Simplify the following using the properties of exponents.

The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 1.25 units.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

The line AB has the following coordinates.

A = (1, 4)

B = (6, 4)

The distance between AB is given as:

AB = √(6 - 1)² + (4 - 4)²

AB = √(5)²

AB = 5

The slope of AB = 0.

For the dilated rectangle the slope remains the same.

The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 5/4 = 1.25 units.

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The correct question is:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{4} {x}^{2} - 4 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{4} {x}^{2} = 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} = 4 \times 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \sqrt{4 \times 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \pm4[/tex]

[ but since we have been asked for positive solution, it will be 4 ]

Hence, the correct choice is : A.) 4

Answer:

n = 3

Step-by-step explanation:

Starting equation:

2n + 4 = n + 7

Subtract by n on both sides:

n + 4 = 7

Subtract 4 on both sides

n = 3

Check to see if the answer works:

2(3) + 4 = 3 + 7

6 + 4 = 3 + 7

10 = 10

The solution works

n = 3

Answer:

121

Step-by-step explanation:

1242-150=1092/9 = 121 (remainder 3)

Answer: 121

Step-by-step explanation: 1241 - 150 / 9

Answer:

Step-by-step explanation:

Let's call the length of the winning jump "w".

Sarah's best jump is 12% more than her first jump, which was 4.25m. So her best jump was 4.25m * 1.12 = 4.77m.

However, her best jump is 15% lower than the winning jump, so we can set up an equation to solve for w:

4.77m * 1.15 = w

Solving for w:

w = 4.77m * 1.15 = 5.51m

So the winning jump was 5.51m.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer: Y would be 4

If you look at the graph and find 7 on the x axis where the inputs are, you can see that if you go up, the only output for 7 is 4.

Answer:

A

Step-by-step explanation:

The line has a negative slope, with a y-intercept of (0,-3), and an x-intercept of (-2,0)

According to the information, the area of the parallelogram plotted from the points would be: 36 cm²

To find the area of the parallelogram we must divide the parallelogram into a quadrilateral section and another triangular section and find the area of these segments.

According to the above, we can infer that the area of the quadrilateral zone would be

On the other hand, the area of the triangular section would be:

Additionally, we must multiply the area of the triangular segment by two because there are two triangular sections in the parallelogram. Finally we have to add the area of the quadrilateral and triangle segments to get the total area.

Note: This question is incomplete. Here is the complete information:

TASK

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Answer:

A.  9.4 mi

Step-by-step explanation:

Sketch a right triangle with legs of 8 and 5.  Shortest distance back to the starting point is the hypotenuse (h) of the triangle:

h² = 8² + 5² = 89

h = √89 = 9.43 mi

The best way to represents the change in the vertices of rectangle ABCD to rectangle A'B'C'D' in the attached graph is given by :

option A. (x, y ) → (2x, 2y).

From the attached graph we have,

Coordinates of rectangle ABCD are :

Coordinate of vertex A ( -3, -2 )

Coordinate of  vertex  B ( -3,  2 )

Coordinate of  vertex  C ( 3, 2 )

Coordinate of  vertex  D ( 3, -2 )

And coordinates of A'B'C'D' are:

Coordinate of  vertex  A' ( -6, -4 )

Coordinate of  vertex  B' ( -6, 4 )

Coordinate of  vertex  C' ( 6, 4 )

Coordinate of  vertex D' ( 6, -4 )

Coordinate of rectangle ABCD gets dilated by the scale factor of :

Scale factor of 'x' coordinate  = -6 / -3

                                                 = 2

Scale factor of 'y' coordinate  = -4 / -2

                                                 = 2

Change in the vertices of rectangle ABCD to A'B'C'D' is given by :

( x , y ) → ( 2x , 2y )

Therefore, the vertices of rectangle ABCD changed to A'B'C'D' is equal to option A. ( x , y ) → ( 2x , 2y ).

The above question is incomplete, the complete question is:

Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?

A) (x, y ) → (2x, 2y)

B) (x, y ) → (1. 5x, 1. 5y)

C) (x, y ) → (3x, 3y)

D) (x, y ) → (4x, 4y)

Graph is attached.

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The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The diagonals of the rhombus will be the same as the dimension of the rectangle that is 8 cm and 6 cm.

Then the area of the rhombus is given as,

A = (Product of diagonal of rhombus) / 2

A = (8 x 6) / 2

A = 48 / 2

A = 24 square centimeters

The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

The diagram is shown below.

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After 3 years the rate of simple interest charged at this to Chloe bank is  7%

We can start by using the formula for simple interest:

Simple Interest = Principal * Rate * Time

where the principal is the amount borrowed, the rate is the interest rate as a decimal, and the time is the duration of the loan in years.

Plugging in the given values, we get:

168 = 800 * Rate * 3

Solving for the rate, we get:

Rate = 168 / (800 * 3) = 0.07

Hence,

The rate of simple interest charged at this bank is 0.07, or 7% as a percentage.

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The total number of possible passwords is 17,576,000.

There are several steps involved in calculating the total number of possible passwords.

Step 1: Determine the number of possible choices for the first lowercase letter. Since there are 26 letters in the alphabet, and the password consists of lowercase letters, there are 26 choices for the first letter.

Step 2: Determine the number of possible choices for the second lowercase letter. Since there are 26 letters in the alphabet and repetition is allowed, there are 26 choices for the second letter.

Step 3: Determine the number of possible choices for the capital letter. Since the password requires a capital letter, there are 26 choices for this position.

Step 4: Determine the number of possible choices for the first digit. Since there are 10 digits (0-9), there are 10 choices for the first digit.

Step 5: Determine the number of possible choices for the second digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the second digit.

Step 6: Determine the number of possible choices for the third digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the third digit.

Step 7: Determine the number of possible choices for the fourth digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the fourth digit.

Step 8: Multiply the number of choices for each position together to get the total number of possible passwords.

Using the multiplication rule of counting, we get:

Total number of possible passwords = (Number of choices for the first lowercase letter) x (Number of choices for the second lowercase letter) x (Number of choices for the capital letter) x (Number of choices for the first digit) x (Number of choices for the second digit) x (Number of choices for the third digit) x (Number of choices for the fourth digit)

Total number of possible passwords = 26 x 26 x 26 x 10 x 10 x 10 x 10

Total number of possible passwords = 17,576,000

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The linear regression of the data is given as follows:

y = 25.1x + 150.4.

The estimate for the year in which the profit would reach $482,000 is of:

2019.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points for this problem are given as follows:

(0, 147), (1, 167), (2, 209), (3, 239), (4, 250), (5, 267).

Hence the equation is of:

y = 25.1x + 150.4.

The estimate for the year in which the profit would reach $482,000 is x years after 2006, when y = 482, hence:

482 = 25.1x + 150.4.

x = (482 - 150.4)/25.1

x = 13.

2006 + 13 = 2019 -> year.

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a) The Equation is  7.65x + 50 = 149.45.

b) The customer used the car for 13 hours.

c)  If the car used for 2 days i.e., 48 hours then the amount will be $471.12

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given that;

Members of a car sharing program pay a fee of $50 per month plus $7.65 for every hour they use a car.

And, a members bill was $149.45 last month.

a) Let number of hours for the customer use a car last month = x

So, 7.65x + 50 = 149.45

7.65x = 149.45 - 50

7.65x = 99.45

x = 13

b) The customer used the car for 13 hours.

c) If the car used for 2 days i.e., 48 hours

= 7.65x + 50

= 7.65(48)+ 50

= 471.2

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The final count of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set is 39.

To determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set {1, 2, 3, 5, 8, 13, 21, 34, 55}, we can use a process of elimination.

First, we can list all the possible sums of two distinct elements of the set. This gives us a total of 28 sums.

Next, we can identify all the integers between 3 and 89 that can be expressed as the sum of two distinct elements of the set. We can do this by checking each integer between 3 and 89 to see if it can be written as a sum of two elements of the set. If an integer can be written as a sum of two elements of the set, we can cross it off the list.

After eliminating all the integers that can be written as a sum of two elements of the set, we are left with the integers that cannot be expressed as such.

In summary, we can determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set by listing all possible sums, identifying the integers that can be expressed as such sums, and eliminating them from the list.

The remaining integers are those that cannot be expressed as the sum of exactly two elements of the set.

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Answer:

160 pounds of algae

Step-by-step explanation:

10 times 2 is 20   ( first 5 hours )

20 times 2 is 40  (10 hours)

40 times 2 is 80 (15 hours)

80 times 2 is 160 ( 20 hours)

there would be 160 pounds of algae

Answer:

since y = 0 when x = 0

Step-by-step explanation:

We can start by solving for y in the equation:

y * x = 3/5 y

Dividing both sides by y:

x = 3/5

So the equation y * x = 3/5 y can be simplified to:

y = 5/3 x

This equation shows that there is a proportional relationship between y and x, where y is always equal to 5/3 times x. This relationship can be represented on a graph by plotting points (x, y) and drawing a line through them. The slope of the line will be 5/3, and the y-intercept will be 0, since y = 0 when x = 0.

Answer:

y = ±1/√5

Step-by-step explanation:

3y = 3/5y

⇒3y×5y = 3

⇒15y² = 3

⇒y² = 3/15

⇒y² = 1/5

⇒y = ±1/√5

The shortest distance is 5.83 miles as we calculate this by distance formula.

A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:

PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])

The school is located 5 miles west of your home the co ordinate is (-5,0)

The playground is 3 miles south of the school so co - ordinate is (0,-3)

shortest distance  = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])

√([tex]5^{2} +3^{2}[/tex]) = √34

=5.830 miles

And this Question also can be do by right angle triangle method

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Answer:

i think this the answer

Step-by-step explanation:

26×14=ans

20×14+6×14=the same answer

10×26+4×26=same answer

The value of sin (θ/2) in the trigonometry is π/9

Information given in the problem

tan θ = 7/8,

where

0 < θ <  π/2

solving for θ, from tan θ = 7/8

tan θ = 7/8

θ = arc tan (7/8)

θ = 0.7188 radians

soling for sin (θ/2)

= sin (θ/2)

= sin (0.7188/2)

= 0.3517 approximately π / 9

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The value of x is given as follows:

x = 40.5.

Similar triangles share these two features:

The two triangles in this problem are similar, with the bisection, hence the proportional relationship for the side lengths is given as follows:

x/45 = 18/20

The relationship can be simplified as follows:

x/45 = 0.9.

Applying cross multiplication, the value of x is obtained as follows:

x = 45 x 0.9

x = 40.5.

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It is a biased sample.

What is meant by a random sample?

Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.

A random sample is one in which each individual, thing, or event has an equal chance of being chosen. Compared to other types of samples, a random sample has a higher likelihood of being representative of the total population. A skewed sample is one that does not fairly represent the population as a whole.

Here Dorthy considered only the first 20 people and not the whole population so this is not a random sample and it is a biased sample.

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A)  The mean of 2018 scores: μ₂₀₁₈ = 75

 The mean of 2019 scores: μ₂₀₁₉ = 75

 The standard deviation of 2018 scores: s₂₀₁₈ = 2.07

 The standard deviation of 2019 scores: s₂₀₁₉ = 5.26

B) The primary difference is that variation is higher in the 2018 season than the 2019 season.

A)

We know that the mean is nothing but the sum of all scores divided by the number of scores.

Thus the mean for 2018 scores is:

μ₂₀₁₈ = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8

μ₂₀₁₈ = 75

Similarly the mean for 2019 scores is:

μ₂₀₁₉ = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8

μ₂₀₁₉ = 75

We know that the formula for the standard deviation is:

[tex]s=\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1} }[/tex]

where s sample standard deviation

n the size of the sample

[tex]x_i[/tex] each value from the sample

[tex]\bar{x}[/tex] the sample mean

Using this formula, the standard deviation for 2018 scores is:

s₂₀₁₈ = [tex]\frac{\sqrt{ (73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 +(74-75)^2 + (76-75)^2} }{7}[/tex]

s₂₀₁₈ = 2.07

And the standard deviation for 2019 scores is:

s₂₀₁₉ = [tex]\frac{\sqrt{ (70-75)^2 + (69-75)^2 + (74-75)^2 + (76-75)^2 + (84-75)^2 + (79-75)^2 +(70-75)^2 + (78-75)^2} }{7}[/tex]

s₂₀₁₉ = 5.26

B)

We cwn observe that both the two years have the same mean but the 2019 scores have higher variation as compared to 2018 scores.

Thus, the variation in scores was higher in 2019.

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Find the complete question below.

The number of solutions of the system of equations is given as follows:

D. Infinitely many solutions.

The system of equations is defined as follows:

The second equation was obtained multiplying the first equation by 3, meaning that the two equations are multiples, and thus the system of equations has an infinity number of solutions and the correct option is given by option D.

The system of equations is defined as follows:

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By empirical rule, 99.7% of the students have a grade point average which is between 1.38 and 3.84.

Suppose that the grade point average of undergraduate students at one university has a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41.

Here, μ = 2.61 , σ = 0.41

Using the empirical rule :

The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.

2.61 − 0.41 = 2.2

2.61 + 0.41 = 3.02

The range of numbers is 2.2 to 3.02

The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.

2.61 − 2(0.41) = 1.79

2.61 + 2(0.41) = 3.43

The range of numbers is 1.79 to 3.43

Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.

2.61 − 3(0.41) = 1.38

2.61+3(0.41) = 3.84

The range of numbers is 1.38 to 3.84.

Hence, 99.7% of the students have a grade point average which is between 1.38 and 3.84.  

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The solution set to the inequality is w > 3

From the question, we have the following parameters that can be used in our computation:

w+ 4<4 (w - 2)

Open the bracket

So, we have the following representation

w+ 4 < 4w - 8

Evaluate the like terms

So, we have the following representation

12 < 3w

Divide by 3

4 < w

So, we have

w > 4

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Answer:

w = 25 / 4 feet wide.

Step-by-step explanation:

Let's call the width of the walkway "w."

The area of the rectangular pool is 13 * 27 = 351 ft^2.

The area of the walkway can be calculated by adding up the area of four rectangles, one around each side of the pool:

2 * (13 + w) * w + 2 * (27 + w) * w = 384

Expanding the equation:

2 * 13w + 2w^2 + 2 * 27w + 2w^2 = 384

Combining like terms:

2w^2 + 40w = 384

Solving for w^2:

2w^2 + 40w - 384 = 0

Using the quadratic formula:

w = (-40 ± √(40^2 - 4 * 2 * -384)) / (2 * 2)

Simplifying:

w = (-40 ± √(1600 + 3072)) / 4

w = (-40 ± √4272) / 4

w = (-40 ± 65) / 4

w = (25 / 4) or (-105 / 4)

Since w must be a positive value, w = 25 / 4 feet wide.

Answer:look it up frfr

Step-by-step explanation: