Solve the right triangle by completing the table below

By applying the Pythagorean theorem to the provided question, we can say that in this triangle =>

AC =[tex]\sqrt{115}[/tex]

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Pythagorean theorem applies here, in this triangle

AC = [tex]A^2 + B^2[/tex]

AC  = [tex]\sqrt{14^2 -9^2}[/tex]

AC = [tex]\sqrt{115}[/tex]

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The equation of a circle whose center is (0,.-5) and radius is 7 as required is; (x - 0)² + (y + 5)² = 7².

It follows from circle equations that; (x - a)² + (y - b)² = r² represents the equation of a circle whose center is; (a, b) and radius is; r.

Hence, for the given circle whose center is (0,.-5) and radius is 7.

(x - 0)² + (y + 5)² = 7²

Therefore, it can be inferred that the equation of the circle in discuss is; (x - 0)² + (y + 5)² = 7².

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The simplest radical form is x⁵.

Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.

The given radical form is [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex].

The radical and root of a number are the same thing.

Simplifying a radical eliminates the square roots, cube roots, fourth roots, etc.

In the given expression, 1/6 is the 6th root, in both numerator and denominator cancel out 6th root x.

That is,  [tex]\frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }}[/tex] =x⁵ ([tex]x^{\frac{1}{6} }[/tex]  in the denominator is gets cancelled with [tex]x^{\frac{1}{6} }[/tex] in the numerator)

Therefore, the simplest radical form is x⁵.

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When the smaller data point is included, the mean will drop when compared to the other values, but the median may increase or decrease depending on whether the collection of numbers is even or odd.

1. Calculate the original set of numbers' mean and median.

2. Include the lesser data point in the collection.

3. Determine the updated median and mean.

4. Evaluate the original mean and median in comparison to the new mean and median. Depending on whether the collection of numbers is even or odd, the median will decline while the mean will increase.

We must first determine the mean and median of the initial set of data in order to evaluate how the addition of a smaller data point will impact those values. Adding together all the values and dividing by the total number of values yields the mean. We place the middle value in the set of integers after sorting them from least to largest to determine the median. We include the new, smaller data point in the set after finding the mean and median. We next perform the same calculations as previously to determine the new mean and median. Finally, we contrast the updated mean and median with the baseline values. The median may stay the same or drop depending on whether the set of numbers is even or odd, while the mean often decreases as it is compared to other values. The mean and median of a set of numbers can therefore be significantly affected by the addition of a tiny data point.

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The complete question is

how do you know how adding a smaller data point will affect the mean or median if its smaller than them other value.

The positions of points is shown below.

A point in mathematics is symbolised by a dot (.) and used to indicate an accurate location in space. It lacks all three dimensions—length, width, and height. It has no size, in other terms. A point's name is typically written in all caps.

Given:

We have to mark a point in three position in according to the line.

First, point on line means point should be marked on the line.

Then, the point above the line means that the point should be located on the upper side of the line.

Lastly, the point below the line means that the point should be located on the lower side of the line.

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There are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

To find the number of acres in a lot, you can use the following formula:

Number of acres = (length in feet) x (width in feet) / 43,560

First, convert the length and width from miles to feet. There are 5,280 feet in a mile, so:

Length in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet
Width in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet

Next, plug these values into the formula:

Number of acres = (2,640 feet) x (2,640 feet) / 43,560 = 174,240,000 / 43,560 = 160 acres

Therefore, there are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

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Answer:

7,000 Rupees

Step-by-step explanation:

Using the information given in the problem to set up two equations and by solving them

25% of the number is 80.

An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two parts: the left-hand side and the right-hand side, separated by an equal sign (=). The left-hand side and right-hand side can contain variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.

Let's call the number we're looking for "x". We can use the information given in the problem to set up two equations:

0.7x = 224 (equation 1)

0.95x = 304 (equation 2)

We want to find 25% of the same number, which can be written as 0.25x. We can solve for x using either equation 1 or equation 2 and then plug that value into 0.25x to find the answer.

Let's solve for x using equation 2:

0.95x = 304

x = 304/0.95

x = 320

Now that we know x is 320, we can find 25% of that number:

0.25x = 0.25(320) = 80

So 25% of the number we were looking for is 80.

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The Roth IRA will provide Ethan with the most future benefit, with the IRA valued at $195,902.08 and the Roth at $211,633.75. The difference in the future value of the two accounts is $15,731.67.

A purchase made with the intention of creating income or capital growth is known as an investment. An asset's value increasing over time is referred to as appreciation. When a person invests in a thing, they do not intend to utilise it as a source of immediate consumption, but rather as a tool for future economic growth.

The Roth IRA will provide Ethan with the most future benefit. The IRA will be valued $195,902.08 after 30 years, while the Roth IRA will be worth $211,633.75. As a result, the Roth IRA is valued $15,731.67 more than the IRA.

To determine the IRA's future value, use the formula FV = P(1+r)n, where P is the monthly payment, r is the interest rate, and n is the number of periods (in this case, 30 years). With our data in, we get: FV = 416.66(1+0.025)30 = $195,902.08.

We may apply the same approach to compute the future value of the Roth IRA, but with a $5,000 yearly payout. With our values in, we get: FV = 5000(1+0.025)30 = $211,633.75.

The difference in the future value of the two accounts is $15,731.67, which is the amount that the Roth IRA will be worth more than the IRA.

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The equation that would give the solution of  x ≤ 4 is -2x ≤-8

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

the equation is given as -2x ≤-8. We are to solve the inequality so as to get the value of x

we are to divide through -2x ≤-8 by -2

-2x / -2 ≤ -8 / -2

x ≤ 4

the other parts of the question are not clearly stated

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The inverse of f(x) is restricted to the domain x ≥ 1, since this is when[tex]x^2 − 2x + 1[/tex] is always greater than 0.

To find the inverse function of f(x), we must first determine the domain of f(x). We can do this by finding the values of x where f(x) is greater than or equal to 0.

We can start by setting f(x) to 0 and solving for x:

[tex]x^2 − 2x + 1 = 0[/tex]

[tex]x^2 − 2x + 1 − 1 = 0 − 1[/tex]

[tex]x^2 − 2x = -1[/tex]

(x − 1)(x − 1) = -1

x = 1

Therefore, the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.

The inverse of a function f(x) is a function that "undoes" f(x). In order to find the inverse of a function, the domain of the function must first be identified. This is done by solving f(x) = 0 and determining which values of x make the equation equal to 0.In the case of f(x) =[tex]x^2[/tex] − 2x + 1, the equation is equal to 0 when x = 1. This means that the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.Once the domain of the function is restricted, the inverse function can be found by switching the x and y values, and solving for the new equation. This process can be used to find the inverse of any function, as long as the domain is appropriately restricted.

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The inverse function of f(x) = [tex]\frac{x-7}{x+4}[/tex] is f⁻¹(x) = [tex]\frac{4x+7}{1-x}[/tex].

A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1." Here, (-1) should not be confused with an exponent or a reciprocal.

Given that the function is f(x) = [tex]\frac{x-7}{x+4}[/tex]

Change f(x) (or whatever the function name is) to "y".  In this case you'd get:

y = [tex]\frac{x-7}{x+4}[/tex]

Now, switch x and y.  Wherever you see y, put x.  And wherever you see x, put y.

x = [tex]\frac{y-7}{y+4}[/tex]

Solve the new equation for y.

x (y + 4) = y - 7

xy + 4x = y - 7

4x + 7 = y - xy

4x + 7 = y (1 - x)

y = [tex]\frac{4x+7}{1-x}[/tex]

Change y back to function notation.  The correct notation for the "inverse of f(x)" is "f⁻¹(x)".  So that would give you:

f⁻¹(x) = [tex]\frac{4x+7}{1-x}[/tex]

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The graph of the linear inequality y > -4  is given below.

Linear inequalities are expressions that use inequality symbols to compare two linear expressions. When a polynomial of degree 1 is contrasted with another algebraic expression of a degree less than or equal to 1, this comparison results in a linear inequality, which is an inequality including at least one linear algebraic expression. There are many different ways to represent different types of linear inequalities.

Given linear inequality is y > -4 which represents y region will be in the positive range or greater than -4.

The graph of this linear inequality is given below.

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The approximate difference between the values of the cars after 4 years is $134.82.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

To find the difference between the values of the cars after 4 years, we can subtract the value of Mason's car from the value of Brian's car at t = 4.

f(4) = 21,500(0.87)^4 ≈ 11,426.91

g(4) = 19,200(0.91)^4 ≈ 11,292.09

Therefore, the approximate difference between the values of the cars after 4 years is:

f(4) - g(4) ≈ 11,426.91 - 11,292.09 ≈ 134.82

So the approximate difference is $134.82.

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Answer:

x = 28

m∠A = 76°

m∠B = 104°

Step-by-step explanation:

Given the figure we can see that the two angles which measure

2x + 20 and 4x - 8 are adjacent linear angles and therefore they are supplementary angles which further means they add up to 180°

So

2x + 20 + 4x - 8 = 180

2x + 4x + 20 - 8 = 180\

6x + 12 = 180

6x = 180 - 12

6x = 168

x = 168/6

x = 28

We also have the property that angles that are vertically opposite each other at the vertex of the intersection of two lines are equal

So the angle represented by 2x + 20 = 2(28) + 20 = 56 + 20 = 76°

∠A is a vertically opposite angle to this angle and therefore the magnitude of ∠A denoted by m∠A = 76°

The angle represented by 4x - 8 = 4(28) - 8 = 112 - 8 = 104°

Since ∠B is a vertically opposite angle to this angle we have

m∠B = 104°

The equation of the straight line would be -

y = 2x.

Given is that a straight line passes through the points (2, 4) and (3, 6).

We can write the slope as -

m = (6 - 4)/(3 - 2)

m = 2/1

m = 2

For the point (2, 4), we can write -

y = 2x + c

c = 4 - 4

c = 0

Therefore, the equation of the straight line would be -

y = 2x.

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Answer:

B. More money was given than expected in 1994

Step-by-step explanation:

Nowhere is it mentioned what amount was expected as donations. Only actual amounts received are shown on the graph

Hence this is an assumption and not necessarily fact

Equation: 4x = 56  

Answer: 14 tickets

Step-by-step explanation:  

4x = 56  

Lavonne's tickets sold 4 times as many as Kenneth's. This means we would need to multiply Kennneth's ticket by 4 to equal Lavonne's.

4x/4 = 56/4

Now you need to solve the equation by isolating x. Here you have to divide both sides by 4.

x = 14

Kenneth sold 14 tickets.

4(14) = 56

The length of the segment AB is 3.5 cm  

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

We have segments ratio as shown:

BC/AB = CD/ED

=> (AC - AB)/AB = (EC - ED)/ED

=> (14-AB)/AB = (84-21)/21 = 3

    Let AB=x

=>  (14-x)/x = 3

=> 14-x = 3x

=> 14 = 3x+x = 4x

=> 14/4 = x

=> x=3.5 cm

AB=x = 3.5 cm  

The length of the segment AB is 3.5 cm  

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Answer:

Step-by-step explanation:

48----------------100%

x------------------75%

x=36

Answer:

2.73 meters away from the building.

Step-by-step explanation:

To find the distance from the building to the flagpole, we can use the tangent function. Let's call the distance from the building to the flagpole "d".

The tangent of the angle of elevation is equal to the height of the flagpole (h) divided by the distance from the building to the flagpole (d):

tan 48° = h / d

The tangent of the angle of depression is equal to the distance from the building to the flagpole (d) divided by the height of the observer (3.5 m):

tan 35° = d / 3.5

We can use these two equations to find the value of d. Solving the first equation for h:

h = tan 48° * d

And substituting that into the second equation:

tan 35° = d / (tan 48° * d / 3.5)

Solving for d:

d = 3.5 * tan 35° / tan 48°

Using a calculator, we can find that:

d = 3.5 * tan 35° / tan 48° = 3.5 * 1.3602668 / 1.7415198 = 2.73 m

So the flagpole is 2.73 meters away from the building.

Answer:

To rewrite the expression 27 - 4x + x² in the form (x + a)² + b, we can complete the square.

Starting with x² + (-4x) + 27:

x² - 4x + 4x² = 4x² - 4x

Adding (4/2)² = 4 to both sides:

4x² - 4x + 4 = 4x² - 4x + 4

The expression is now in the form (x - 2)² + 0, so a = -2 and b = 0.

Therefore, 27 - 4x + x² = (x - 2)² + 0.

The value of x for the similar triangles is equal to 13.

We have the triangles to be similar, this implies that the length 8 of the smaller triangle is similar to the length x - 1 of the larger triangle

and the length 10 of the smaller triangle is similar to the length x + 2 of the larger triangle

so;

10/(x + 2) = 8/(x - 1)

10(x - 1) = 8(x + 2) {cross multiplication}

10x - 10 = 8x + 16

10x - 8x = 16 + 10 {collect like terms}

2x = 26

x = 26/6 {divide through by 6}

x = 13.

Therefore, the value of x for the similar triangles is equal to 13.

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Answer:

im him

Step-by-step explanation:

The left Riemann Sum approximation for the integral of 20(4x² - 2x)dx over the interval [0, 20] with four equal subintervals is 165250.

In calculus, the integral is a mathematical tool that allows us to find the area under a curve. It is an important concept that is used in many fields of science and engineering. One way to estimate the value of an integral is by using a Riemann Sum, which involves dividing the region under the curve into small rectangles and adding up their areas.

In this case, we will be using a left Riemann Sum with four equal subintervals to estimate the integral of 20(4x² - 2x)dx.

To use a left Riemann Sum, we need to first divide the interval of integration into equal subintervals. In this case, we have four subintervals of width

=> (b - a)/n = (20 - 0)/4 = 5.

The left endpoint of each subinterval will be used as the height of the rectangle that represents the area under the curve in that subinterval.

Next, we need to evaluate the function 20(4x² - 2x) at the left endpoints of each subinterval. These values will be used as the heights of the rectangles. The left endpoints are 0, 5, 10, and 15, so we have:

f(0) = 20(4(0)² - 2(0)) = 0

f(5) = 20(4(5)² - 2(5)) = 1900

f(10) = 20(4(10)² - 2(10)) = 7200

f(15) = 20(4(15)² - 2(15)) = 15150

We can now find the area of each rectangle by multiplying its height by its width (5). The total area is the sum of these areas:

(0)(5) + (1900)(5) + (7200)(5) + (15150)(5) = 165250

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We can use the Pythagorean theorem to solve this problem. Let's call the distance from the ball to the center of the green "d". We know that the marker is 150 yards from the center of the green, and the golfer has paced off 35 yards in a direction 110 degrees from the marker.

Let's use x to represent the horizontal distance from the marker to the ball, and y to represent the vertical distance from the marker to the ball. Then, we have:

x = 35 * cos(110)

y = 35 * sin(110)

Using the Pythagorean theorem, we can find the distance "d" from the ball to the center of the green:

d^2 = x^2 + (y + 150)^2

Plugging in the values for x and y, we get:

d^2 = 35^2 * cos(110)^2 + (35 * sin(110) + 150)^2

d^2 = 1225 + (150 + 35 * sin(110))^2

Using a calculator, we can find that sin(110) = 0.939, so:

d^2 = 1225 + (150 + 31.65)^2

d^2 = 1225 + (181.65)^2

d^2 = 1225 + 32762.7225

Taking the square root of both sides:

d = sqrt(1225 + 32762.7225)

d = sqrt(33987.7225)

d = 183.83

Rounding to the nearest yard:

d = 184 yards

So, the ball is 184 yards from the center of the green.

It is a continuous variable, as it can take on any value within a certain range (i.e., any value between a positive delay and a negative early arrival).

The variable described is quantitative, as it represents a numerical measurement of time, which is a continuous variable that can take on any value within a certain range. The range includes both positive values, representing delays, and negative values, representing early arrivals. This variable is a useful metric for tracking the performance of transportation systems or airlines, as it provides an objective measure of the amount of time a flight is delayed or arrives early. By analyzing the distribution of arrival delay times, policymakers and transportation providers can identify patterns, trends, and potential areas for improvement in their service delivery.

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Robin ride her bike this week 35 miles.

Robin rides her bike 3 miles to school.

She rides home a different way that is 4 miles long.

This week, Robin rode to school and back 5 times.

For one time ride to school from house = Rode to School + Rode To home

For one time ride to school from house = 3 + 4

For one time ride to school from house = 7

Robin rides total of 5 times.

So, For five time ride to school from house = 5 × For one time ride to school from house

For five time ride to school from house = 5 × 7

For five time ride to school from house = 35 miles

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The complete question is:

Robin rides her bike 3 miles to school. She rides home a different way that is 4 miles long. This week, Robin rode to school and back 5 times. How many miles did Robin ride her bike this week?

The overlapping events when rolling a single six-sided die are (a) "getting an even number" and "getting a number less than 5."

The overlapping event occurs in option (a), where getting an even number and getting a number less than 5 have some numbers in common. The numbers 2 and 4 are both even and less than 5. Hence, these two events overlap. The other options do not overlap because getting a prime number, getting a number greater than 5, and getting a 2 do not have any numbers in common. The overlapping events when rolling a single six-sided die are (a) "getting an even number" and "getting a number less than 5."

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