Prove that a triangle with coordinates

A(5, 6), B(8,5), and C(2, -3) is a right triangle.

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Required base of the triangle is 6 ft.

What is the area of triangle?

The area of a triangle can be calculated using the formula:

Area = (base × height) / 2

where the base and height of the triangle are perpendicular to each other.

Alternatively, if you know the length of all three sides of the triangle, you can use Heron's formula to calculate the area:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle (i.e. half the perimeter) and a, b, and c are the lengths of the three sides.

To find the base of the given triangle when the area and height are given, we can use the formula:

Area = 1/2 x base x height

We are given that the area of the triangle is 24 ft² and the height is 8 ft². Substituting these values into the formula, we get:

24 = 1/2 x base x 8

Multiplying both sides by 2/8, we get:

base = 6

Therefore, the base of the triangle is 6 ft.

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Correct question is "The area of the triangle is 24 ft² and height of the triangle is 8 ft². Find base of the triangle?"

Answer:

B

Step-by-step explanation:

Answer:

B is correct

Step-by-step explanation:

√5 ≈ 2,24

since it is - √5 the answer must be -2,24 so B is correct

Answer:

Adults= 7

children= 9

Step-by-step explanation:

Step one:

given data

Adult tickets to a play cost $22. Tickets for children cost $15

let adult be x

and children be y

so

22x+15y= 228------1

x+y= 11----------------2

x= 11-y

Step two:

from 1

22(11-y)+15y= 228

242-22y+15y= 228

collect like terms

-7y= 228-242

7y= 14

divide both sides by 7

x= 2

from

x+y=11

y=11-2

y= 9

Answer:

Kevin should do 15 shock replacements and 6 brake replacements every week to maximize his weekly income.

Step-by-step explanation:

Both jobs take the same amount of time to complete (2 hours), therefore, in order to maximize his income, Kevin should prioritize the job that gives him the greatest income, which is replacing shocks.

If each job takes 2 hours and he works at most 42 hours per week, Kevin can complete 21 jobs per week. He should aim to do as little break replacements as possible and as many shock replacements as possible to maximize income.

If he completes at least 6 break replacements, the remaining jobs should all be shock replacements:

\(S=21-6\\S=15\)

Kevin should do 15 shock replacements and 6 brake replacements every week to maximize his weekly income.

Kevin has been working as an auto-mechanic. For maximizing weekly income Kevin should do 6 breaks replacement and 4 shock replacements. The time required for performing both the tasks has been equal. Since the time required has been the same, to increase the income, the task resulting in more income has been prioritized

Given :

Since there have been more income with shock replacement, the brake replacement task has been prioritized.

The time Kevin works in a week has been 42 hours. Since each job takes 2 hours, the number of jobs he can perform has been 21 jobs.

The routine jobs of brake replacement performed by Kevin have been 6. Thus to increase his income, the rest jobs have been of shock replacement.

The number of shock replacement tasks performed by the Kevin =

= 21 - 6

= 15

The number of shock replacement jobs = 15.

Thus for increasing the income Kevin has to perform 6 brake replacement tasks and 15 shock replacement tasks.

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The idea that group work theories are appropriate for all clients all the time is a myth (Third option).

About Group Process:

The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.

Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.

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Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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Answer:

EF=35

EG=22

Step-by-step explanation:

EF

7y-14=2y+21

5y=35

y=7

EF=7(7)-14=49-14=35

EG

15x+7=12x+10

3x=3

x=1

EG=15(1)+7=15+7=22

Answer:

(a). 35 units ; (b). 44 units

Step-by-step explanation:

(a). 7y - 14 = 2y + 21 ⇒ y = 7

EF = 7(7) - 14 = 35 units

(b). EJ = JG

15x + 7 = 12x + 10 ⇒ x = 1

EG = 2 × (15(1) + 7) = 44 units

Answer:

1). (x, y) → [(x + 7), (y + 1)]

2). (9, 10)

3). (x, y) → (-x, y)

4). (-2, 9)

5). (-9, 10)

Step-by-step explanation:

Given: Triangle ABC is translated 7 units right and 1 unit up, then reflected across the y-axis.

Rule for the translation of A is,

(x, y) → [(x + 7), (y + 1)]

After the translation point A moves to,

(2, 9) → [(2+7), (9+1)]

        → (9, 10)

The rule for a reflection over the y-axis is,

(x, y) → (-x, y)

The coordinates of A after the reflection are,

(2, 9) → (-2, 9)

The final position of A,

(-9, 10)

The equation of the line passing through the points (1,3) with slope = -4 is

y = -4x + 7

The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

m = (y - y1) / (x - x1)

where m = -4

y1 = 3

x1 = -1

-4 = (y - 3) / (x - 1)

-4(x - 1) = y - 3

-4x + 4 = y - 3

y = -4x + 7

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A person weighing 173 pounds can burn 10.7 calories per minute.

The given equation is ŷ=2.2+0.05x.

To solve this question, we can use the equation given, ŷ=2.2+0.05x. We can insert the known weight value, 173 pounds, to calculate the anticipated calories burned per minute.

y = 2.2 + 0.05x

y = 2.2 + 0.05 × 173

y = 10.7

Therefore, a person weighing 173 pounds can burn 10.7 calories per minute.

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"Your question is incomplete, probably the complete question/missing part is:"

By observing a set of data values, Thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: ŷ=2.2+0.05x

Based on the information gathered by Thomas, select the statement that is true.

a) A person weighing 149 pounds can burn 9.8 calories per minute.

b) A person weighing 134 pounds can burn 8.9 calories per minute.

c) A person weighing 125 pounds can burn 8.3 calories per minute.

d) A person weighing 173 pounds can burn 10.7 calories per minute.

Answer:

A person weighing 134 pounds can burn 8.9 calories a minute.

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

2x+4 = (x²)²÷2

2x + 4 = x^4/2

x^4 = 4x + 8

x^4 - 4x - 8 = 0

We can try trial an error to solve this

Looks like x = 2 fits it:

2^4 - 4(2) - 8

= 16 -8 -8 = 0

so x = 2 is one solution.

I can't find any other solution among other integers.

To find the other solutions you can draw a graph manually or by using software.

There will be either 1 or 3 more real solutions.

I used software to draw the graph and found one other solution:

x = -1.296

Answer:

he will pay 55.16

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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Answer:

rectangle

Step-by-step explanation:

in a rectangle, all 4 angles are 90° but only opposite sides are congruent

Answer:

15$

Step-by-step explanation:

To find the dimensions of the rectangle with maximum area, we need to consider the relationship between the rectangle and the semicircle.

Let's assume that the base of the rectangle is the diameter of the semicircle. Since the radius of the semicircle is given as 16, the diameter (and base of the rectangle) will be 2 * 16 = 32.

Now, we need to determine the height of the rectangle. Since the other two vertices of the rectangle lie on the semicircle, the height of the rectangle will be the distance from the center of the semicircle to the top edge of the rectangle.

The center of the semicircle is also the midpoint of the base of the rectangle, so the distance from the center to the top edge of the rectangle will be equal to the radius of the semicircle.

Therefore, the height of the rectangle will be 16.

Hence, the dimensions of the rectangle with maximum area are:

Base: 32

Height: 16

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Answer:

The answer is literally 3/4 as a fraction and you have to shade 15 parts.

The z-score is 0 and the probability that the sample mean will be greater than 59.8 is 0.5000

From the question, the given parameters about the distribution are

The z-score

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (59.8 - 59.8)/18.0

Evaluate

z = 0

The probability

The probability that the sample mean will be greater than 59.8 is then calculated as:

P(x > 59.8) = P(z > 0)

From the z table of probabilities, we have;

P(x > 59.8) = 0.5

Hence, the probability is 0.5000

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Answer:

A,   38

Step-by-step explanation:

the 180 - 114 = 66, so the vertical angle is 66, x = 38, 38 x 2 = 76 + 38 + 66 = 180

Answer:

p=-7

Step-by-step explanation:

-11+10(p+10)=4-5(2p+11)

Firstly, expand the bracket

-11+10p+100=4-10p-55

Next, you collect like terms

10p+10p=4-55-100+11

20p=-140

Divide through by the coefficient of p

20p/20=-140/20

p=-7

Answer:

37 degrees

Step-by-step explanation:

1. m∠CBA = 71+45 = 116 degrees

2. m∠CBA = m∠CDA because of the quadrilateral property of opposite sides.

3. m∠CBA + m∠CDA = 2*116 = 232.

4. Total angle measure of a quadrilateral is 360 degrees, so m∠BAD + m∠BCD = 360-232 = 128 degrees.

5. m∠BAD = m∠BCD = 128/2 = 64 degrees

6. m∠BAC = m∠BAD - m∠CAD = 64 - 27 = 37 degrees

By using Binomial Distribution  of probability, it is obtained that

Probability  that the number of heads is 13 or more =  \(137980(\frac{1}{2})^{20}\)

What is Binomial Distribution?

Binomial distribution is a discrete type probability distribution whose probability mass function is

P(X = k) = \({n \choose k} p^k(1 - p)^{n-k}\)

p is the probability of success.

Here Binomial distribution of probability is used

P(X \(\geq\) 13) = P(X = 13) + P(X = 14) + ........ + P(X = 20)

P(X = 13) = \({20 \choose 13} (\frac{1}{2})^{13}( 1 - \frac{1}{2}})^{20-13}\)

              = \({20 \choose 13} (\frac{1}{2})^{13}( \frac{1}{2}})^{7}\)

              =\({20 \choose1 3} (\frac{1}{2})^{20}\)

P(X = 14) = \({20 \choose14} (\frac{1}{2})^{20}\)

P(X = 20) = \({20 \choose20} (\frac{1}{2})^{20}\)

Total Probability = \(({20 \choose 13} + {20 \choose 14} + .... {20 \choose 20})(\frac{1}{2})^{20}\)

                  = (77520 + 38760 + 15504 + 4845 + 1140 + 190 + 20 + 1)\((\frac{1}{2})^{20}\)

                   = \(137980(\frac{1}{2})^{20}\)

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Answer:

The measure of the three angles are;

The first angle is 62°

The second angle is 28°

The third angle is 90°

Step-by-step explanation:

The given information are;

The shape of the parking lot = Triangular

Let the angles of the triangle be given as follows

First angle = A

Second angle = B

Third angle = C

The given triangle interior angle dimensions are;

A = 6 + 2× B

C = A + B

However, we have;

A + B + C = 180° (Angle sum property for a triangle)

Therefore;

A + B + C = 180° gives;

C + C = 180° (Transitive property)

2·C = 180°

C = 180°/2 = 90°

C = 90°

However, C = A + B  therefore;

90° = A + B and, A = 6 + 2 × B, we get;

A + B = 90° (Symmetric property)

6 + 2× B + B = 90° (Substitution property)

6 + 3·B = 90°

3·B = 90° - 6° = 84°

B = 84°/3 = 28°

B = 28°

From, A = 6 + 2 × B, we have;

A = 6 + 2 × 28° = 62°

A = 62°

First angle = A = 62°

Second angle = B = 28°

Third angle = C = 90°

The measure of the three angles are;

First angle is 62°

Second angle is 28°

Third angle is 90°.

C = 10t + 8, C = 12t is the set of equations used to model the situation.

Given that,

Online orders for concert tickets are $10 each, but there is a $8 service fee for each purchase. If you purchase your tickets the night of the show at the door, they cost $12 apiece.

Complete the sentence ( Let C be the total cost and let t be the number of tickets).

Online ticket purchases cost $10 plus an extra $8 service fee.

Consequently, total cost,C = 10t + 8

At the door, tickets are $12.

Consequently, total cost, C = 12t.

The equations used to model the situation are as follows:

C = 10t + 8

C = 12t

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Symbolic models are those that are based on mathematical formulas.

The goal of symbolic modelling is to help clients become more aware of their own "symbolic domain of experience," allowing them to create their own "metaphor landscape" and explore internal metaphors, which are believed by conceptual metaphor theory to influence behaviour.

What benefits do symbolic models offer?

One of the most significant and defining technologies of next-generation modelling methodologies is swiftly emerging as symbolic computation. It allows the freedom to easily create model equations, manage models more effectively, and reach the best outcomes more quickly.

Describe domain through an example.

the domain name example.com might be connected to the address 198.102. 434.8.

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Answer: No

Step-by-step explanation:

Graph: You can use the vertical line test to determine if it is a function. Draw a vertical line (going up and down) on the graph. If it only intersects one

point, then it is a function. If it crosses two points, it is not a function.

Chart: If the x repeats and the y does not repeat, it is not a function. y can repeat as much as it wants, as long as the x does not.

Lines: If one x connects to multiple y, it is not a function. If one y connects to multiple x, it is a function.

Coordinates: Same as the chart