Graph the line that passes through the points (-9,8) and (-7,8) and determine the equation of the line

According to the vertical angles theorem, m∠1 = 117°.

Based on the corresponding angles theorem, m∠2 = 117°.

The set of angle pairs formed that are directly opposite each other when two straight lines intersect or when two parallel lines are crossed by a transversal are said to be vertical angles, and therefore congruent to each other based on the vertical angles theorem.

When two lines are intersected by a transversal, the angles that are on the same transversal and lie in relative position or corner in the two parallel lines are said to be corresponding angles which are congruent based on the corresponding angles theorem.

Using the information given in the diagram attached below, angles 1 and 117° are vertical angles.

Therefore:

m∠1 = 117° [vertical angles theorem]

Angles 1 and 2 are corresponding angles. Therefore:

m∠2 = m∠1

Substitute

m∠2 = 117° [corresponding angles theorem]

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The polynomial f(x) = 2x³ + ax² + bx + 6 is exactly divisible by 2x - 3. The values of a and b are a = 131/27 and b = -71/9

To solve the problem, use the polynomial remainder theorem. If a polynomial f(x) is divided by a linear function with zero x = a, then the remainder r = f(a).

The given polynomial is:

f(x) = 2x³ + ax² + bx + 6

- The polynomial is exactly divisible by (2x-3) means:

f(3/2) = 0

2. (3/2)³ + a(3/2)² + b(3/2) + 6 = 0

27 + 9a + 6b + 24 = 0

9a + 6b = - 51 (equation 1)

- f(x) divided by (x+3) has remainder -28

f(-3) = -28

2. (-3)³ + a(-3)² + b(-3) + 6 = -28

9a - 3b = 20  (equation 2)

Substract equation 2 from equation 1

9a + 6b = -51

9a - 3b =  20 _

      9b = -71

         b = -71/9

9a - 3(-71/9) = 20

9a = 131/3

a = 131/27

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Pi written as 3.l4 and π in mathematics is the ratio for the diameter of a circle to the circumference of that circle. The value is unending

Pi, which is represented by the Greek letter p, or, is a shorthand for the ratio of a circle's diameter to its circumference. No matter how big the circle is, this ratio will always be equal to pi. The value of pi is about 3.14 in decimal notation.

We are to multiply Pi to any equation

let the equation be (20.5 + 3x)[tex]\pi[/tex]

pi is represented in numbers by 3.14

Hence we would have the equation to be of the form

(20.5 + 3x)3.14

multiply through the bracket

64.37 + 9.42x

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Answer:

360 sq feet

Step-by-step explanation:

The width of the room is given in the question, 12 feet.

We don't know the length. Let's call the length x.

x = length

We were also given the perimeter, 81, that's the distance around the sides...

all the sides added up.



Use x for the long wall.

Use x-3 for the wall with the door in it.

x + 12 + x-3 + 12 = 81

combine like terms

2x + 21 = 81

subtract 21

2x = 60

divide by 2

x = 30

The room is 30 feet long by 12 feet wide.

Area =

length × width

= 30 × 12

= 360

The area of the room is 360sq feet.

Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.

Given,

Volume = 2.5 cm³

Mass = 10 g

For density:

Mass ÷ volume

10 ÷ 2.5

4

Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

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After using the probability distribution table, the given table does not show a probability distribution. The statement 1 is correct.

In the given question, we have to check which statement is correct regarding to the given option.

The given statements are:

(1) This table does not show a probability distribution.

(2) This table shows a probability distribution.

Before checking the statement we learn about a probability distribution table.

In a probability distribution table every result of a statistical experiment is connected to the likelihood that the result will actually occur. An experiment's result is recorded as a random variable, which is typically written with a capital letter.

As we can see that there is given the probability of having the blue, green, yellow and red color.

So the given table does not show a probability distribution.

So the statement 1 is correct.

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Answer:

Step-by-step explanation:

it help by showinbng thta

Answer:

so there are 3825 worker in total

Step-by-step explanation:

675=15%

women=85%

how much workers are 5%=675/3 =225

225=5%

how many workers is 85%= 85/5=17

                                    85%=225x17=3825

Answer:

yes it is???

Step-by-step explanation:

Answer: 0.86 pounds of fruit

Step-by-step explanation:

8.3-7.44=0.86

Ester, Sarai, and Kurry each selected a number: 0.009, 0.09, and 0.9, respectively.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes. For instance, 3+3+3+3+3 can be expressed as 3 5.

the ester's number is equal to one-tenth of the Sarai number.

= 1 / 10 × 0.09 = 0.009

to determine Kurry's number, multiply Sarai's number by 10

= 10 × 0.09 = 0.9

Therefore, it can be inferred that Kurry chose 0.9, Ester chose 0.009, and Sarai chose 0.09.

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Answer:

Another Professional Player

The proportional relationship between the cost and weight is given as y = 0.89x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The absolute expense for clothing administration, in dollars, relies upon the heaviness of the clothing, in pounds. This relationship is corresponding, as it costs $22.25 for 25 pounds of clothing and $36.49 for 41 pounds of clothing.

The equations are given below.

22.25 = 25m + c          ...1

36.49 = 41m + c           ...2

From equations 1 and 2, then we have

41m - 25m = 36.49 - 22.25

16m = 14.24

m = 0.89

Then the value of c will be given as,

22.25 = 25 (0.89) + c

c = 0

The proportional relationship between the cost and weight is given as y = 0.89x.

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The annual dividend for 500 shares was $710.

The annual dividend is a function of the dividend per share and the number of shares held by a stockholder.

Dividends are always declared per share with a stated dollar amount or percentage.

Dividends represent the portion of the profits earned by an entity that it decides to distribute to the shareholders.

Dividends are a kind of financial reward to stockholders for their investment in the entity.

The dividend per share = $1.42

Market price per share = $96

The number of shares held = 500

The dividend received for the year = $710 ($1.42 x 500)

Thus, the holder of 500 shares in Walt Disney Co. will get $710 in a year the company declared and paid a $1.42 annual dividend.

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The required equation of line in standard form that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y = 1 is

y = (3/8)x - 13/4

How to find equation of line if one point and equation of perpendicular line is given?

To find the equation of line which is perpendicular to another line

According to the given question:

Let the required equation of line be y = mx + b

where m is the slope of line and b is the y-intercept

Now, 8x + 3y = 1 is perpendicular to the line. Hence, the slopes of both line will satisfy m₁. m₂ = -1

Standard form of the given line is

y = (-8/3)x + 1/3

∴ m₁ = -8/3

Finding m₂, (-8/3). m₂ = -1

∴ m₂ = 3/8 ------ (1)

Using the given point (6, -1) to find y-intercept in the equation

y = (3/8)x + b

-1 = (3/8)(6) + b

∴ b = -13/4

Therefore the required equation of line in standard form is

y = (3/8)x - 13/4

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Answer:

y=3+5x

Step-by-step explanation:

Add 5x to both sides.

The Equation of line is y= -1/3x + 5/3

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

x-intercept = (3,0) and y-intercept =  (0,1).

slope, m= 0-1/ 3-0= -1/3

so, The slope-intercept form of the equation of a line is

y= mx + b

y= -1/3x +b

Now, the passes through (-1, 2) we get

2= -1/3(-1) + b

2- 1/3= b

b= 5/3

So, the Equation of line is y= -1/3x + 5/3

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A solution to −34x+2=(14)x+1 is x = 1/48

In this question, we have been given functions f(x) = -34x + 2 and g(x) =(14)x + 1

We need to find the solutions to −34x + 2 = (14)x + 1

i.e., we need to find the solution to f(x) = g(x)

Consider, f(x) = g(x)

-34x + 2 = (14)x + 1

-34x + 2 - 14x = 14x + 1 - 14x

-48x + 2 = 1

-48x = -1

x = 1/48

Therefore, a solution to −34x+2=(14)x+1 is x = 1/48

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Answer:

Corinna will have to run at 7 meters per second to get there at the same time as Deanna.

Step-by-step explanation:

So to find the distance of Deanna's route, you can use the Pythagorean theorem.

a^2 + b^2 = c^2

60^2 + 80^2 = 10000

c^2 = 10000

Take the square root of both sides.

c = 100

So Deanna runs 100 meters at 5 meters per second.

100/5 = 20

She runs for 20 seconds.

To find Corinne's distance, we add 60 and 80, which is 140.

To find how fast she need to run to get there in 20 seconds, you divide 140 by 20, which gets 7 (meters per second). You can also think of it like this: to run 140 meters in 20 seconds, she has to run at 140 meters per 20 seconds, which you can simplify (like a fraction) to 7/1, or just 7

The speed of each train is 125kph and 145kph.

Here it is given that the distance between the two trains is 810 miles after traveling for 3 hours.

The difference in their speed is 20 kph.

Let x be the speed of one train. So by this, we get the speed of the second train that is x + 20.

Formula to calculate speed is:

Speed = Distance / Time

Distance = Speed × Time

Distance covered by first train = x × 3

Distance covered by second train = (x + 20) × 3

Total distance = 810

So we get;

3x + (x + 20)3 = 810

3x + 3x + 60 = 810

6x = 750

x = 125

x + 20 = 125 + 20 = 145

Therefore we get the speed of both trains which is 125kpp and 145 kph.

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Answer:

[tex] \frac{ {m}^3{} }{25} [/tex]

Step-by-step explanation:

that is the answer

Answer: 82 is the answer

Step-by-step explanation: I just did this question and worked it out and it said it was right

Answer: check the image attached

Step-by-step explanation:

Hope this helps

Answer:

Just point the graph on Y=33x+0

Step-by-step explanation:

There's no B or starting point, so you would just plant the point on 0,33

Step-by-step explanation:

The answer is: A=210÷26.2=8.2

B=now we have to turn minutes in to haurs 210:60=3.5 now 26.2÷3.5=29.7

Answer:

A) 26.2/210= .125 miles per minute

B) 210/26.2= 8.02 minutes per mile

C) the other runner talks about the same rate as b), not a).

Step-by-step explanation:

A)[tex]\frac{26.2}{210\\}[/tex] and B)[tex]\frac{210}{26.2}[/tex] :)  

C)the runner was referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.

If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.

During the problem disaggregation process, the logic trees should have branches that are both mutually exclusive and collectively exhaustive.

Problem disaggregation refers to the process of breaking down the larger higher-level operation into smaller plans and shorter periods. It refers to the use of analysis, logic, and facts to evaluate and understand each element of the problem in terms of causes and driver of the situation using logic trees. Logic trees improve the problem definition and aid in understanding an issue in more detail. There are different types of logic trees used in the process – factor logic tree, inductive logic tree, deductive logic tree, hypothesis tree, and decision tree. The logic trees should have branches that are MECE – mutually exclusive and collectively exhaustive. It is the second and an important step in the seven steps bulletproof problem-solving process used for complex solving.

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The discrete and continuous random variables are-

a) Discrete; (b) Continuous; (c) Discrete; (d) Continuous; (e) Discrete; (f) Continuous

(a) So because number of new accounts is counted, (a) discrete (like, non-negative integers).

(b) Continuous, given that the interval between customer arrivals may have decimal values (like 2.9 minutes or 27.75 seconds).

(c) Because the quantity of clients is counted, (c) discrete (like, non-negative integers).

(d) Continuous, as the fuel consumption can have decimal values (like 15.5 gallons).

(e) Since this number of minorities is counted, (e) discrete (like, non-negative integers).

(f) Continuous since the outdoor temperature can be expressed in decimal degrees (e.g., 7.78 C).

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Dora solved the equation.

She multiplies 4 inside the bracket. But she fails to know that 4× -1 = -4. Instead she multiplied that 4×-1 = -41. This is her first mistake.

In the second step, she shifted -41 to the right side in order to find the value of x. As -41 gets shifted to right side , -41 becomes +41 and added with +11 to get 52. which is totally a wrong method.

Step-by-step explanation:

Here is the exact method of solvation.

[tex]{ \blue{ \bold{4(x - 1) = 11}}}[/tex]

[tex]{ \blue{ \bold{4x - 4 = 11}}}[/tex]

[tex]{ \blue{ \bold{4x = 11 + 4}}}[/tex]

[tex]{ \blue{ \bold{4x = 15}}}[/tex]

[tex]{ \blue{ \boxed{ \red{ \sf{x = \frac{15}{4}}}}}} [/tex]

Answer:

The smaller number is 4.

Step-by-step explanation:

X and Y are the two numbers

x+y=12

x-y=-4

Subtract these two equations

(x+y=12)

-(x-y=-4)

—————-

2y=16

y=8

Plug it in to any equation:

x+y=12

x+8=12

x=4

(x,y) = (8,20), (6,24), and (10,17).are three alternative combinations of pumpkins and squash that Latisha may buy to depict the circumstance.

Latisha's total wealth is $17.

More than 10 veggies are the number of vegetables that Latisha wants to purchase.

A pumpkin costs $5.50.

An autumn squash costs $3.50.

Let n pumpkins purchased equal x.

Purchased number of autumn squash = y

There are three alternative squash and pumpkin combination that Latisha might buy to symbolize the circumstance.

With x acting as the independent variable, we may identify many y's.

x ( Pumpkin)                   y(Autumn squash) (integral value)

    8                                                                20

    6                                                                24

   10                                                              17

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