A right triangle with coordinates A (-2,5), B (-2, 9) and C (4,5) is first rotated 90 degrees counterclockwise and
then translated 2 units left and 3 units down to form triangle A'B'C'. What is the measure of angle B'A'C',
in degrees, in the resulting figure?

The next step in the series is, shown in Option C.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

There are three steps are shown.

Now, In first step, only one line shown.

In second line the line is left to first line.

And, So on.

Hence, The next step in the series is, shown in Option C.

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Answer:

30 students

Step-by-step explanation:

First, we need to find exactly how many students went to school by car and how many went on the bus.

To do this, we simply multiply the fraction of students that used each transportation method by the total number of students.

[tex]\# \textrm{ of students by car} = \dfrac{3}{8} \times 240 = \dfrac{3 \times 240}{8} = \dfrac{720}{8} = 90 \textrm{ students}[/tex]

So, 90 students went to school by car.

[tex]\# \textrm{ of students on bus} = \dfrac{6}{12} \times 240 = \dfrac{1}{2} \times 240 = \dfrac{240}{2} = 120 \textrm{ students}[/tex]

So, 120 students went to school on the bus.

The number of students that walked to school is the same as the number of students who didn't go in a car or on the bus, so to find the number of students that walked to school, we can subtract the number of students that went by car and on the bus from the total number of students.

[tex]\# \textrm{ of students that walked} = 240 - 90 - 120 = 30 \textrm{ students}[/tex]

Answer:

The solution is the point (-3,2)

Step-by-step explanation:

x + 2y = 1  Subtract 2y from both sides

x + 2y - 2y = 1 - 2y

x = 1 - 2y  Substitute 1 - 2y in for x in the second equation and solve for y.

5x -4y = -23

5(1 - 2y)  -4y = -23  Distribute the 5

5(1) - 5(2y) - 4y = -23

5 -10y - 4y = -23  Combine like terms

5 -14y = -23  Subtract 5 from both sides

5 -5  - 14y = -23 -5

-14y = -28  Divide both sides by -14

[tex]\frac{-14y}{-14}[/tex] =  [tex]\frac{-28}{-14}[/tex]

y = 2

Solve for y

x + 2y = 1  Substitute in 2 for y and solve for x

x + 2(2) = 1

x + 4 = 1   Subtract 4 from both sides

x + 4 - 4 = 1 - 4

x = -3

The solution is the point (-3,2)

Check:

2 + 2y = 1

-3 + 2(2) = 1

-3 + 4 = 1

1 - 1  checks

5x - 4y = -23

5(-3) - 4(2) -23

-15 - 8 = -23

-23 = -23

Answer:

The area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2

Step-by-step explanation:

To increase the size of a triangle by a scale factor of 10/3, you can multiply each side length of the triangle by 10/3.

The new dimensions of the triangle would be (10/3) * 9ft = 30ft and (10/3) * 12ft = 40ft.

The area of a triangle is given by the formula A = (1/2) * b * h, where b is the length of the base and h is the height of the triangle.

Using the new dimensions of the triangle, the area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2.

The coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:

A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The vertices of the original polygon for this problem are given as follows:

A(-1,-1), B (0, 1), C (2, 2), and D (2, -1).

The scale factor for the dilation in this problem is given as follows:

k = 2.

Hence the coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:

A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).

(as each coordinate of each vertex was multiplied by the scale factor of 2).

The problem is incomplete, hence the coordinates of the vertices of the image after the dilation were obtained to show how the dilation works.

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The amounts of goo after each hour are given as follows:

The time that it takes for the goo to return to original size is given as follows:

n hours, for which:

[tex](2)^n(0.25)^n = 1[/tex]

An increasing exponential function is defined as follows:

y = a(1 + r)^x.

For which the parameters are given as follows:

Her sample is of 10 grams, and the amopunt of goo increases by 100%, hence the parameter values' are given as follows:

a = 10, r = 1.

Thus the exponential function is defined as follows:

y = 10(2)^n.

Then the amounts are given as follows:

A decreasing exponential function is given as follows:

y = a(1 - r)^x.

The goo shrinks by 75% every hour, hence:

r = 0.75.

The amount after n hours is of 10(2)^n, hence the shrinking function is given as follows:

[tex]y = 10(2)^n(0.25)^n[/tex]

It returns to the original amount when:

y = 10.

Hence:

[tex]10 = 10(2)^n(0.25)^n[/tex]

[tex](2)^n(0.25)^n = 1[/tex]

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a. The exact volume, in cubic inches, of water flowing out of the pipe every second is 32π cubic inches.

b. The height, in inches, of the water in the tank after 5 minutes is 600 feet.

c. It will take 0.132 minutes to fill 75% of the tank

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, Water flows at 2 feet per second through a pipe with a diameter of 8 inches so it is a cylindrical shape.

Therefore, The exact volume, in cubic inches, of water flowing out of the pipe every second is,

= π(4)²×2.

= 32π cubic inches.

The volume of the cylindrical tank is,

= π(7.5)²×6.

= 337.5π cubic inches.

The height, in inches, of the water in the tank after 5 minutes would be

= (32π×300)/π×16).

= 600 feet.

Now, 75% of 337.5π cubic inches is (0.75×337.5π) = 253.125π cubic inches.

Therefore the time required to fill 75% of the tank is,

= [(253.125π/32π)]/60 minutes.

= 7.91/60 minutes.

= 0.132 minutes.

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Answer:

6 for the number of triangles or 7 because all the triangles form a hole triangle

Step-by-step explanation:

Answer: The answer is 6. If you add the triangle that all the small triangles are within, then you would get 7.

The option D is correct.Because this equation holds the vertically opposite angle theorem.

Vertically Opposite Angles are holds when two lines intersect each other then the opposite angles formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

Vertical opposite angles that are opposite each other when two lines cross are also known as vertical angles because the two angles share the same corner. Opposite angles are also congruent angles.The equation of a vertical line is given by x = a or x = -a

Now we find

According to vertical opposite angle

x-8=40-2x

x+2x=40+8

3x=48

x=16

We can find value of x by usng vertical opposite angle.

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The distance from the top of the tree of height 30 tall to the end of the shadow is 50.

Distance is the length between two point.

To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.

Note: The tree and the shadow form a right angle.

Formula:

Where:

From the question,

Given:

Susbtitute these values into equation 1

Hence, the distance from the top of the tree to the end of the shadow is 50.

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Answer:

Since the term "3" contains no variables, "3" IS a constant term. In the expression 2x - 5 the constant term is -5.

Answer:

10

I wish you luck in your assignments.

Using the Double Number Line above, note that the unit that helps to find the missing numbers is given as:

Note that a unit rate is like a secret code to help you compare things. It helps you find missing numbers on a number line. For example, if 4 cookies cost $2, you can use the unit rate of $0.50/cookie to find out how much 8 cookies cost."

In the above case, we have several clues about the rate. The first relationship on the line is between 1 and 3.

But it only makes when we compare it to other iterations on the line such as 2 and 6.

Note that we can establish a relationship here which is that the greater number must be divided by three to get the lower number. That is:

3/3 = 1

6/3 = 2

Note well that the relationship between 0, 3, and 6 on the number line tell us that the upper units graduate in progressions of 3. that is:

0, 3, 6, 9, etc.

Thus, the missing numbers are:

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We add  (x +7 ) (x - 10) up to -3 and multiply to -70.

What is a quadratic equation?

Any equation in algebra that can be written in the standard form where x denotes an unknown value and a, b, and c denote known numbers, where a 0 is a quadratic equation.

Here,

We illustrate and prove that -9 and 10 multiply to -90 and add up to 1:

7 × -10 = -70

-10 + 7 = -3

We are trying to determine how to factor the following quadratic equation.

x²  -3 x - 70 = 0

If so, the solution to factor the quadratic equation above is:

(x +7 ) (x - 10)

To summarize, -10 and 7 multiplied by -70 and add up to -3, you know that the following is true:

x² -3x - 70

= (x +7 ) (x - 10)

Hence, we add  (x +7 ) (x - 10) up to -3 and multiply by -70.

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There you have it, your answer

Step-by-step explanation:

Easy

For the given issue, x has a value of 4. The offered solution is the solution extraneous .

When we solve equations, we often obtain values that aren't actually the answer to the equation.

A root of a transformed equation that isn't a root of the previous iteration because it was left out of the original equation's domain is known as a extraneous solution.

√(11x + 5) = 7

(11x + 5) = 7²

11x + 5 = 49

11x = 49 - 5

11x = 44

x = 4

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Answer:

1216 inches

Step-by-step explanation:

First you multiply ¼ by 76 times 64

which gives you 1216 inches

Answer:

24 miles

Step-by-step explanation:

each distance between points is 6.

6+6+6+6=24 miles

The ordered pair solution to the function f(x) is (6, -9) because f(6) = -9,

An equation is an expression relating numbers and variables.

A function is a rule that defines the relationship between the dependent and independent variable. Dependent variables are variables that depends on others variable while independent variables are variables that does not depends on others variable

A solution to a function is the values of the variable that makes the equation true.

Given the function f(x) have solution of f(6) = -9. The ordered pair is (6, -9)

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To solve this problem, we can set up the following equation:

Torrie + John = Sonia - John

This equation represents the fact that John has the same number of dollars more than Torrie as he has less than Sonia. We can then substitute the given values for Torrie, Sonia, and John to solve for John:

430 + John = 760 - John

Combining like terms, we get:

2 * John = 330

Dividing both sides of the equation by 2, we get:

John = 165

Thus, John has $165.

Step-by-step explanation:

first we need to identify the lines themselves.

the line from bottom left to top right is simply

y = x

the line is solid, so the points on the line are included.

the dotted line (the points on the line itself are not included) goes through

(0, 2) and (3, 0)

the y-intercept is therefore 2 (the y value when x = 0).

and for the slope

x changes by +3 (from 0 to 3).

y changes by -2 (from 2 to 0).

the slope is -2/+3 = -2/3

and the line is

y = (-2/3)x + 2

we see that the desired gray area is above both lines (">"), and we need to consider, whether the points in the lines are included or not.

so, the system of inequalities is

y >= x

y > (-2/3)x + 2

The range of the absolute function will be from 0 to 9. Then the correct option is A.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The domain means all the possible values of x and the range means all the possible values of y.

From the graph, the range of the absolute function will be from 0 to 9.

Then the correct option is A.

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The complete question is attached below.

The density of the material is 1533.3 grams per quarts.

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

Given that, the density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume.

The formula to find the density is Density=Mass/Volume

Density =6900/4.5

Density= 1533.3 grams per quarts

Therefore, the density of the material is 1533.3 grams per quarts.

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Answer:

40 + 5 = 45

45 ÷ 9 = 5

Therefore, he will have 5 boxes of rocks.

Answer:

Step-by-step explanation:

3

Step-by-step explanation:

this means :

f(x) / (x + 2) = (x² - 5x + 8) + 8/(x + 2)

f(x) = (x + 2)(x² - 5x + 8) + 8 =

= x³ - 5x² + 8x + 2x² - 10x + 16 + 8 =

= x³ - 3x² - 2x + 24

Answer:

The answer is zero

Step-by-step explanation:

Hope it helps

Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

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Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

The bridge opening times when there are 60 minutes in an hour will be 45/60 and 10/60.

From the information, a boat will pass the Colby drawbridge and then the Wave drawbridge and then the Wave drawbridge.

From the table, Colby is on the 3/4 hour. This will be:

= 3/4 × 60

= 45

Also, Wave Bridge will be:

= 1/6 × 60

= 10

Therefore, it's 45/60 and 10/60 because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.

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Complete question

On the Dell River, a boat will pass the Colby drawbridge and then the Wave drawbridge and then the Wave drawbridge. Rename each of the two drawbridge opening times. There are 60 minutes in an hour, so use 60 as a common denominator. Then, rename each opening time using another common denominator

Bridge name:

1. Asher Cross

2. Colby

3. Rainbow

4. Red Bank

5. Wave

Time of Opening:

1. On the hour

2. On the 3/4 hour

3. On the 2/3 hour

4. On the 1/4 hour

5. On the 1/6 hour

Answer:

Step-by-step explanation:

take 9 divided by 5 wich = 1.8