international poll, the man thing that makes adolescents feel loved is having parents who:______ a. tell them daily that they love them. b. trust them. c. make sacrifices for them. d. use an authoritative parenting style. The temperature inside a vehicle can rise ____ degrees higher than the outside temperature. A small ball weighs 1.4 N.gravitational field strength, g = 9.8 N / kgCalculate the mass of the ball. Which plot element refers to previous events and leads to the storys ending?expositionrising actionclimaxfalling action What is the probability that a registered voter voted in the election? in th fig , d is the mid point of ab and cd is perpendicular to ab. prove abc is congurence to bcd. If a restriction enzyme has as its recognition sequence "ATCCTA," how many restriction sites would appear in the lambda genome, which is approximately 54,000 bp? For a large batch of cupcakes, the robots use 1/5 of a gallon of milk. They pour it into two separate cups , each the same size. How much milk goes into each measuring cup? Judy reminisces about when her children were young. She reveals to her daughter that she often felt tired and discouraged during those times. Seeing her children as parents helps Judy realize that she was and is a good mother. This is an example of:A. possible selfB. self-esteemC. life reviewD. the fluctuating self Oklahoma taxes which of the following goods that most other states with sales tax do not?electronics food clothing cars Why,in your opinion, is Celia happy to see Minny each day There are 20 cars in my building's parking lot. All of the cars are red or white. Also, all the cars are either 2-door or 4-door. 12 of them are red, 15 of them are 4-door, and 4 of them are 2-door and white. How many of the cars are 4-door and red? If output is above its natural rate, then according to sticky-wage theory a. workers and firms will strike bargains for higher wages. This increase in wages shifts the short-run aggregate supply curve right. b. workers and firms will strike bargains for higher wages. This increase in wages shifts the short-run aggregate supply curve left. c. workers and firms will strike bargains for lower wages. This decrease in wages shifts the short-run aggregate supply curve right. d. workers and firms will strike bargains for lower wages. This decrease in wages shifts the short-run aggregate supply cur Question 1 with 1 blank os conductores son lentos. Conducen . Unattempted Question 2 with 1 blankEsa doctora es amable. Siempre nos saluda . UnattemptedQuestion 3 with 1 blankLos autobuses de mi ciudad son frecuentes. Pasan por la parada . UnattemptedQuestion 4 with 1 blankRosa y Julia son chicas muy alegres. Les encanta bailar y cantar . UnattemptedQuestion 5 with 1 blankMario y t hablan un espaol perfecto. Hablan espaol . UnattemptedQuestion 6 with 1 blankLos pacientes visitan al doctor de manera constante. Lo visitan . UnattemptedQuestion 7 with 1 blankLlegar tarde es normal para David. Llega tarde . UnattemptedQuestion 8 with 1 blankMe gusta trabajar de manera independiente. Trabajo If a reflection takes triangle CAT to C'A'T', what is A'C'?triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of 3 units, side TC has a measure of 4 units, and side AC has a measure of 5 units 3 4 5 Cannot be determined The idea that the relationship between a worker and employer is voluntary and can be terminated at any time, by either party, is the" employment-at-will doctrine. due process principle. corporate governance system. arbitrary employment doctrine. Steam Workshop Downloader