The graph of a rational function is shown below. Write the equation that represents this function.

Answer:

y=2/3

Step-by-step explanation:

2y+4y=6-3y

⇔ 2y+4y+3y=6

⇔ 9y=6

⇔ y=6/9=2/3

The answer is:

y = 2/3

Work/explanation:

For now, I focus on the left side and combine the like terms:

\(\bf{2y+4y=6-3y}\)

\(\bf{6y=6-3y}\)

Add 3y to each side

\(\bf{6y+3y=6}\)

Combine like terms

\(\bf{9y=6}\)

Divide each side by 9

\(\bf{y=\dfrac{6}{9}}\)

\(\bf{y=\dfrac{2}{3}}\)

Hence, the answer is 2/3.

Answer:-39

Step-by-step explanation:

The first thing is to open the bracket.

By doing that, the question becomes -37-2.

note that plus×minus=minus.

Hence,-39 as the final answer

Answer:

An inequality correctly shows the relationship between the total cost of the two plumbing companies is \(675+24.5x \leq 650+25.75x\)

Step-by-step explanation:

Pat’s Plumbing Company

Cost of inspecting house = $650

Cost of labor per hour = $25.75

Cost of labor in x hours = 25.75x

Total cost = 650+25.75x

AAA Plumbing

Cost of inspecting house = $675

Cost of labor per hour = $24.50

Cost of labor in x hours = 24.5x

Total cost = 675+24.5x

We are given that AAA Plumbing will cost no more than Pat’s Plumbing Company

\(675+24.5x \leq 650+25.75x\)

Hence An inequality correctly shows the relationship between the total cost of the two plumbing companies is \(675+24.5x \leq 650+25.75x\)

Answer:

carlo scored 65 out of 100 item in math. what percent of the test did he get correctly

The solution of the system is then given by:

x = t[1 -1 1 0.5 0.5 0.33] + s[0 -2 1 1 -2 1]

This is the general solution of the system in the form of a sum of scalar multiples of fixed column vectors.

The system of linear equations can be written in matrix form as:

[1 0 1 2 1 3 | 1]

[2 1 2 4 0 10| 5]

[3 1 3 6 6 15| 8]

where the augmented matrix is [A | B].

To solve the system using the method of specifying appropriate free variables, we first convert the coefficient matrix into reduced row echelon form using Gaussian elimination.

In reduced row echelon form, the first non-zero element of each row (known as the leading entry) is 1, and the leading entries of lower rows are to the right of the leading entries of higher rows.

Applying Gaussian elimination to the coefficient matrix, we get:

[1 0 1 2 1 3 | 1]

[0 1 0 2 -2 7| 0]

[0 0 0 0 0 0| 0]

We can see that there are two non-zero rows, indicating that the system has two independent equations.

We can choose two of the variables to be free variables, and express the other variables in terms of the free ones.

Let's choose x1 and x3 as the free variables.

We can find x2 as follows:

x2 = -x1 - 2x3 + 7

And we can find x4, x5 and x6 as follows:

x4 = (1 - x1 - x3)/2

x5 = 1 - x1 - 2x3 + 2x4

x6 = (1 - x1 - x3 - 2x4)/3

So the general solution of the system can be expressed as a sum of scalar multiples of fixed column vectors:

x1 = t

x2 = -t - 2s + 7

x3 = s

x4 = (1 - t - s)/2

x5 = 1 - t - 2s + (1 - t - s)/2

x6 = (1 - t - s)/3

where t and s are scalars.

For more questions on Gaussian elimination to the coefficient matrix

https://brainly.com/question/28681914

#SPJ4

The distance between the points (-1, 5) and (-7, -3) is 10 units.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Point 1 (-1,5)

Point 2 (-7,-3)​

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √[(-7 - (-1))² + (-3 - 5)²]

D = √[(-7 + 1)² + (-3 - 5)²]

D = √[-6² + (-8)²]

D = √[36 + 64]

D = √100

D = 10

Therefore, the distance is 10 units.

Learn more about the distance formula here: brainly.com/question/24509115

#SPJ1

Answer:

24 ft

Step-by-step explanation:

to find the perimeter of rug is you have to add 9+9+3+3= 24

Answer:

(-6, 7)

Step-by-step explanation:

90 degrees counterclockwise / 270 degrees clockwise:

(x,y) -> (-y,x)
180 degrees counterclockwise / 180 degrees clockwise:

(x,y) -> (-x,-y)

270 degrees counterclockwise / 90 degrees clockwise:

(x,y) -> (y,-x)

Answer:

\(-\frac{9}{1}\)

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

Answer:

A

Step-by-step explanation:

\(\frac{10}{30}\) = \(\frac{x}{15}\) ( cross- multiply )

30x = 10 × 15 = 150 ( divide both sides by 30 )

x = \(\frac{150}{30}\) = 5

HELLO

So the answer for this is A=5

Here is the explanation for this question

10/30=x/15  (given)

if, x/15=10/30 then,

x=10/30*15

by solving this we the value of x= 5

Answer:

Σ( xi ) / n ; $29

Step-by-step explanation:

Given the following data:

X= $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26

Number of observations (n) = 12

Mean formula (m) = ( Σ xi ) / n

Where i = each individual value in X

Mean water bill for the years is thus :

m = Σ [(27 + 31 + 30 + 26 + 25 + 27 + 37 + 33 + 32 + 28 + 26 + 26)] / 12

m = 348 / 12

m = 29

Hence, the mean water bill for the year is $29

Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

The (g.f)(x)  of the two functions is:

(g.f) (x) = 6x + 37

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To find (g.f) (x), follow the steps below:

1. Substitute the value of f(x) into the function g(x).

2. Then simplify the expression.

That is:

f(x) = 3x+18

g(x) = 2x+1

Thus, we have:

(g.f) (x) = g(f(x))

(g.f) (x) = g(3x+18)

(g.f) (x) = 2(3x+18) + 1

(g.f) (x) = 6x+36 + 1

(g.f) (x) = 6x + 37

Learn more about function on:

brainly.com/question/1415456

#SPJ1

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answer:

.......................... you do know you could skip math class and do better in your other classes and you will still move to the next grade pls make me as Brainliest

Step-by-step explanation:

The quadratic regression equation is y = 1.38x^2 - 5.77x + 0.96

From the question, we have the following parameters that can be used in our computation:

(-1,8), (5,-4), (7,8), (2,-6)

Using a graphing calculator, we have the following summary:

function value

mean of x 3.25

mean of y 1.5

correlation coefficient r 0.9990171837

A 1.380577428

B -5.769028871

C 0.9553805774

The equation is represented as

y = ax^2 + bx + c

So,, we habe

y = 1.38x^2 - 5.77x + 0.96

Hence, the equation is y = 1.38x^2 - 5.77x + 0.96

Read more about regression at

https://brainly.com/question/25987747

#SPJ1

Answer:

Step-by-step explanation:

Initial number is 1 so a = 1

Weekly growth rate is 400% which is 4 times increase, therefore b = 4

So the function becomes:

Answer:

\(52.1-1.984\frac{12.3}{\sqrt{100}}=49.66\)    

\(52.1 +1.984\frac{12.3}{\sqrt{100}}=54.54\)    

The 95% confidence interval would be given by (49.66;54.54)    

Step-by-step explanation:

Information given

\(\bar X= 52.1\) represent the sample mean

\(\mu\) population mean (variable of interest)

s=12.3 represent the sample standard deviation

n=100 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

The degrees of freedom are given by:

\(df=n-1=100-1=99\)

The Confidence is 0.95 or 95%, and the significance would be \(\alpha=0.05\) and \(\alpha/2 =0.025\), the critical value for this case is: \(t_{\alpha/2}=1.984\)

Replacing the info given we got:

\(52.1- 1.984\frac{12.3}{\sqrt{100}}=49.66\)    

\(52.1 +1.984\frac{12.3}{\sqrt{100}}=54.54\)    

The 95% confidence interval would be given by (49.66;54.54)    

For the given problem, the correct answer is: "Reject the claim that the mean weight is different from 14 oz when it is actually 14 oz."

In the given problem,

It is claimed by cereal manufacturer that the average weight of the cereal in its packets is 14 oz. To test this claim , we may use a hypothesis test in which the null hypothesis (H0) is that the cereal in the packets has a mean weight of 14 oz and the alternative hypothesis (H1) iwill be that it does not.

Assume we run the test and get a result that causes us to reject the null hypothesis (H0). This indicates that we discovered an evidence to support the alternative hypothesis (H1), which states that the average weight of the cereal in the packets is not 14 oz.

Learn more about type I error here:

https://brainly.com/question/24320889

#SPJ1

Question:

Where are the equations?

Answer:

Answer: graph 1:no graph 2:no graph 3: yes graph 4: yes graph 5: no

graph 6: no

Step-by-step explanation:

Answer:

Graph 1 I think is yes because when determining if a function, you do the vertical line test meaning you place an imaginary vertically on the graph and if there is 2 points on the line at once, like for graph 5 or 6, then it isn't a function.

Therefore,

Graph 1: Yes

Graph 2: No

Graph 3: Yes

Graph 4: Yes

Graph 5: No

Graph 6: No

Answer:

\(b.)= (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)

Step-by-step explanation:

Given;

velocity of the diver, v = 25 mph

direction of his dive, θ = 60°

The vertical component of the velocity is given by;

\(-V_y = vsin\theta \ \ (below \ horizontal \ is \ in \ negative\ y-direction)\\\\V_y =-(25)(sin 60)\\\\V_y =-(25)(\frac{\sqrt{3} }{2} )\)

The horizontal component of the velocity is given by;

\(V_x =vcos\theta\\\\V_x =(25)(cos 60 )\\\\V_x =(25)(\frac{1 }{2} )\\\\V_x = \frac{25}{2}\)

Therefore, the component form of the velocity vector is given by;

\((V_x, \ V_y) = (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)

correct option = \(b.)= (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)

Answer:

B: (25/2, - 25√3/2)

Step-by-step explanation:

First find the values

v = 25 mph

θ = 60°

Vertical:

\(V_{y}\) = -vsin(θ) (Negative because it is below the x axis.)

\(V_{y}\) = (-25)(sin(60))

\(V_{x}\) = (-25)(\(\frac{\sqrt{3} }{2}\))

\(V_{y}\) = \(\frac{-25\sqrt{3} }{2}\)

Horizontal:

\(V_{x}\) = vcos(θ)

\(V_{x}\) = (25)(cos(60))

\(V_{x}\) = (25)(1/2)

\(V_{x}\) = \(\frac{25}{2}\)

Putting them together we get:

(\(\frac{25}{2}\), \(\frac{-25\sqrt{3} }{2}\)) or B

The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.

A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.

A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.

A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.

A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.

In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

For more questions on Histogram.

https://brainly.com/question/25983327

#SPJ8

Answer:

The resultant polynomial is: \(6x^2-6x+5\)

Step-by-step explanation:

We need to subtract \((x+1)^{2}\) from \(7x^2-4x+6\)

so, we start by performing the multiplication involved in the perfect square of the binomial \((x+1)\), and obtain its expression in separate terms that can be combined:

\((x+1)^{2}=(x+1)\,(x+1)=x^2+x+x+1=x^2+2x+1\)

Now we can subtract this trinomial from  \(7x^2-4x+6\), and  combining like terms to get the resultant polynomial expression:

\(7x^2-4x+6-(x^2+2x+1)=7x^2-4x+6-x^2-2x-1=7x^2-x^2-4x-2x+6-1=6x^2-6x+5\)

Then the resultant polynomial is: \(6x^2-6x+5\)

Answer:

35^8

Step-by-step explanation:

5^8 x 7^8

(5 x 7)^8

=35^8

Answer:

none of the above

Step-by-step explanation:

the square root of 0.36 is 0.6, which is not an option. Please give me the brainliest if this helped:)

Answer:

E, none of the above satisfy the equation

9514 1404 393

Answer:

  x = 10°; angles are 50°, 46°, 84° (CW from left)

Step-by-step explanation:

The sum of the three angles is 180°, so ...

  (6x +10°) +(4x +6°) +(7x +14°) = 180°

  17x +10° = 180°

  17x = 170°

  x = 10°

__

Then the angles are ...

  6x -10° = 6·10° -10° = 50°

  4x +6° - 4·10° +6° = 46°

  7x +14° = 7·10° +14° = 84°

Answer: The percentage change is 56.67%.

Step-by-step explanation:

From 120 meals to 52 meals, change in meals = ( 120- 52) meals

= 68 meals

The percentage change = \(\dfrac{\text{change in meals}}{\text{Original quantity of meals}}\times100\)

\(=\dfrac{68}{120}\times100\\\\=56.67\%\)

Hence, the percentage change is 56.67%.

Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%

We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%

For more such questions on surface area

https://brainly.com/question/30739454

#SPJ8

Step-by-step explanation:

h,k   center is  0,0 and radius is 8

(x-0)^2  + ( y-0)^2 = 8^2

x^2  + y^2  = 64

IM NOT SURE, DO YOU WANT ME TO WORK IT OUT FOR YOU?