MATHEMATICS HIGH SCHOOL

Choose the graph of 3x + y = –2.

Answers

Answer 1

Answer:

Answer:

Option (d) is correct.

Step-by-step explanation:

Given : Equation of line 3x + y = -2

We have to choose the correct graph for the given equation of line 3x + y = -2

Consider the given equation of line 3x + y = -2

We find the points that satisfies the equation of line and plot these to find the equation of line.

Put y = 1

We get

3x + 1 = -2

3x = -2 -1 = -3

x = -1

also, put y = 4

We get

3x + 4 = -2

3x = -2 -4 = - 6

x = - 2

also, when x = 0 , we get, y = -2

We get three points (-1, 1), (0,-2) and (-2, 4)

Now plot these point to obtain graph as shown below.

Related Questions

100 points!!!! and brainliest!!!!You keep track of the daily hot chocolate sales and the outside temperature each day. The data you gathered is shown in the data table below.Hot Chocolate Sales and Outside TemperaturesSales ($)$100$213$830$679$209$189$1,110$456$422$235$199Temperature (°F)92°88°54°62°85°16°52°65°68°89°91°a) Make a scatterplot of the data above. b) Do you notice clusters or outliers in the data? Explain your reasoning. c) How would you describe the correlation in the data? Explain your reasoning.d) What are the independent and dependent variables? Step 2: Evaluating trends of dataBecause you want to prepare and serve the healthiest food possible, you monitor the fat and calorie content of items on your menu. Some of the menu items are included in the graph below.a) Your business partner describes this as a high positive correlation. Is your partner correct? Why or why notb) Using the drawing tools, draw a trend line (line of best fit) on the graph above. c) Judge the closeness of your trend line to the data points. Do you notice a relationship between the data points? d) Is the trend line linear? If so, write a linear equation that represents the trend line. Show your work. Step 3: Making predictions using dataYou and your business partner track the number of customers served and the amount of tips collected per day. The data you gathered is displayed in the chart below.Servers’ Collected TipsCustomers544634675222496455803842Tips ($)$92$80$76$121$109$43$87$114$99$174$88$91a) Create a scatterplot displaying the data in the table. Be sure to include a linear trend line. b) Find the equation of the trend line (line of best fit). Show your work. c) Predict the amount of tips that would be collected if 100 customers were served at the restaurant on a given day. d) Explain how to use the regression calculator to make a reasonable prediction given a data table.
Ann is buying a house that costs $250,000. She is making a down payment of 15 percent, and her closing costs will amount to 3 percent. Over the life of her loan, she will pay $282,089.89 in monthly payments. What is the total cost of her house?
Caroline bought 20 shares of stock at 101/2, and after 10 months the value of the stocks was 111/4. If Caroline were to sell all her shares of this stock, how much profit would she make? A. $10 B. $15 C. $225 D. $210
Solve the inequality. 4(x – 3) – 2x ≥ 5 – (x + 2)
A veterinarian is interested in the average number of pets her clients own. Over the course of a month, she questions each client she meets with and records their responses. The veterinarian calculates the average and draws a conclusion from her data.What kind of statistical study did the veterinarian conduct?A. theoretical studyB. surveyC. experimentD. observational study

Pex Algebra PLS HELP

simplify 3^5 x 3^4

Answers

3 x 3 x 3 x 3 x 3 = 243
3 x 3 x 3 x 3 = 81
243 x 81 = 19,683
You are welcome

Solve-picture question

Answers

The answer is 1/3. Basically start at A, you go up one. Then count over to B and it's 3 spaces over, so you get 1/3.

it's D 1/3 cause your going up 1 and over 3 so that should give you a positive cause the line is going up instead of down . now on the other hand if the line was going down it would me -1/3 cause went down one and over negative three, but in ur case it's ↓

D.) 1/3

-Hope this helped you im 100% sure this is right . :)

Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions.When f(x) becomes f(x) − 3
When f(x) becomes −2 ⋅ f(x)

Answers

First of all, let's review the definition of some concepts.

Even and odd functions:

A function is said to be even if its graph is symmetric with respect to the $y-axis$ , that is:

$y=f(x) \ is \ \mathbf{even} \ if, \ for \ each \ x \ in \ the \ domain \ of \ f, \n f(-x)=f(x)$

On the other hand, a function is said to be odd if its graph is symmetric with respect to the origin, that is:

$y=f(x) \ is \ \mathbf{odd} \ if, \ for \ each \ x \ in \ the \ domain \ of \ f, \n f(-x)=-f(x)$

Analyzing each question for each type of functions using examples of polynomial functions. Thus:

FOR EVEN FUNCTIONS:

1. When $f(x)$ becomes $f(x)-3$

1.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function $f(x)$ into:

$f(x)-3$

We know that the graph $f(x)$ intersects the y-axis when $x=0$ , therefore:

$y=f(0) \ is \ the \ y-intercept \ of \ f$

So:

$y=f(0)-3 \ is \ the \ new \ y-intercept$

So the y-intercept of $f(x)-3$ is three units less than the y-intercept of $f(x)$

1.2. Effects on the regions where the graph is increasing and decreasing

Given that you are shifting the graph downward on the y-axis, there is no any effect on the intervals of the domain. The function $f(x)-3$ increases and decreases in the same intervals of $f(x)$

1.3 The end behavior when the following changes are made.

The function is shifted three units downward, so each point of $f(x)-3$ has the same x-coordinate but the output is three units less than the output of $f(x)$ . Thus, each point will be sketched as:

$For \ y=f(x): \n P(x_(0),f(x_(0))) \n \n For \ y=f(x)-3: \n P(x_(0),f(x_(0))-3)$

FOR ODD FUNCTIONS:

2. When $f(x)$ becomes $f(x)-3$

2.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is three units less. So the graph is shifted three units downward again.

An example is shown in Figure 1. The graph in blue is the function:

$y=f(x)=x^3-x$

and the function in red is:

$y=f(x)-3=x^3-x-3$

This function is odd, so you can see that:

$y-intercept \ of \ f(x)=0 \n y-intercept \ of \ f(x)-3=-3$

2.2. Effects on the regions where the graph is increasing and decreasing

The effects are the same just as in the previous case. So the new function increases and decreases in the same intervals of $f(x)$

In Figure 1 you can see that both functions increase and decrease at the same intervals.

2.3 The end behavior when the following changes are made.

It happens the same, the output is three units less than the output of $f(x)$ . So, you can write the points just as they were written before.

So you can realize this concept by taking a point with the same x-coordinate of both graphs in Figure 1.

FOR EVEN FUNCTIONS:

3. When $f(x)$ becomes $-2.f(x)$

3.1 Effects on the y-intercept

As we know the graph $f(x)$ intersects the y-axis when $x=0$ , therefore:

$y=f(0) \ is \ the \ y-intercept \ again$

And:

$y=-2f(0) \ is \ the \ new \ y-intercept$

So the new y-intercept is the negative of the previous intercept multiplied by 2.

3.2. Effects on the regions where the graph is increasing and decreasing

In the intervals when the function $f(x)$ increases, the function $-2f(x)$ decreases. On the other hand, in the intervals when the function $f(x)$ decreases, the function $-2f(x)$ increases.

3.3 The end behavior when the following changes are made.

Each point of the function $-2f(x)$ has the same x-coordinate just as the function $f(x)$ and the y-coordinate is the negative of the previous coordinate multiplied by 2, that is:

$For \ y=f(x): \n P(x_(0),f(x_(0))) \n \n For \ y=-2f(x): \n P(x_(0),-2f(x_(0)))$

FOR ODD FUNCTIONS:

4. When $f(x)$ becomes $-2f(x)$

See example in Figure 2

$y=f(x)=x^3-x$

and the function in red is:

$y=-2f(x)=-2(x^3-x)$

4.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is the negative of the previous intercept multiplied by 2.

4.2. Effects on the regions where the graph is increasing and decreasing

In this case it happens the same. So in the intervals when the function $f(x)$ increases, the function $-2f(x)$ decreases. On the other hand, in the intervals when the function $f(x)$ decreases, the function $-2f(x)$ increases.

4.3 The end behavior when the following changes are made.

Similarly, each point of the function $-2f(x)$ has the same x-coordinate just as the function $f(x)$ and the y-coordinate is the negative of the previous coordinate multiplied by 2.

The y-intercept of  is  .
Of course, it is 3 less than  , the y-intercept of  .
Subtracting 3 does not change either the regions where the graph is increasing and decreasing, or the end behavior. It just translates the graph 3 units down.
It does not matter is the function is odd or even.

is the mirror image of  stretched along the y-direction.
The y-intercept, the value of  for  , iswhich is  times the y-intercept of  .Because of the negative factor/mirror-like graph, the intervals where  increases are the intervals where  decreases, and vice versa.
The end behavior is similarly reversed.
If  then  .
If  then  .
If  then  .
The same goes for the other end, as  tends to  .
All of the above applies equally to any function, polynomial or not, odd, even, or neither odd not even.
Of course, if polynomial functions are understood to have a non-zero degree,  never happens for a polynomial function.

Ann entered a race which required a run of 10 km north and a bike of 120 km west. Determine her running speed if she cycled ten times faster than she ran and the total race took her four hours to complete.

Answers

x - running speed
10x - speed on bike

v = s/t
s - distance
t - time

t = s/v

s₁ = 10 km
s₂ = 120 km

$(10)/(x) + (120)/(10x) = 4\n\n(10)/(x) + (12)/(x) = 4\ \ //*x\n\n10 + 12 = 4x\n\n4x = 22\ \ //:4\n\nx =(22)/(4) = 5,5\ km/h$

Solution:
Running speed = 5,5 km/h

Where would the square root of 130 be located on the number line

Answers

$√(130)=\boxed{11.40175425099138}\ it\ would\ be\ located\ in\ between\ 11\ and\ 12.$

A square quilt for a child’s bed has a border made up of 44 pieces with an area of x each, and 4 small squares with an area of 1 square inch each. The main part of the quilt is made of 121 squares with an area of x 2 each. Find an expression for the area of the quilt.

Answers

Answer:

A = ( 11x + 2 )²

Step-by-step explanation:

To find the total area of the quilt, we need to add up all the areas given:

If the border has 44 pieces with an area of x each one, that area is 44x.

The area of 4 squares of 1 in² each is 4×1 in² = 4 in².

The main part is made up of 121 squares with an area of x², which is 121x².

Adding those areas up, we get the expression for the total area:

A = 121x² + 44x + 4

You can easily notice that 121 = 11² and 4 = 2². If you double its product (2·11·2) = 44

So:

A = ( 11x + 2 )²