Reba is playing on the slide. Over and over, she climbs the 9-foot ladder, goes down the slide, and walks 3 feet to get back to the ladder. How far does Reba travel each time she repeats this process? If necessary, round to the nearest tenth.

ANSWER

EXPLANATION

The equation of a circle is given by:

where (h, k) = center of the circle

r = radius of the circle

The center of a circle is the midpoint of the endpoints of the diameter of the circle. Hence, to find the center of the circle, we have to find the midpoint of the diameter:

where (x1, y1) and (x2, y2) are the endpoints of the diameter.

Hence, the center of the circle is:

To find the radius of the circle, we have to find the distance between any endpoint of the circle and the center of the circle.

To do this apply the formula for distance between two points:

Therefore, the radius of the circle is:

Hence, the equation of the circle is:

the rriangle is 3 4 5 triangle so 5×5 is 25

the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.​

Let

L ------> the lenght

W ----> the width

we know that

the area of rectangle is

A=L*W

A=63 yd2

63=L*W -------> equation 1

and

L=2W+11 ------> equation 2

substitute equation 2 in equation 1

63=(2W+11)*w

2W^2+11w-63=0

solve the quadratic equation using the formula

a=2

b=11

c=-63

substitute

the solutions for W are

w=3.5 and w=-9 (is not a solution, because is negative)

so

Find the value of L

L=2W+11 -------> L=2(3.5)+11

L=18

therefore

the dimensions are

SOLUTION

The questions is outside scope

The slope intercept form of a line can be expressed as,

Here, m is the slope of the line and c is the y intercept.

Comparing the above equation with the given equation of a line y=-5x+2, we get

m=-5.

The slope of a line perpendicular to line with slope m is -1/m.

Hence, the slope of line perpendicular to y=-5x+2 is,

The new line is given to be passing through point with coordinates (x1, y1)=(3, -1).

The point slope form of a line passing through point with coordinates (x1, y1)=(3, -1) and having slope m1 is,

Therefore, the slope-intercept form of the equation of the line perpendicular to y = -5x + 2 and passing through (3,-1) is,

For supplementary angles, we can do the following equality

What we have to do, is to clear "x" to find its value.

In conclusion, the value of x is 33

To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.

First we need to write both equations in terms of y:

now we need to find two points for each of this lines. To do this we give values to the variable x and find y.

For the equation 2x-y=-1, if x=0 then:

so we have the point (0,1).

If x=1, then:

so we have the point (1,3).

Now we plot this points on the plane and join them with a straight line.

Now we look for two points of the second equation.

If x=0, then:

so we have the point (0,-3)

If x=1, then:

so we have the point (1,-1).

We plot the points and join them wiith a line, then we have:

once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.

Therefore the system of equations has no solutions.

To detrmine the formula of the polynomial, we check for the roots on the graph:

when y = 0, x = -2

when y = 0, x = 4

We have two roots.

x = -2

x + 2 = 0

x = 4

x - 4 = 0

3rd factor is x = 0

Hence, we have two factors: x(x + 2) and (x - 4)

The polynomial function using the factors:

Next, we find the value of a:

To get a , we pick a point on the graph. let the point be (0, -4)

substitute the point in the function above:

The formula of the polynomial becomes:

It takes Garret Choose min to remove 1 ft of hem. He should multiply the number of minutes by Choose... to determine the number of minutes it will take to remove 5 ft of hem.

The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach will come in handy for topics involving ratio and proportion, algebra, geometry, etc. In the unitary technique, we always count the value of a unit or one quantity first before figuring out the values of more or fewer quantities. This method is referred to as the "unitary method" for this purpose.

There are two types of unitary methods because they result in two types of variations and those are given below:

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The domain of the function f(x) that has a range of [-2, ∞) is [-2, ∞)

The inverse of a function that maps x into y, maps y into x.

The given coordinates of the points on the radical function, f(x) are; (-3, -2), (1, 0), (6, 1)

To determine the domain of

[tex] {f}^{ - 1}( x)[/tex]

The graph of the inverse of a function is given by the reflection of the graph of the function across the line y = x

The reflection of the point (x, y) across the line y = x, gives the point (y, x)

The points on the graph of the inverse of the function, f(x), [tex] {f}^{ - 1} (x)[/tex] are therefore;

[tex]( - 3, \: - 2) \: \underrightarrow{R_{(y=x)}} \: ( - 2, \: - 3)[/tex]

[tex]( 1, \: 0) \: \underrightarrow{R_{(y=x)}} \: ( 0, \: 1)[/tex]

( 6, \: 1) \: \underrightarrow{R_{(y=x)}} \: ( 1, \: 6)

The coordinates of the points on the graph of the inverse of the function, f(x) are; (-2, -3), (1, 0), (1, 6)

Given that the coordinate of point (x, y) on the image of the inverse function is (y, x), and that the graph of the function, f(x) starts at the point (-3, -2) and is increasing to infinity, (∞, ∞), such that the range of y–values is [-2, ∞) the inverse function, [tex] {f}^{ - 1}( x)[/tex], which starts at the point (-2, -3) continues to infinity, has a domain that is the same as the range of f(x), which gives;

The domain of the inverse of the function, [tex] {f}^{ - 1}( x)[/tex], using interval notation is; [-2, ∞)

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SOLUTION

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Write the formula for calculating compound amount

where

A = final compounded amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

STEP 2: Write the given data

Semiannually means that n will be 2

STEP 3: Calculate the compound amount

Hence, the compounded amount after 4 years is $18,748.1972

By using the completing the square method, f(x) = x² − 8x + 3 in vertex form is: B. f(x) = (x − 4)² − 13.

In this exercise, you're required to rewrite the given function in vertex form by using the completing the square method. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

h and k represents the vertex of the graph.

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

f(x) = x² − 8x + 3

f(x) = x² − 8x + (8/2)² - 13

f(x) = x² − 8x + (4)² - 13

f(x) = x² − 8x + 16 - 13

f(x) = (x² − 8x + 16) - 13

f(x) = (x − 4)² − 13

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Answer:

The first option is correct

Explanation:

Two negatives makes a positive.

The quadrants of a coordinate plane are:

Then, we can say that the rectangle PQRS is in the first quadrant.

Hello!

In a sample of 1100 people, the specific candidate got 624 votes. So, we can write it as 624/1100.

And if the total of voters is 40,000, how many votes this specific candidate will receive? We can write it as x/40,000.

Now, let's equal both fractions look:

Approximately 22691 votes.

Given from the number line:

D = -2 and F = 13

So, the distance DF = 13 - (-2) = 13 + 2 = 15

1) find E such that, DE : EF = 2 : 1

so,

so, x : (15 - x) = 2 : 1

x = 30 - 2x

3x = 30

x = 10

So, E = -2 + 10 = 8

=========================================================================

2) E is 4/5 of the distance from F to D

So, the distance from F = 4/5 * 15 = 12

So, E = 13 - 12 = 1

=====================================================================

3) the ratio of DE : EF = 2 : 3

So,

3x = 2 ( 15 - x)

3x = 30 - 2x

5x = 30

x = 30/5 = 6

E = -2 + 6 = 4

=================================================

4) E is 1/3 of the distance from D to F

So, the distance DE = 1/3 * 15 = 5

So, E = -2 + 5 = 3

=====================================================

As a summery:

1) E = 8

2) E = 1

3) E = 4

4) E = 3

Explanation

The question wants us to obtain the margin of error

A margin of error tells you how many percentages points your results will differ from the real population value.

The formula to be used is

To do so, we will have to list out the parameters to be used

The next step will be to find the z-score value for a confidence level of 80%.

From the statistical table, we have

So, we can input the given data obtained into the formula

So we will have

So the margin of error (M.E.) = 4.163 (To 3 decimal places)

Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

The given system of equation :

x - y = 5 ( 1 )

- x - y = - 11 ( 2 )

Add the equation ( 1 ) & ( 2 )

x - y + ( -x - y ) = 5 + ( -11 )

x - y -x - y = 5 - 11

x - x - y - y = -6

0 - 2y = - 6

y = -6/( -2)

y = 3

Substitute the value of y = 3 in the equation ( 1)

x - y = 5

x - 3 = 5

x = 5 + 3

x = 8

Answer : x = 8, y = 3

Inverse proportionality is when the value of one quantity increases with respect to a decrease in another, they behave opposite in nature.

It is represented by the following expression:

Since P=24 when Q=3, we can substitute and solve for the constant k:

Then, the equation that represents the inverse variation would be:

Given:

point (8,8).

slope 11/6

The slope intercept form is,

where m is the slope and b is the y-intercept.

we know that m=11/6 so subistute in the equation.

Now, let us plug in the point in the equation to find the value of b that is the y-intercept.

ANSWER

y = -7

EXPLANATION

To solve using the substitution method we have to clear x from one of the equations as a function of y. For example, for equation 2:

Then replace x in the first equation by this expression:

And solve for y:

Explanation:

We have to find 5% of the original cost first:

And then add it to the original price:

Since it's a price, we have to round this result to the nearest hundredth

Answer:

The new price is $23.09

Given:

The quadrilateral PQRS is given.

The aim is to locate the given quadrilateral into first quadrant only.

The graph will be reflected across x=4 then the graph will not be located to the first quadrant.

The frequency of middle C = 262 Hz

The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:

This can be re-written as:

Middle C is 9 semitones below the concert pitch

That is, n = -9

To find the frequency of middle C, substitute n = -9 into the equation for F

The frequency of middle C = 262 Hz

Solution

We have the following expression:

Here we have 3 terms:

Variable terms:

Constant term

Explanation:

If 'x' is the amount each owner will pay, there are 8 owners and the total amount to pay is $5,400 the equation to solve is:

Solving for x:

Answer:

Each owner has to pay $675

In triangle PQR

Construction: Draw PX perpendicular to QR where x lies on QR

Since:

PX perpendicular to QR

In the 2 triangles PXQ and PXR

given

proved up

PX = PX ------- common side in the 2 triangles

Triangle PXQ congruent to triangle PXR by the AAS theorem of congruency

As a result of congruency

PQ = PR ------- proved

Step 1 : Let's review the information given to us to answer the problem correctly:

• Annual salary of the governor of New York = $ 1,790,000

• Annual salary of the governor of Tennessee = $ 940,000

Step 2: Let x to represent the annual salary of the governor of New York

and let's find the ratio of the salary of the governor of Tennessee, as follows:

940,000/1,790,000 = 0.525

Step 3: Now, let's write the equation for calculating the salary of the governor of Tennessee for any given year, this way:

• 0.525x = Annual salary of the governor of Tennessee

•

Step 4: If the salary of the governor of New York for the next year is 2,000,000, then we can calculate the salary of the governor of Tennessee, this way:

0.525x = 0.525 * 2,000,000 = 1,050,000

The annual salary of the governor of Tennessee woudl be 1,050,000

The most appropriate choice for area of rectangle will be given by -

Area of classroom = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]

What is area of rectangle?

Rectangle is a four sided figure whose parallel sides are equal and whose every angle is 90°

The total space taken by the rectangle is called area of the rectangle.

If the length of the rectangle be l and the breadth of the rectangle be b, then area of the rectangle is given by

Area = [tex]l \times b[/tex]

Here,

Length of classroom = [tex]6\frac{4}{5}[/tex] m = [tex]\frac{34}{5}[/tex] m

Width of classroom = [tex]1\frac{3}{8}[/tex] m = [tex]\frac{11}{8}[/tex] m

Area of classroom = [tex]\frac{34}{5} \times \frac{11}{8}[/tex]

                               = [tex]\frac{187}{40}[/tex]

                               = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]

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