A ladder is placed against the side of a house. The base of the ladder rests 2 feet from the house, and the top of the ladder meets a window sill that is 13 feet up from the ground. How long is the ladder?.

After dilation, the size of the image will change and the shape of the image will be same

Dilating an image means the changing the size of the image, but the shape of the image will be same

Dilation is the process of changing the size of the image without changing the shape of the image

The image after the dilation is called as the pre image.

The dilation can be done by using the scale factor or normally increase or decrease the size,

If the dilation of an image done by scale factor, the size is increased or decreased according to the value of scale factor. If it is greater than 1 the size increases and if it is between 0 and 1 the size decreases

Therefore, size of the image will change after the dilation

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The maximum number is nothing but a number having the largest value in the data set.

We know that the maximum number is nothing but a number having the largest value in the data set.

To find the maximum number in a list of numbers, we go through the whole list of numbers and compare each values.

The maximum number in the list is the largest value found when all values have been compared.

For example, in the list of numbers 23, 98, 76, 90, 17, 71

the maximum number is 98

Therefore, the maximum number in the list is the largest value found when all values have been compared.

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Answer: C = 16

Step-by-step explanation:

1. Subtract 9 on both sides

[tex]-1=-\frac{5}{8} c+9[/tex]

[tex]-9[/tex]              [tex]-9[/tex]

----

2. Solve [tex]-1 - 9[/tex]

[tex]-10=-\frac{5}{8}c[/tex]

3. Multiply both sides by 8 to remove the fraction

[tex](8)-10=-\frac{5}{8}(8)[/tex]

4. Solve 8 x -10

[tex]-80=-5c[/tex]

5. Divide both sides by -5

[tex]\frac{-80}{-5} =\frac{-5}{-5} c[/tex]

[tex]\frac{-80}{-5} =c[/tex]

[tex]16=c[/tex]

[tex]c=16[/tex]

DONEEEE!!

Over the two days, the group traveled an average speed of 2.79 miles per hour.

Given:

during the first leg of a backpacking trip, a group of hikers covered 10.4 miles in 3 hours and 1 minute.

he next day, the group hiked 8.6 miles in 3 hours and 47 minutes.

we are asked to find the group's average speed over the two days = ?

average speed = total distance / total time

total distance =  10.4 + 8.6 mi = 19 miles

total time =  ( 181 + 227 min ) = 408 min

hence average speed = ( 10.4 + 8.6 mi) / ( ( 181 + 227 min )/60 min/hr) =2.79 mi/hr

Hence we get the average speed as 2.79 miles/hour.

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The missing side of the triangle is approximately 10.2 m. This solution assumes that the given sides form a right triangle.

To find the missing side of a triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The formula for the Pythagorean theorem is:

a^2 + b^2 = c^2

where a and b are the lengths of the two sides of the triangle and c is the length of the hypotenuse.

The lengths of two sides of the triangle, 8.3 m and 5.9 m, and you need to find the length of the third side (the hypotenuse).

You can use the Pythagorean theorem to solve for the missing side as follows:

c^2 = a^2 + b^2

c^2 = 8.3^2 + 5.9^2

c = sqrt(8.3^2 + 5.9^2)

c = sqrt(69.29 + 34.81)

c = sqrt(104.1)

c = 10.2 m

Therefore, the missing side of the triangle is approximately 10.2 m.

This solution assumes that the given sides form a right triangle. If the triangle is not a right triangle, the Pythagorean theorem may not be applicable and a different method may be needed to find the missing side.

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Yang Liwei took 1.5 hours to orbit the earth one time.

A route that an object in space follows around another is known as an orbit.. An orbit is a regular, repeating path that one object in space takes around another one.

Given that the Yang Liwei orbited the Earth 14 times in 21 hours for the country of China.

To find the time period in one time,

Required time period = time period of total travel / number of times he orbited

Required time period = 21 / 14

Required time period = 3/2

Required time period = 1.5 hours

Hence, Yang Liwei will take 1.5 hours to orbit the earth one time.

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Based on the margin of error, an estimate of the total number of feral cat complaints for planet Purple is A. Between 1018.5 and 1361.5 complaints.

4,500 cities make up the entire population of planet Purple.

350 cities make up the random sample.

Average complaints are 3.4.

Error or margin = 0.49

[350 x (3.4 + 0.49)] Upper limit = 1,361.5

Lower limit: 1,081.5 (350 times (3.4 - 0.49).

As a result, Option A's estimated number of feral cat complaints floats above the error margin.

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Answer:61

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Because there were 110 people at the concert, that means only 110 seats were filled. So we can think of the problem as its own equation if we word it like this:

110     is    55%    of    how many seats

110     =   0.55    x      ?

Now to solve by dividing 110 by 0.55

110/0.55 = 200

The past verb of the word split is to divide any number or a group into smaller or subgroups.

Explanation:

The past verb of the word split is :

Therefore, the past verb of the word split is given to divide a number or any group into smaller parts or subgroups.

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By solving the given equation x/7 - 6 = - x/6 + 5 we get x value = 462/13.

What is called the equation?

Given that :

     x/7 - 6 = - x/6 + 5

Multiply the denominators with numerator on both sides

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

                  x - 42 / 7 = - x + 30 / 6

Multiply both denominators with numerator on both sides

                  6 (x - 42) = 7 (- x + 30)

Multiply 6 and 7 inside the bracket

                   6x - 252 = - 7x + 210

Separate x terms and constant terms

                    6x + 7x = 210 + 252

                           13x = 462

                              x = 462 / 13

Therefore, x = 462 /13

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Answer:

the answer would be 17x

Step-by-step explanation:

Answer:

17x

Step-by-step explanation:

Simplify  2x times 7  to  14x= 14x+3x

17x

Answer:

Step-by-step explanation:

2 because in a hour there is 60 minutes so you just divide 120 by 6 and you get 2 km per minute

The principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

What is continuous compounding?

There is no cap on how frequently interest can accumulate thanks to continuous compounding. A balance can compound continuously an unlimited number of times, which means interest is earned on it constantly.

We have,

9 years in an account with a 3.9% annual interest rate compounded continuously,

an investment is worth a total of $17,757.16.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.9/100

r = 0.039 per year,

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Hence, the principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

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Answer:

$12,500.75

Step-by-step explanation:

I got it right.

Answer:

1.1667

Step-by-step explanation:

Brainliest please!

Answer:

Perimeter of Rectangle is 44m

A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.

According to the given information

Area of Rectangle = l × b

Area of Rectangle = 105 [tex]m^{2}[/tex]

Length of one side = 7 m

Let the length of the adjacent side = b

Area of Rectangle given = 7 × b

                     105   = 7 × b

                       b    =  [tex]\frac{105}{7}[/tex]

                       b   = 15 m

Perimeter of Rectangle given = 2( l + b )

                                        = 2 ( 7 + 15 )

                                        = 2 × 22

                                        = 44m

Perimeter of Rectangle is 44m

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Answer:

[tex]b) 5^{\frac{1}{12} }[/tex]

Step-by-step explanation:

∛5 = 5^1/3

⁴√5 = 5^1/4

Then:

∛5 / ⁴√5 = (5^1/3) / (5^1/4)

              = 5^(1/3 - 1/4)

1/3 - 1/4 = 4/12 - 3/12 = 1/12          

Then:

5^(1/3 - 1/4) = 5^1/12

= [tex]5^{\frac{1}{12} }[/tex]

**** The symbol ^ means that the expression on the right is an exponent.

Example:

5^1/3

means  1/3 is an exponent,

The interest rate, to the nearest tenth of a percent, would be required in order for Jaya to end up with $10,900 is 3 %.

To calculate the future value, we need to use the following formula on each investment:

FV = PV  e^(it),

where FV =Future value, PV=Present Value, e =Euler’s number, i =nominal rate per year, t =Number of years.

Given that Jaya is going to invest $8,000 and leave it in an account for 6 years.

FV =PV * e^(i*t),

P = $8,000

t= 6 years

FV = 10,900

10,900 =8,000 e^(i*6)

i = 3%,

Thus, the interest rate, would be required for Jaya to end up with $10,900 is 3 %.

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The magnitude and direction of the resultant force are respectively; F = 44.954 N and θ = 36.47°.

We are given two forces as;

F₁ = 34 N

F₂ = 46 N

Angle between the two forces; θ =  42°

Now, the formula to find the resultant of the two forces is gotten by using the cosine rule as;

F = √[F₁² + F₂² + 2F₁F₂cos θ]

Where θ represents the angle between the two force vectors

Thus;

F = √[34² + 46² + 2(34 * 46 * cos 42]

F = 44.954 N

the direction will be;

θ = tan⁻¹(34/46)

θ = 36.47°

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Answer:

$575 after 5 years

Step-by-step explanation

3% of 500= 15

15 × 5= 75

500 + 75= $575

Answer:

2p(6p + 5)

Step-by-step explanation:

12p² + 10p ← factor out 2p from each term

= 2p(6p + 5)

Given ▲ ABC and  ▲DEF are the examples of AAS congruence theorem.

According to the AAS, or Angle Angle Side congruence rule, two triangles are said to be congruent if two pairs of corresponding angles and the opposite or non-included sides are equal to one another.

The sides are not included between the angles but rather run in either direction of the angles, whereas the angles are sequential and corresponding in nature.

let's consider 2 triangles ▲ ABC ,  ▲DEF.

A at top B left C right . D at top E left F right side

∠B = ∠E

∠C = ∠F

AB = DE.

We can see that ∠B = E and ∠C = F if we superimpose the two triangles on top of one another. The lengths of the excluded sides, AB and DE, are also equal. As a result, we can state that ABC ≅ DEF.

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The minimum sample size is 11 needed to be 90% confident that the sample mean is within 1 point of the true population mean.

What is the mean?

Given:

Standard deviation, σ = 2points

Confidence level = 90%

Sample mean, ε = 1 point

At 90% confidence level

1 - α = 0.90

α = 1 -0.90

α = 0.10

α/2 = 0.05

Zα / 2 = Z₀.₀₅

= 1.645

To find n

n = (Zα / 2 )*(σ)²

= (1.645)² * (2)² / (1)²

= (2.706) * 4

= 10.8241

n = 11

Hence, the minimum sample size is 11 needed to be 90% confident that the sample mean is within 1 point of the true population mean.

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The interval on which the graph is increasing and decreasing are ( -∞,3] and [3,∞) respectively.

There is no interval where the function is constant.

In order to solve this question we need to study the graph attached,

From the graph, we could see that the plotting of the graph is starting from the negative axes and we could observe an increasing slope in the function, and the increment stopped after reaching point B(3,0), we can also observe that the value of the y-axis increases with that of the x-axis.

The interval at B(0,3) must be wrote down as ( -∞,3]

Again we could see a sudden drop in the slope of the function of the graph as the slope of the graph this time starts decreasing and moves to infinity and again we could observe that the value of the x-axis starts decreasing with the decrease in the value of the y-axis.

The function was constant at a null interval.

Therefore, The interval on which the graph is increasing and decreasing are ( -∞,3] and [3,∞) respectively and there is no interval where the function is constant.

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By using the concept of vector, it can be calculated that

Component form of vector v = (-4 , 5)

What is a vector?

Vector is anything that has magnitude and direction and follow the vector addition law. Vector is a very important tool in mathematics and physics.

Here,

The initial point of vector v is (1, -4) and the terminal point of vector v is      (-3, 1)

Component form of vector v = (-3 - 1, 1 - (-4)) = (-4 , 5)

Second option is correct

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Answer:

-x² -10x -26

Step-by-step explanation:

Substitute x in f(x) with x + 5:

f(g(x)) = - (x+5)² - 1

= - (x² + 10x + 25) -1

= -x² -10x -25 -1

= -x² -10x -26

No, The dilation doesn't change the shape of the image

Dilation is a type of a transform where an image size either increase or decrease but has the same shape as the original. In other words, the dilation is similar to the original.

All dilations have a center and a scale factor. The center is the point of reference for the dilation (like the vanishing point in a perspective drawing)

Scale factor tells us how much the figure stretches or shrinks. A scale factor is typically labeled  "k" and is always greater than zero.  It is the ratio of the sizes of the original figure with the dilated figure

The only change in the dilation process is that the distance between the points changes. It means that the length of the sides of the original image and the dilated image may vary.

Therefore , Dilation doesn't changes the shape

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Answer:

A and B

Step-by-step explanation:

-(5/3) = -1.67

-5/3 = -1.67

5/-3 = -1.67

5/3 ≠ -1.67

-5/-3 ≠ -1.67

-(-5/3) ≠ -1.67