Which triangle congruence postulate or theorem proves that these triangles
are congruent?

The rate of change of water level in inches per hour is 7.5 inches per hour.

According to the question,

We have the following information:

At 1:00, the water level in a pool is 13 inches. At 3:00, the water level is 28 inches.

Now, in order to find the rate of change of water level, we will find the increase in water level in the given time.

So, the elapsed is 2 hours (3-1).

Increase in water level:

28-13

15 inches

Now, rate of change:

Increase in water level/number of hours

15/2

7.5 inches per hour

Hence, the rate of change of water level in inches per hour is 7.5 inches per hour.

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Has 5 1/2 cups or 11/2

Needs 1 3/4 or 7/4

Divide how much she has by how much she needs

(11/2) / (7/4)

Is also the same as

(11/2) * (4/7)

Which equals

= 44/14

= 22/7

or 3 1/7

The equation relating N to M be N = 3M and

Kevin needs to read 57 Novels in 19 months.

Given, Kevin needs to read 3 novels each month.

Let N be the number of novels Kevin needs to read in M months.

According to question,

1 month = 3 novels

M months = 3M novels

Now, as he needs to read a total of N novels.

So, N = 3M.

Also, the number of novels he needs to read in 19 months be,

N = 3×19

N = 57 novels.

Hence, the equation relating N to M be N = 3M and the number of novels Kevin needs to read in 19 months be 57.

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Hannah travel for 40 minutes when Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48 minutes.

In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.

Given,

Let Raoul travel in minutes be x

So, Hannah travel in minutes will be 5x

Together, they travel for 48 minutes.

Equation:

x + 5x = 48

6x = 48

x = 8

Hannah travel in minutes will be 5x.

Total travel by Hannah:

5(8)

40

Hannah travel for 40 minutes when Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48 minutes.

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Answer: x=2±√3

Step-by-step explanation:

[tex]\displaystyle\\x^2-4x+1=0\\\\ax^2+bx+c=0\\\\a=1\ \ \ \ \ b=-4\ \ \ \ \ c=1\\\\D=b^2-4ac\\\\D=(-4)^2-4(1)(1)\\\\D=16-4\\\\D=12\\\\\sqrt{D} =\sqrt{12}\\\\\sqrt{D}=\sqrt{3(4)} \\\\\sqrt{D}=2\sqrt{3}\\\\ Hence,\\\\x=\frac{-bб\sqrt{D} }{2c} \\\\x=\frac{-(-4)б2\sqrt{3} }{2(1)} \\\\x=\frac{4б2\sqrt{3} }{2} \\\\x=\frac{2(2б\sqrt{3}) }{2} \\\\x=2б\sqrt{3}[/tex]

The value of solution of equation is,

⇒ x = (2 ± √3)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

Quadratic equation is,

⇒ x² - 4x + 1 = 0

Now, We can simplify as;

⇒ x² - 4x + 1 = 0

⇒ x = - (-4) ± √(-4)² - 4×1×1 / 2

⇒ x = (4 ± √16 - 4) / 2

⇒ x = (4 ± √12) / 2

⇒ x = (4 ± 2√3) / 2

⇒ x = (2 ± √3)

Thus, The value of solution of equation is,

⇒ x = (2 ± √3)

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Sale price of the house should be $141509

Amount = $150000

Commission% = 6 %

By formula

Selling price x commission rate = commission paid

SP × 6% = commission paid

(6·SP)/100 =  commission paid …. (1)

Again by formula

Selling price – commission paid = net amount to seller

SP - (6·SP)/100 = 150000   (from equation 1)

SP ( 1 - 0.06) = 150000

SP = 141509.43 ≈ 141509

$141509 should be the sale price of the house.

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The adjustment factor (T) which adjusts the exponential smoothing forecast , does this adjustment for a. Trend.

A big part of the Adjusted exponential smoothing forecasting method is the use of an adjustment factor which has the purpose of adjusting the smoothing forecast for a trend.

If this trend is found, then there is a need to smoothen it out of the data so that the model is more trustworthy. It is important that this trend is removed to ensure that the forecast does not have a time bias.

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The correct choice for the given Column A is given below respectively to Column B i.e. 1(a), 2(b), 3(d), 4(f), and 5(c).

What is an angle?

Two straight lines or rays intersecting at the same endpoint is called an angle. The vertex of an angle is the point at which all points meet.

From question,

angle 7 and 6 = Vertical angles

angle 1 and 8 = Alternate Exterior angle

angle 4 and 5 = Alternate Interior angle

angle 2 and 6 = Corresponding angle

angle 6 and 8 = Supplementary angle

Hence, the respective answer for the given column A is provided above in Column B.

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Answer:

x = 60, -70

Step-by-step explanation:

Let's move the constant (-130) to the right by adding it to both sides.

[tex]\sqrt{x} 4(x+5)^{2} =130[/tex]

Now, we can rewrite the equation as (since the square root and square cancel):
2 × | x + 5 | = 130

To get rid of the 2 multiplication, we can divide both sides by 2:

| x + 5 | = 65

This leaves us with 2 equations:

x + 5 = 65

x + 5 = -65

Simplify.

x1 = 60

x2 = -65

The 1/2, 5/12, and 1/2 hour duration it takes Tiffany, Gary, and Noland to walk round the park provides the following;

1) The time in minutes it takes Tiffany to walk round the park is 30 minutes

Gary takes 25 minutes and Noland takes 20 minutes to walk round the park

2) Tiffany will go round 12 times, Gary will go round 12 times and Noland will go round the park 15 times before all three will meet again.

3) The solution to question 2 is arrived at by dividing the least common multiple of 30, 25, and 20, which is 300 by 30, 25, and 20 respectively

The least common multiple also known as the L.C.M. is the least number two or more numbers have as their multiples.

The time it takes Tiffany to walk around the track = 1/2 hour

The time it takes Gary to walk round the park = 5/12 hour

The time it takes Noland to walk round the park  = 1/3 hour

1) The duration in minutes it takes each person to walk round the park are found using the conversion factor for minutes and hours as follows;

60 minutes = 1 hour

Therefore;

1/2 hour = 30 minutes

It takes Tiffany 30 minutes to walk around the track

5/12 hour = 25 minutes

It takes Gary 25 minutes to walk around the track

1/3 hours = 20 minutes

It takes Noland 20 minutes to walk round the park

2) The number of times each person will go round the track before all three meet again is given by the least common multiple of 30, 25, and 20, which is 300

Therefore;

The number of times Tiffany would walk round the park before all three meet again is 300 ÷ 30 = 10

The number of times Gary would walk round the park = 300 ÷ 25 = 12

The number of times Noland walks round the park = 300 ÷ 20 = 15

When all three meet again, Tiffany will halve walked 10 times, Gary would have walked 12 times and Noland would have walked 15 times round the park.

3) The solution for question 2 was arrived at by looking for the lowest common multiple of the durations it takes each of the three persons to walk round the park. The least common multiple provides the time at which all three will have made complete cycles simultaneously.

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The volume of an object is entirely dependent on its height. You need to know an object's geometric shape, such as its cube, rectangle, or pyramid, in order to calculate its height.

What are geometric shapes?

Geometric shapes are closed figures created using points, line segments, circles, and curves. Such shapes can be seen everywhere around us.

Rectangular Objects' Height

Height x Depth x Width is the equation for a solid rectangle's volume. To get the height of a rectangular item, divide the volume by the product of the length and width.

Size of Cube

A cube is a type of rectangle with identical sides. Therefore, cube the length of any side to find the volume. Calculate the cube root of a cube's volume to determine the height.

Cylinder's height

A cylinder is a straight rod or peg with a circular cross-section that is circular from top to bottom and has the same radius. The circle's area (pi x radius2) multiplied by the height gives the object's volume. To determine the height of a cylinder, divide its volume by the radius's squared value multiplied by pi.

Size of the Pyramid

A square pyramid has four triangular sides that come together at a point on the summit and a flat square base. Volume is calculated as follows: length x width x height. To get a pyramid's height, multiply the volume by three and then divide the result by the base's surface area.

Height of Pyramid

A square pyramid has a flat square base and four triangular sides that meet at a point on the top. The volume formula is length x width x height ÷ 3. Triple the volume of a pyramid and then divide that amount by the area of the base to calculate its height.

size of the prism

Prisms come in a variety of shapes, some have bases that are triangular, while others have bases that are rectangular. Both times, the cross-section is the same throughout, just like a cylinder. The area of the base times the height equals the prism's volume. Therefore, multiply the base area of a prism by its volume to determine its height.

Therefore, the volume of an object is entirely dependent on its height. You need to know an object's geometric shape, such as its cube, rectangle, or pyramid, in order to calculate its height.

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The Solutions for given inequalities are -2, 5, and -4

Inequalities are algebraic expressions in which both sides are not equal to each other. In inequality, we compare two values with signs like less than (<) (or less than or equal to), greater than (>) (or greater than or equal to), or not equal to sign(≠), etc.

Here we have three inequalities

m -1 < -3, - 4y < - 20, and 5 + b > 1  

We can solve each equation and can give a graph as given below

m -1 < -3  

Add 1 on both sides

=> m - 1 + 1 < -3 + 1

=> m < -2

- 4y < - 20  

Divide both sides with - 4 on both sides

=> - 4y/4 < - 20/4

=>  -y  < - 5

Multiply with -1 on both sides

=> -1(-y) < -5(-1)

=>   y < 5

5 + b > 1  

Subtract - 5 on both sides

=> 5 + b - 5 > 1 - 5

=> b > -4

Therefore,

The Solutions for given inequalities are -2, 5, and -4

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The next equation will be 6²-4²=2×10.

Here, we have given three equations and we have to find out the next equation.

The first three equations are like this

1. 3²-1²=2×4

2. 4²-2²=2×6

3. 5²-3²=2×8

Now,

As from the equation

On the L.H.S. we can see that every time it is creating a sequence

Like,  every time it is subtracting square value of the one’s from the another number’s square

Which is the value we got from adding 2 in first value.

And on the R.H.S.

We can say that every time 2 multiplies with the next even number than the previous one

So,

The last equation was 5²-3²=2×8

Therefore,

The next equation will be

6²-4²=2×10

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Answer: $7.95

Step-by-step explanation:

95.40/12

= $7.95

Answer:

unit rate per book

= $95.40 ÷ 12 books

= $7.95 per book

The  z-score to percentile of 1 = -2.326

In this question, we need to find the z-score to percentile of 1

We know that a Z-scores is a normalized score that used to compare values relative to their population. z-score represents a specific location in the normal distribution, so that there is a certain area that is to the left of that z-score. The percentile associated to a z-score is nothing but the area to the left of that z-score.

the  z-score to percentile of 1 = -2.326

Therefore, the  z-score to percentile of 1 = -2.326

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Answer:

The x-intercept is -3

Step-by-step explanation:

Answer:

x = -3, y = 3  ----> (-3,0) and  (0, 3)

Step-by-step explanation:

Required: Find the X-intercept.

1) Let y = 0 to find the x-intercept (s):

0 = x + 3

2) Subtract 3 from both sides.

-3 = x

3) Switch sides.

x = -3

Just to find the y-intercept.

1) Let x = 0 to find the y-intercept (s):

y = 0 + 3

2) Simplify:
y = 3

The equation of the line that passes though the point (-6,-7) and is perpendicular to the line 6x + 5y = 30 is y = (5/6)x -2 .

In the question ,

it is given that

the required line is perpendicular to the line 6x + 5y = 30 ,

rewriting the line we get

5y = -6x + 30

y = (-6/5)x + 6

the slope of perpendicular is -6/5 ,

the slope of the required line will be 5/6 .

The equation of the line passing through (-6,-7) with slope 5/6 is written as

(y - (-7)) = (5/6)(x - (-6))

y + 7 = (5/6)(x + 6)

y + 7 = (5/6)x + 5

y = (5/6)x + 5 -7

y = (5/6)x -2

Therefore  , the equation of the line is y = (5/6)x -2 .

The given question is incomplete , the complete question is

What is an equation of the line that passes through the point (−6,−7) and is perpendicular to the line 6x+5y=30 ?

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Value of x is 2 and y is 0 of the equations 2x + y = 4 and x - y = 2.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Given,

Equation:

2x + y = 4

x - y = 2

From equation 2,

x = 2 + y

Equating in equation 1,

Using substitution method,

2(2+ y) + y = 4

4 + 2y + y = 4

3y = 0

y = 0

x = 2 + y

x = 2+ 0

x = 2

Value of x is 2 and y is 0 of the equations 2x + y = 4 and x - y = 2.

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Answer:

Step-by-step explanation:

12x6 = 72

So 40x2

72 pies she needs 80

So awnser is no she needs 2 more boxes

The angles are equal because the angles are corresponding and the value of x is 7.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

It is given that:

Two parallel lines are intersected by a transversal.

The angles shown in the picture is called corresponding angles.

The angles are equal to each other

75 = 11x - 2

11x = 77

x = 7

Thus, the angles are equal because the angles are corresponding and the value of x is 7.

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Answer:

Step-by-step explanation:

The margin of error is obtained by multiplying the standard error by t*.

The margin of error can be calculated in two ways, depending on whether you have population parameters or sample statistics:

Margin of error (parameter) = critical value x population standard deviation Margin of error (statistic) = Critical value x Sample standard error

A margin of error is a statistical metric that accounts for the difference between actual and projected survey results in a random sample.

In layman's terms, the margin of error measures the degree of unpredictability in data and research results. The margin of error formula is calculated by multiplying a critical factor. The result is then divided by the square root of the sample's number of observations.

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Kayla's expected value for a 2- point shot is 1 point.

What is expected value?

The expected value, also known as expectation, expectancy, arithmetical expectation, mean, average, first or moment, is a generalization of the weighted average in the field of probability theory. Informally, the estimation is the arithmetic mean of a significant number of values of a random variable that were independently chosen. A weighted average of all potential outcomes constitutes the expected value of the a random variable with such a finite number of outcomes. When there is a continuum of potential outcomes, integration defines the expectation. The expectation is provided by Lebesgue integration in the measure theory-based axiomatic foundation for probability.

Sol- The expected value is calcuated using the formula:

EV= x.P(x)

where x is the weight/value of the event, and P(x) is the probability of the event occurring.

For a 2-point shot, we have:

X=2

P(x) = 50/100 = 0.5

There for the expected value will be -

EV = 2×0.5 = 1

Thus,

The expected value will be 1 point.

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Answer:

$129.27 Sale price Including tax

Step-by-step explanation:

Original Price - Discount = Sale Price

130 - 130(0.12) = 114.40

114.40 + 114.40(0.13) = 129.27 Include sale tax

The amount it would cost Rachel to shelve her book collection is $51.80.

The first step is to determine the total width of the 79 books in the collection.

Total width = width of one book x total number of books

Total width = 1.5 x 79

Total width = 118.50 inches

The second step is to calculate the number of shelves that would be needed for the book collection.

Number of shelves that would be needed = total width of the collection / width of one shelf

Number of shelves that would be needed = 118.50 / 34.50

Number of shelves that would be needed = 3.4 ≈ 4

Total cost to shelve the book collection = cost of one shelf x total number of shelves needed

Total cost to shelve the book collection = 4 x $12.95 = $51.80

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By solving a system of equations, we can see tha the value of b is 3.81

We know that we have a exponential function of the form:

f(x)=  a*(b)^x

And we know that:

f(5) = 20 and f(9) = 211

Then we can write a system of equations:

20 = a*(b)^5

211 = a*(b)^9

If we take the quotient between the second equation and the first one, we get:

211/20 = (a*(b)^9)/(a*(b)^5)

211/20 = b^(9 - 5)

211 = b^4

(211)^(1/4) = b

3,81 = b

The value of b is 3.81

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Answer:

Assuming this is a triangle, angles would equal up to 180 degrees

Step-by-step explanation:

105 + 25 = 135

180 - 135 = a, a = 45 degrees

The proportionality is a relation between two quantities. The equation for the given cases can be written as 3g = 5m,  5m = 3g, 5g = 3m and g = 8 m.

When two quantities have some dependence in their values they can be said to be proportional to each other.

It can be of two types such as direct and indirect.

The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies that the value of one quantity is increasing while the other is decreasing.

Given that,

The number of gallons of water = g,

The number of minutes = m,

And, the equation for the given condition as,

g = 3 / 5 m

The equation for each minute the washing machine runs, it uses five thirds gallons of water is given as,

g = 5 / 3 m

=> 3g = 5m

The equation for each minute the washing machine runs, it uses three fifths of a gallon of water is given as,

m = 3 / 5 g

=> 5m = 3g

The equation for each gallon of water the washing machine uses, it runs for three fifths of a minute is given as,

g = 3 / 5 m

=> 5g = 3m

The equation for each gallon of water the washing machine uses, it runs for 8 minutes is given as,

g = 8 m

Hence, the equation for the given conditions can be written as,

3g = 5m,  5m = 3g, 5g = 3m and g = 8 m.

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The equation of ellipse in standard form is:

[(2x + 18)² /8²] + [(y + 5)² /8²] = 1

The equation of the ellipse in general conic form is,

4x² + y² + 72x+10y + 285 = 0

comparing given equation with Ax^2+Bxy+Cy^2+Dx+Ey+F=0 we get,

A = 4, B = 0, C = 1, D = 72, E = 10, F = 285

Consider given equation of conic,

4x² + y² + 72x+10y + 285 = 0

4x² +72x + y² + 10y = - 285

4x² +72x + 324 + y² + 10y = - 285 + 324

(2x + 18)² + y² + 10y + 25 = - 285 + 324 + 25

(2x + 18)² + (y + 5)² = 64

(2x + 18)² + (y + 5)² = 8²

(2x + 18)² /8² + (y + 5)² /8² = 1

Therefore, the equation of ellipse in standard form is:

[(2x + 18)² /8²] + [(y + 5)² /8²] = 1

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