The points A(0,5), B(4,2), and C(0,2) form the vertices of a right triangle in the coordinate plane.
What is the equation of the line that forms the hypotenuse?

The Inverse Function Line Test

A given graph represents a function only if for every value of x there is only one corresponding value of y.

This can be checked by using a vertical line and moving it through the x-axis. If that line intersects the graph more than once, then the graph does not correspond to a function.

The image shows a graph and if we move our imaginary vertical line from x=-2 to x=7 that line would intersect the graph only once. This means that the graph corresponds to a function in the domain [-2,7].

For the inverse function to exist, the horizontal line test must be passed.

Imagine a horizontal line moving through the y-axis. It would intersect the graph only once from y=0 to y=6.

We can conclude this graph corresponds to a function and it has an inverse function because it passed the horizontal line test.

Answer: D.

The measure of ∡KJR is 69°.

What is the sum of two supplementary angles?
Two angles are referred to as supplementary angles if their combined value is 180°. A straight angle is created when supplementary angles are combined (180°).
In other words, ∡A and ∡B are supplementary if ∡A plus ∡B equals 180°. Angles A and B are described as "supplements" of one another in this context.
In math, A° + B° = 180°.

Given, m∡RJI = 12x - 3, m∡KJR = 6x - 5, m∡KJI = 172°
As seen from diagram, m∡RJI + m∡KJR = m∡KJI
⇒ (12x-3)+(6x-50) = 172° ⇒ 18x - 53 = 172° ⇒ x = ([172 + 53]/18)° = 12.5°
Therefore, the value of x = 12.5°
Thus, m∡KJR = 6x - 5 = (6*12.5) - 5 = 69°

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Answer: R(8,1)

Step-by-step explanation:

[tex]\displaystyle\\M(9,2)\ \ \ \ S(10,3)\ \ \ \ R(x,y)=?\\\\M_x=\frac{R_x+S_x}{2} \\\\\Rightarrow\ 9=\frac{x+10}{2\\\\}[/tex]

Multiply both parts of the equation by 2:

[tex]9(2)=x+10\\18=x+10\\18-10=x+10-10\\8=x[/tex]

[tex]\displaystyle\\M_y=\frac{R_y+S_y}{2} \\2=\frac{y+3}{2}[/tex]

Multiply both parts of the equation by 2:

[tex]2(2)=y+3\\4=y+3\\4-3=y+3-3\\1=y[/tex]

⇒   R(8,1)

Answer:

267 times 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find The Edge Of The Cube Whose Leteral Surface Area Is 36cm^2

LSA of cube = x^2 + x^2 + x^2 + x^2 = 4x^2

so

4x^2 = 36

x^2 = 9

x = 3

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

check

4 * 3^2 =

4 * 9 =

36

the answer is good

Answer: 3 cm

Step-by-step explanation:

Option C correctly represents the function.

For the given question;

From the definition of the function, two values in the domain can not have the same image, thus option a and b are incorrect.

Only option c correctly described the function, as for every value of out put there is only one input.

Thus, option c correctly described the function.

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Step-by-step explanation:

the approach of the other answer is basically correct, but we need to use the correct numbers.

so, I assume that the 33% of the first solution is correct, and not the 23% mentioned later.

x = liters of the 33% solution.

y = liters of the 17% solution.

we know that

x + y = 1.8

and therefore

x = 1.8 - y

and then we want to enforce the desired result (ab% are simply 0.ab)

0.33x + 0.17y = 0.22×1.8

we use the identity from above in this equation :

0.33(1.8 - y) + 0.17y = 0.396

0.594 - 0.33y + 0.17y = 0.396

0.198 - 0.16y = 0

0.198 = 0.16y

y = 1.2375 liters

x = 1.8 - y = 1.8 - 1.2375 = 0.5625 liters

if the first solution is truly only 23%, then we only need to change the number :

0.23(1.8 - y) + 0.17y = 0.396

0.414 - 0.23y + 0.17y = 0.396

0.018 - 0.06y = 0

0.018 = 0.06y

y = 0.3 liters

x = 1.8 - y = 1.8 - 0.3 = 1.5 liters

Answer: The decrease in price is $64, and the sale price is $192.

Step-by-step explanation:

0.25 * $256 = $64

$256 - $64 = $192

The solution to the given system of linear equations is x = 3, y = -3. That is, (3, -3)

The graph of the system of equations is shown below

From the question, we are to determine the apparent solution to the given system of linear equations

The given system of equations is

y = -2x + 3

y = 1/3x - 4

Set the two equations equal

That is,

-2x + 3 = 1/3x - 4

Multiply through by 3

-6x + 9 = x - 12

Add 6x to both sides of the equation

-6x + 6x + 9 = x + 6x - 12

9 = 7x - 12

Add 12 to both sides of the equation

9 + 12 = 7x - 12 + 12

21 = 7x

x = 21/7

x = 3

Substitute the value of x into the first equation

y = -2x + 3

y = -2(3) + 3

y = - 6 + 3

y = - 3

The solution is (3, -3)

The graph is shown below

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Answer:

Step-by-step explanation:

(1,0),(2,6). Explanation: express the equation, giving y in terms of x. ⇒y=6x−6. now choose any value for x , substitute into the equation

Answer:

20

Step-by-step explanation:

Simplify the following:

(2 sqrt(5))^2

Multiply each exponent in 2 sqrt(5) by 2:

2^2×5^(2/2)

2/2 = 1:

2^2×5

2^2 = 4:

4×5

4×5 = 20:

Answer:  20

Answer: 2:7

Step-by-step explanation:

[tex]\displaystyle\\\frac{6}{15+6} =\\\\\frac{6}{21} =\\\\\frac{2(3)}{7(3)} =\\\\\frac{2}{7} =\\\\2:7[/tex]

The ratio of triangles to total shapes in simplest form is 2 : 7.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, There are 15 squares and 6 triangles.

Therefore, The total number of shapes is (15 + 6) = 21.

So, The ratio of triangles to total shapes is,

triangle/total shapes = 5/15 + 6.

triangles/total shapes = 6/21.

triangles : total shapes = 6 : 21 = 2 : 7

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120% is considered an enlargement since the scale factor is greater than one.

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

It is considered a reduction of the scale factor is less than one, and an enlargement if the scale factor is greater than one.

120% = 1.2 > 1, hence an enlargement.

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Answer:

a)Figure C

b) Figure A, B, and C

c)Figure B and C

Step-by-step explanation:

Note squares are rectangles

Answer:

105 cause you will divide to get the total

Using an exponential function, it is found that:

An exponential function is modeled according to the following rule:

[tex]y = ab^{\frac{x}{n}}[/tex]

In which:

Considering that the pool has 1500 gallons, and drains 3% every 5 minutes, the parameters of the function are given as follows:

a = 1500, b = 1 - 0.03 = 0.97, n = 5.

Hence the amount of water in the poll after x minutes is given by:

[tex]y = 1500(0.97)^{\frac{x}{5}}[/tex]

After 50 minutes, the amount of water in the pool is:

[tex]y = 1500(0.97)^{\frac{50}{5}} = 1500(0.97)^{10} = 1106[/tex]

1106 gallons.

The poll will have less than 1000 gallons when:

y = 1000 (we can use it because the function decreases continuously).

Hence:

[tex]1500(0.97)^{\frac{x}{5}} = 1000[/tex]

[tex](0.97)^{\frac{x}{5}} = \frac{1000}{1500}[/tex]

[tex](0.97)^{\frac{x}{5}} = \frac{2}{3}[/tex]

[tex]\log{(0.97)^{\frac{x}{5}}} = \log{\left(\frac{2}{3}\right)}[/tex]

[tex]\frac{x}{5}\log{0.97} = \log{\left(\frac{2}{3}\right)}[/tex]

[tex]x = 5\frac{\log{\left(\frac{2}{3}\right)}}{\log{(0.97)}}[/tex]

x = 66.6 minutes.

The capacity of the pool is missing, and it is of 1500 gallons.

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The multiplication of polynomials (3x² - 5x + 7) and (2x² - 5x + 7) is:

6x^4 - 25x³ + 60x² - 70x + 49

In this question, we have been given two polynomials 3x² - 5x + 7 and 2x² - 5x + 7

We need to multiply given polynomials.

(3x² - 5x + 7) × (2x² - 5x + 7)                          ............(Given polynomials)

= 3x²(2x² - 5x + 7) - 5x(2x² - 5x + 7) + 7(2x² - 5x + 7)      ..........(Distribute)

= 6x^4 - 15x³ + 21x² - 10x³ + 25x² - 35x + 14x² - 35x + 49     .....(Simplify)

= 6x^4 - 15x³ - 10x³ + 21x² + 25x² + 14x² - 35x -35x + 49

= 6x^4 - 25x³ + 60x² - 70x + 49

Therefore, the multiplication of polynomials (3x² - 5x + 7) and (2x² - 5x + 7) is 6x^4 - 25x³ + 60x² - 70x + 49

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The statement that cannot be assumed based on the diagram is ∠DBC is vertical to ∠FDE.

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Solving for f

Adjacent angles of a parallelogram are supplementary, so (f+30)+72=180. It follows that f=78.

Solving for g

Opposite sides of a parallelogram are congruent, so 25=8g-3. It follows that g=3.5.

Answer:

Commutative Property for Multiplication

Answer:

Commutative Property for Multiplication

Step-by-step explanation:

Both methods are observational studies because both include students who do and do not play a musical instrument. So, this method describes an observational study.

Several various kinds of non-experimental studies in which behavior is routinely observed and documented are together referred to as observational research. A variable or combination of variables must be described in order to be the focus of observational research.

In a broader sense, the objective is to capture a moment in time of certain traits of a person, group, or environment. We cannot draw causal inferences from observational research since nothing is altered or controlled, as previously said, making it non-experimental. Although they may also be quantitative or both, the data that are gathered in observational research investigations are frequently qualitative in nature (mixed-methods).

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Answer:

IF ITS THIS QUESTION

An article in a psychology journal claims that young students who play a musical instrument tend to have higher test scores on state math exams. To assess the claim, a government official considers two methods to collect data.

Method 1: Contact many city schools and ask them to provide summary data on state math exam performance and students who participate in music lessons.

Method 2: Choose two city schools and provide free music lessons to students who register. At the end of the year, compare state math exam scores for students who participated in the music lessons with the scores for those who did not.

Step-by-step explanation:

THE AWNSER IS C

Method 2 is an observational study because students can choose to participate in the music lessons.

An observational study is a type of research in which researchers observe and record the behavior of a group of individuals, but do not manipulate or intervene in any way. In this case, Method 2 describes an observational study because the researchers are not manipulating the students' participation in music lessons. Instead, the students are free to choose whether or not to participate in the music lessons, and the researchers simply observe and record the state math exam scores for both groups of students. In contrast, Method 1 is not an observational study because it involves collecting summary data on state math exam performance and music lesson participation, rather than observing and recording the behavior of the students.

For the linear function y = 9 - 5x, it is found that:

A linear function, in slope-intercept format, is modeled according to the following rule below:

y = mx + b

In which:

In the context of this problem, the linear function is modeled as follows:

y = 9 - 5x.

In standard format, with the slope in front, we have that:

y = -5x + 9.

Meaning that the coefficients are given as follows:

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Answer:

1. acute angle (less than <90)

2. right angle (approximately <90)

3. obtuse angle (more than <90)

4. acute angle (less than <90)

The property used is Distributive property

What is Distributive property ?

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Given, equation

5x+9+5x+12

Step 1 =(5x+9)+(5x+12)

Step 2 = 5x+(9 +5x)+12

Step 3 = 5x+(5x+9)+12

Step 4 =(5x+5x)+(9+12)

Step 5 = (5 + 5)x+ (9 + 12)

Step 6 = 10x + 21

The property used in this equation is called Distributive property

Hence, the property use in here Distributive property

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Answer:

Symmetric property of congruence

Annual cost to operate farm B well with cost of natural gas $2.50 per 1,000 cubic feet and uses of 10000cubic feet of natural gas per year is $25.

As given,

Farm A:

Cost of natural gas per 1,000 cubic feet=$2.50

Farm B:

Uses of natural gas per year = 10000cubic feet

Cost of natural gas of farm B is same as farm A

Cost of natural gas per 1,000 cubic feet=$2.50

⇒1cubic feet=2.50/1000

Annual cost to operate 200ft well that uses 10000 cubic feet natural gas

10000 cubic feet=(2.50 ×10000)/1000

                             =$25

Therefore, annual cost to operate farm B well with cost of natural gas $2.50 per 1,000 cubic feet and uses of 10000cubic feet of natural gas per year is $25.

The complete question is:

Farm A has a 100 ft well that uses 7,000 cubic feet of natural gas per year. If the cost of natural gas for farm A is $2.50 per 1,000 cubic feet. And farm B has a 200 ft well that uses 10000 cubic feet of natural gas per year. if the cost of natural gas is the same a farm A, what is the annual cost to operate this well?

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According to the given function, which contains a square root, the domain must contain numbers that are greater than or equal to 5, otherwise, we would obtain the square root of a negative value, which is not real.

It means that the domain is

The range contains numbers greater than 0, this is because the minimum value of the domain is 5, when we evaluate the function at this value, the result is 0, which means that the range is:

The answer is the first option.

Answer:

x = 12, y = 60

Step-by-step explanation:

We have parallel lines, so alternate interior angles are congruent.

6x + 3 = 75

6x = 72

x = 12

The interior angles of a triangle add up to 180 degrees.

45 + 75 + y = 180

120 + y = 180

y = 60