determine the equation of line from the graph

Triangle ABC and the triangle EFG are congruent by the first and third statement.

What is the congruent diagram?

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

In the given example triangle ABC and triangle EFG having one same side of length 2.

By the ASA (Angle side angle) criteria, we want two angles are same then the triangles are congruent.

When "m ∠ B and m ∠ F"  and "m ∠ A and m ∠ E" are same then the triangles are congruent.

Therefore, the first option is correct.

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Answer:

16%.

Explanation:

In a recent math test:

• The average score = 75

• Standard Deviation = 10

To find: The percentage of people who scored an 85 or higher, P(X>85).

First, find the z-score when X=85.

Substitute the given values:

The people who scored an 85 or higher are 1 standard deviation away from the mean.

The percentage of people who scored an 85 or higher is 16%.

Answer:

Step-by-step explanation:

1. b. (2,14)

2. a. (-1,4)

3. c. (-2,2)

Answer:  1. b

               2. a

               3. c

Step-by-step explanation:

We will change the second equation to y form, then we get:

2x - y = - 6

    - y = -2x - 6

      y = 2x + 6

Then we plug in each point to see whether it fixes the equations.

a) 1. y = 3x + 8

      4 ?= 3(-1) + 8

      4 ?= -3 + 8

        4 x 5    

a) 2. y = 2x + 6

      4 ?= 2(-1) + 6

      4 ?= -2 + 6

        4 = 4

Point a is a solution of the second equation, but not a solution for the first equation.

b) 1. y = 3x + 8

   14 ?= 3(2) + 8

   14 ?= 6 + 8

     14 = 14  

b) 2. y = 2x + 6

   14 ?= 2(2) + 6

   14 ?= 4 + 6

     14 x 10  

Point b only fits the first equation, but does not fix (not a solution) of the second equation.

c) 1. y = 3x + 8

 2 ?= 3(-2) + 8

 2  ?= -6 + 8

    2 = 2

c) 2. y = 2x + 6

     2 ?= 2(-2) + 6

     2 ?= - 4 + 6

       2 =  2

Point c fits both the first equations and the second equations.

She travels 61.2 miles for work each week.

Addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

We have been given that the healthcare worker has 3 shifts each week. The route from her house to the hospital is 9.9 miles and the route back to her house is 10.5 miles.

The distance from her house to the hospital = 9.9 miles

The distance back to her house = 10.5 miles.

The total distance travel in one shift = 9.9 + 10.5 = 20.4 miles

The total distance travel in 3 shift = 3 x 20.4 = 61.2 miles

Hence, She travels 61.2 miles for work each week.

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The sample proportion is option(d) i.e, 0.32

What is Proportion?

A proportion is an equation in which two ratios are set equal to each other.

Given,

Number of successful outcomes  = 16

Total number of outcomes = 50

The sample proportion =

Number of successful outcomes / Total number of outcomes

Sample proportion = 16 / 50

                               = 0.32

Hence, the sample proportion is option(d) i.e, 0.32

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Answer:18

Step-by-step explanation:

The graph of g(x) with the graph of f(x): Option D, which is a shift of 2 units to the left, is correct.

What is Function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

We are aware that the graph of the modified function is:

for every parent function f(x).

g(x) = f(x + a)

is a left- or right-shift of the parent function f(x), depending on the value of a.

The shift is 'a' units to the left if a>0.

The shift is 'a' units to the right if a0.

Here, G(x) has been changed as follows:

G(x) = F(x + 2)

i.e. a=2>0.

2 units up: G(x) = F(x) + 2.

2 units down: G(x) = F(x) - 2.

2 units to the left: G(x) = F(x + 2).

2 units to the right: G(x) = F(x - 2).

Hence, Option D, which is a shift of 2 units to the left, is correct.

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By dividing $180 in the ratio of 2:3:4, we get 40,60 and 80

Solution

2 + 3 + 4 = 9

180 ÷ 9 = 20

Hence, we get the quotient of 20.

20 × 2 = 40

20 × 3 = 60

20 × 4 = 80

Hence, by dividing $180 in the ratio of 2:3:4, we get 40,60 and 80

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Answer:

x = 58°

∠P = 58°

∠PQR = 64°

Step-by-step explanation:

If you add the two nonadjacent angles together they will equal the exterior angle. Setup up an equation using that info.

[tex]58 +x=2x[/tex]

Solve for x.

[tex]58 +x-x=2x-x\\58=x[/tex]

Since ∠P is the same as x, ∠P = 58°

To find ∠PQR, add ∠P and ∠R together and then subtract from 180°. You subtract from 180° because the sum of the three angles of a triangle equal 180°.

58 + 58 = 116

180 - 116 = 64°

∠PQR = 64°

Using the normal distribution, the probabilities are given as follows:

a. Between 8 and 12 cases with side effects: 0.582 = 58.2%.

b. More than 16 cases with side effects: 0.0174 = 1.74%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the equation presented below:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution in this problem are given as follows:

p = 0.05, n = 200.

Hence the mean and the standard deviation of the approximation are given as follows:

For item a, using continuity correction, the probability of between 8 and 12 cases with side effects is the p-value of Z when X = 12.5 subtracted by the p-value of Z when X = 7.5, hence:

X = 12.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (12.5 - 10)/3.08

Z = 0.81

Z = 0.81 has a p-value of 0.7910

X = 7.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (7.5 - 10)/3.08

Z = -0.81

Z = -0.81 has a p-value of 0.2090.

0.7910 - 0.2090 = 0.582 probability.

For item b, the probability of finding more than 16 cases with side effects is one subtracted by the p-value of Z when X = 16.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (16.5 - 10)/3.08

Z = 2.11

Z = 2.11 has a probability of 0.9826.

1 - 0.9826 = 0.0174 = 1.74% probability.

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SOLUTION

From the image above

Considering the bigger right angle triangle,

We can obtain the expression of y from the smaller right angle triangle,

Using pythagora's rule, we have

Then, recall

Substite the expression for y², we have

Expand the paranthesis, we have

subtract 9 from both sides, we have

Divide both sides by 6, we obtain

Therefore

Answer: x= 12

SINCE A OF A RECTANGLE IS =L×B

[tex] = (12x - 6)(14 \frac{1}{6} ) \\ = (12x - 6)( \frac{25}{6} ) \\ = \frac{25}{6} (12x) + \frac{25}{6} ( - 6) \\ = 50x - 25[/tex]

THE SIMPLIFIED AREA IS =50x-25

The probability that the sample percentage will deviate from the population proportion by less than 3% is 0.9624, or 96.24%.

We must comprehend the central limit theorem and the normal probability distribution in order to answer this query.

Distribution of Normal Probabilities

The z-score formula can be used to address problems with normal distributions.

The z-score of a measure X in a set with mean and standard deviation can be calculated as follows:

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the probability that the measure's value is less than X, or the percentile of X. 1 is subtracted from the p-value, giving us the likelihood that the value of the metric exceeds X.

Imagine that 9% of a huge shipment of televisions were defective.

As a result, the sample size has a p value of 0.09

As a result, n=393

Standard deviation and the mean

u=p= 0.09

s= sqrt(p(1-p)/n)

s=sqrt(0.09*0.91/393)= 0.0144

What is the likelihood that the sample percentage and population proportion will deviate by less than 3%?

The ratio of 0.09 - 0.03 = 0.06 to 0.09 + 0.03 = 0.12 is the result of subtracting the p-value of Z when X = 0.12 from the p-value of Z when X = 0.06.

X = 0.12

By the Central Limit Theorem

Z= x-u/s

Z=2.08  has a p-value of 0.9812

X = 0.06

Z= x-u/s

Z=-2.08 has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

Therefore, The probability that the sample proportion and population proportion will deviate by less than 3% is 0.9624, or 96.24%.

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Answer:

Step-by-step explanation:

The probability that the sample percentage will deviate from the population proportion by less than 3% is 0.9624.

Distribution of Normal Probabilities

The z-score formula can be used to address problems with normal distributions.

The z-score of a measure X in a set with mean and standard deviation can be calculated as follows:

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p- value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the probability that the measure's value is less than X, or the percentile of X. 1 is subtracted from the p-value, giving us the likelihood that the value of the metric exceeds X.

Imagine that 9% of a huge shipment of televisions were defective.

As a result, the sample size has a p value of 0.09

As a result, n=393

Standard deviation and the mean u=p=0.09 s= sqrt(p(1-p)/n)

s=sqrt(0.09*0.91/393)=0.0144

The ratio of 0.09 -0.03=0.06 to 0.09 + 0.03 =0.12 is the result of subtracting the p-value of Z when X = 0.12 from the p- value of Z when X = 0.06.

X = 0.12

By the Central Limit Theorem

Z=x-u/s

Z-2.08 has a p-value of 0.9812

X = 0.06

Z=x-u/s

Z=-2.08 has a p-value of 0.0188

0.9812 -0.0188=0.9624

Therefore, The probability that the sample proportion and population proportion will deviate by less than 3% is 0.9624, or 96.24%.

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The system of equations has no solution when solving with elimination or substitution

so No solution is the answer

checking

y = 5x -6 ------(1)

y =5x +2------(2)

5x +2 = 5x-6

5x -5x = -6 -2

0 =-8

hence there is no solution since all variables are eliminated

The measure of ∠C in the given triangle is 58°.

According to the question,

We have the following information:

ACD is a triangle where we have BD as an altitude on the side AC.

Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.

Now, we have two right-angled triangle: ABD and CBD.

We have ∠ADB = 32°.

Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).

We know that the sum of the three angles in a triangle is 180°.

In ΔCBD, we have:

∠B + ∠C + ∠CDB = 180°

90° + ∠C + 32° = 180°

∠C + 122° = 180°

∠C = (180-122)°

(Moving 122 from the left hand side to right hand side will result in the change of sign.)

∠C = 58°

Hence, the measurement of ∠C in the given triangle is 58°.

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Given:

There are given that a total of 42 boys and 28 girls in the photography club.

Explanation:

According to the question:

We need to find the ratio.

So,

We can see a total of 28 girls and 6 more girls.

So,

The total number of girls is:

Then,

The numbers of boys to the numbers of girls in the end is:

Final answer:

Hence, the ratio is shown below:

Both equations' solutions are found at the point (-2, 2). When point (-1,4), the 2x-y=-6 yields the correct point. The second equation is as a result. The point (2, 14) is the answer to the first equation because it provides the answer to the first equation but not the second.

The word equation and its cognates in other languages may have slightly different meanings; for example, in French an equation is defined as containing one or more variables, while in English any well-formed formula consisting of two expressions related with an equals sign is an equation. An equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.

3x-y=-8

2x-y=-6

given points are (-1,4), (2,14), (-2,2)

On solving the equation,

3x-y=-8

-(2x-y=-6)

x=-2

y=2

The point (-2,2) is the solution to both equations.

The point (-1,4) on putting in the 3x-y=-8 will not give solution but when put in the 2x-y=-6, it gives the result. so it the solution to second equation.

The point (2,14) is the solution to the first equation as it gives the answer to first but not to the second equation.

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0.895 with 95 repeating on and on as a simplified fraction can be re-written as 887/990.

By critically observing the given number, we can reasonably and logically deduce that it has three (3) repeating digits. Since this number has three (3) repeating digits, we would have to multiply n by 1000 as follows:

1000n = 0.895

1000n = 895.95        .......equation 1.

10n = 8.95            .......equation 2.

Subtracting equation 2 from equation 1, we have:

1000n - 10n = 895.95 - 8.95

990n = 887

Dividing both sides by 990, we have:

n = 887/990

Simplified fraction, n = 887/990.

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Complete Question:

Write 0.895 with 95 repeating on and on as a simplified fraction.

Answer:

x = 113

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 8 , then

sum = 180° × 6 = 1080°

sum the interior angles and equate to 1080

x + 137 + 144 + 139 + 123 + 150 + 142 + 132 = 1080

x + 967 = 1080 ( subtract 967 from both sides )

x = 113

we know that

The domain of a function is the set of all possible values of x

The range of a function is the complete set of all possible resulting values of y

so

In this problem

The domain is the interval {-1,3}

so

The range is the interval {-4,5}

so

answer Option A

The point B has a coordinates of (-3, 7) after the dilation

From the question, the coordinates of the point B are given as

B = (1, 7)

The scale factor of dilation is given as

k = 3

The center of dilation is given as

Center = (3, 7)

The rule of the dilation is calculated using

B' = (k(x - a) + a, k(y - b) + b)

Where

(a, b) = (3, 7)

k = 3

(x, y) = (1, 7)

So, we have

B' = (3 * (1 - 3) + 3, 3 * (7 - 7) + 7)

Evaluate

B' = (-3, 7)

Hence, the coordinates of the point B is (-3, 7)

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Answer:

1/2 -> 3/4 -> 4/5 -> 9/10

Step-by-step explanation:

1/2 = 50%

3/4 = 75%

4/5 = 80%

9/10 = 90%

How to figure out:

1/2 - Divide 100/2 = 50. So 1/2 of 100 is 50 so 50%

3/4 - Divide 100/4 = 25. Now multiply 25 x 3 = 75 so 75%

4/5 - Divide 100/5 = 20. Now multiply 20 x 4 = 80 so 80%

9/10 - Divide 100/10 = 10. Now multiply 10 x 9 = 90 so 90%

The arc length is equal to the measure of the arc in radians only if the radius of the circle is 1 unit, for all the other circles this is false.

For a circle of radius R, if we have an arc defined by an angle of θ radians, then the length of that arc is:

L = R*θ

Particularly, the length is equal to the measure in radians only if the radius of the circle is R = 1:

L = 1*θ

So the statement is only true for the unit circle but is false for every other circle.

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Proportionately, if there are 6 blue beads in the bag, and blue beards are 6 or 2/9 of the total beads, the number of purple beads in the bag is 21.

Proportion refers to the numerical ratio of a value to another.

Proportion shows the quantity of a value contained in another variable.

Since proportions are fractional values, like ratios, they are represented using decimals, fractions, and percentages.

The ratio of blue beards to purple beads = 2:7 or 2/9

The number of blue beads in the bag = 6

The total number of beads in the bag = 27 (6/2 x 9)

The number of purple beads in the bag = 21 (27 x 7/9)

Thus, based on the given proportional ratio of the blue beads to the purple beads, there are 21 purple beads in the bag.

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The graph of the linear function 5x + 3y = 20 is given at the end of the answer.

To build the graph of a linear function, we identify two points on the line, and then plot a line passing through them.

In this problem, the function is:

5x + 3y = 20.

The points that we are going to choose are the intercepts. The x-intercept is the value of x when y = 0, hence:

5x = 20

x = 20/5

x = 4.

Meaning that point (4,0) is on the graph of the function.

The y-intercept is the value of y when x = 0, hence:

3y = 20

y = 20/3

y = 6.67.

Meaning that point (0, 6.67) is on the graph of the function.

The graph is plotted with a line passing through the points (4,0) and (0, 6.67).

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The correct representation of the inequality is x > 5 or –6x + 15 < 10 – 5x.

The inequality can be best represented as follows;

–3(2x – 5) < 5(2 – x)

An inequality is a mathematical expression that has the signs <, >, ≤ and ≥.

Therefore,

–3(2x – 5) < 5(2 – x)

open the brackets

- 6x + 15 < 10 - 5x

Lets solve further by subtracting 15 from both sides of the inequality.

- 6x + 15 < 10 - 5x

- 6x + 15 - 15 < 10 - 15 - 5x

- 6x < - 5 - 5x

add 5x to both sides of the inequality.

- 6x < - 5 - 5x

- 6x + 5x < - 5 - 5x + 5x

-x < - 5

divide both sides by  -1

Therefore,

x > 5

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The solution of the given inequality is x > 5 which is the correct representation of x > 5 or –6x + 15 < 10 – 5x.

The inequality is given in the question as

–3(2x – 5) < 5(2 – x)

Open the parenthesis and apply the distributive property of multiplication,

⇒ - 6x + 15  <  10 - 5x

Subtract 15 from both sides of the above inequality,

⇒ - 6x + 15 - 15 < 10 - 15 - 5x

⇒ - 6x < - 5 - 5x

Add 5x to both sides of the inequality,

⇒ - 6x + 5x < - 5 - 5x + 5x

⇒ -x < - 5

Multiply both sides by  -1 and flip the sign of inequality

⇒ x > 5

Therefore, the solution of the given inequality is x > 5.

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Answer: 1

Step-by-step explanation: Rise over run, Rise/run. The rise is how much the line goes up or down vertically. The run is how far the line goes until it intersects through a square. The slope is 1 because if you look at the line specifically at the first dot, you just have to go down one and right one as it intersects the square to find the slope.

By likelihood, she can utilize the pens in 1024 distinct ways during the week.

Probability is the study of possible outcomes of events, together with the probabilities and distributions of those occurrences.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

To calculate probability, divide the total number of outcomes by the total number of possible possibilities. There are differences between probability and odds.

Odds are computed by dividing the likelihood that an event will occur by the likelihood that it won't.

From the stated circumstance,

Total ways = [tex]4^{5}[/tex]= 1024

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