Write an equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5).

y =

Answer:

10 and 24units

Step-by-step explanation:

Pythagoras' Theorem applies to right angle triangles with the formula:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is the longest side, with a and b the shorter ones (interchangable)

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]

Now we can find the side lengths.

[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]

Therefore the side lengths are 10 and 24 units.

Answer: 18pi + 36 + (36-4.5pi)+4.5pi= 22.5pi + 36 + (36-4.5pi)

Step-by-step explanation:

CDEF is a square so all sides of CDEF are 6cm.

This tells us the area of CDEF which is 36cm squared

This tells us the radius of AE which is the side FE which we know is 6cm.

Area of a half circle= pi x r squared/2

Area of AE= pi x 36/2= 18pi

Now, look at the square with the half circle inside ABCF. If the half circle was part of the shaded square, the area would be 36cm squared. But since it isn't we need to minus the area of the half circle from 36cm square (area of ABCF)

Area of half circle BC= pi x 3 squared/2= pi x 9/2= 4.5pi.

So the area of ABCF is 36-4.5pi.

CD would also have an area of 4.5pi as it is the exact same half circle.

Area of AE=18pi cm squared

Area of CDEF= 36cm squared

Area of ABCF= 36-4.5pi

Area of CD= 4.5pi

18pi+36+(36-4.5pi)+4.5pi

simplified to:

22.5pi + 36 + (36-4.5pi)

Answer:

288

Step-by-step explanation:

32 x 9=288

Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.

Let's first try to understand what is a fraction.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

A fraction would be 5/10, for instance.

Here, the numerator is 5 and the denominator is 10.

6/8 is a fraction.

6/8 can be simplified further.

6/8 = 3/4

9/12 is also a fraction.

9/12 can be simplified further.

9/12 = 3/4

To compare 2 fractions first we try to make the same denominator.

we have the same value. so they are equivalent.

Given question is incomplete complete the question here:

Are 6/8 and 9/12 equivalent?

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Whatever the case a quadrilateral has always a sum of interior angles = 360°.

A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which cannot be collinear. A quadrilateral has four sides, four angles, and four vertices. The word "quadrilateral" is derived from the Latin words "quadra" (four) and "latus" (sides). A quadrilateral may or may not have equal lengths on each of its four sides.

A quadrilateral is a polygon with four sides, four angles, and four vertices. The arrangement of the vertices must be considered whenever a quadrilateral is named. For instance, the following quadrilateral should be referred to as ABCD, BCDA, ADCB, or DCBA. Since they alter the order of vertices in which a quadrilateral is formed, it cannot be called ACBD or DBAC.

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Answer:

she has rode 16 miles this week

Step-by-step explanation:

3 miles on monday 3 times that many on tuesday plus 4 miles one wensaday add them all up

3 times 3 is 9 plus 3 is 12 plus 4 is 16 there fore 16 miles in totale

sorry for my speling erros

She rode a total distance of 16 miles this week.

An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

The distance rode by Lexi per day is mentioned below -

Monday - Lexi rode 3 miles on a bike.

Tuesday - Lexi rode 3 times more than she did Monday.

Wednesday - Lexi rode an additional 4 miles.

We can write the expression to find the total distance in miles covered by Lexi as -

d = d{M} + d{T} + d{W}

d = 3 + (3 + 3) + 4

d = 3 + 6 + 4

d = 13 miles

Therefore, she rode a total distance of 16 miles this week.

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Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : (X-5)-1

Thus,

after substituting the value of x with 9

We get,

=> (X-5) -1

=>(9-5)-1

=> 4 -1

=> 3

Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

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The probability best prediction for the number of times that Ellen will draw a blue marble is 200.

Number of blue marbles: 222

Number of red marbles: 333

Total number of marbles: 555

Probability of drawing a blue marble:

222/555

= 0.4

Number of times drawing a blue marble:

300300300 x 0.4

= 120,120,120

Rounded to nearest whole number:

120,120

Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is

222/555

= 0.4.

Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.

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The explanation of four quadrant are explained below.

In the coordinate plane the first coordinate or the x-coordinate will refer to the number which corresponds with the point's horizontal location as determined by the number on the x-axis.

And the second coordinate known as the y-coordinate, will refer to the number which corresponds with the point's vertical location as determined by the number on the y-axis.

By using these x and y values, we have divide the graph, into four part such as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.

Here we want to know that each quadrant contains certain directions.

=> Quadrant 1 placed on 0 to 90 degrees.

=> Quadrant 2 placed on 90 to 180 degrees.

=> Quadrant 3 placed on 180 to 270 degrees.

=> Quadrant 4 placed on 270 to 360 degrees.

And the value in the quadrant are like as follows:

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The amount earned by the bookstore if all of the packages of supplies are sold is given as follows:

$60.

Before obtaining the amount earned, we must obtain the number of packages, with is given by the greatest common factor of the amounts of each item.

The amounts of each item are given as follows:

36, 48 and 24.

Their greatest common factor is obtained factoring them simultaneously by the same prime factors as follows:

36 - 48 - 24|2

18 - 24 - 12|2

9 - 12 - 6|3

3 - 4 - 2

Hence:

gcf(36, 48, 24) = 2² x 3 = 12.

Which is the number of packages. As each package sells for $5, the amount earned is given as follows:

12 x 5 = $60.

Each package is composed by:

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On solving the provided question, we can say that the values of the equation here will be y +1 = 8X 8y = 16 => y = 9.455

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

y+1= -4(x - 2) 2x8y = 16​

x = 0

y +1 = 8X 8y = 16

y = 9.455

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Answer:

13

Step-by-step explanation:

mean= (10+19+20+13+13+2+10+8+25+10)/10=130/10=13

The mean number of first cousins for the given sample is 13. Thus, Option C is correct.

Mean is the arithmetic average of the given set of observations.

Mean for ungrouped or raw data is obtained by adding all the observations and dividing it by the number of observations.

Mean = Sum of all the observations/ Total number of observations.

Mean = ∑( x1 + x2 + x3 .... xn /n)

Where X bar represents mean, n is no. of observations and ∑ denotes sigma i.e. sum of all the values.

No. of observations (n) =10

Mean = ∑ (10 + 19 + 20 + 13 + 13 + 2 + 10 + 8 + 25 + 10) / 10

Mean = 130 / 10

= 13

Therefore, Option C is the correct answer.

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The error is that the student rounded off the outcome after combining the numbers.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number.

For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

So, we have:

162 + 287 + 395 = 840

The error:

After adding the numbers, the student rounded the result.

If the learner had added the numbers first and then rounded the result, they would have received the correct answer of 850 instead of 840.

When estimating totals, students should be taught to round numbers first before adding them.

Therefore, the error is that the student rounded the outcome after combining the numbers.

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Correct question:
A third-grade student is asked to find the best-estimated answer for the problem below by rounding to the nearest ten.

162 + 287 + 395

The student gets an answer of 840. Which of the following best describes the student's error?

Definition of Ray:

'A part of a line that has one endpoint and extends indefinitely in one direction'.

The correct statement is A.

A ray is a part of the line having one fixed point and the other point does not have an end. It means that a ray has one terminating end and the other end is extending infinitely.

Given definitions of ray:

A. a part of a line that has one endpoint and extends indefinitely in one direction.

B. the set of all points in a plane that are a given distance away from a given point.

C. lines that lie in the same plane and do not intersect.

D. a part of a line that has two endpoints.

Only statement A satisfies the definition of ray.

Hence, the definition of ray is described by statement A.

A part of a line that has one endpoint and extends indefinitely in one direction.

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The given equation 1 value of F(x) is 0.109 and in equation 2 F(x) is -4 respectively.

Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle. This concept is given by the Greek mathematician Hipparchus.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional figures. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.

if x⁰=π in eq1

then [tex]f(x)= sin\ 2 \pi[/tex]

[tex]f(x) = 0.109[/tex]

if x⁰= -1 in eq2

then [tex]f(x)=3(-1)-(-1)^2[/tex]

[tex]f(x) = -4[/tex]

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The expected time until the tourist arrives in the city is 4.75 hours.

The expected time until the tourist arrives at the city can be calculated by using the formula for the expected value:

Expected value = (probability of outcome 1) x (value of outcome 1) + (probability of outcome 2) x (value of outcome 2) + ...

In this case, there are two possible outcomes: the tourist takes road A or road B.

If the tourist takes road A, the expected time until he arrives in the city is the average of the two possible travel times (4 hours and 8 hours). The probability of this outcome is 0.5 (the tourist has an equal chance of choosing either road). So, the expected value for this outcome is (0.5) x (4 + 8)/2 = 6 hours.

If the tourist takes road B, the expected time until he arrives in the city is 7 hours. The probability of this outcome is also 0.5. So, the expected value for this outcome is (0.5) x 7 = 3.5 hours.

To find the overall expected time until the tourist arrives in the city, we add up the expected values for each outcome:

Expected time = (0.5) x 6 + (0.5) x 3.5 = 4.75 hours

So the expected time until the tourist arrives in the city is 4.75 hours.

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The trigonometric ratio as a fraction for sinC is  , and the decimal is 0.80.

The trigonometric functions are actual functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

The widely used trigonometric functions are sine, cosine and tangent. The trigonometric functions also operate the inverse of the functions.

For the given triangle the trigonometric values are as follows:

For angle A the opposite side is CB, the adjacent side is AB and the hypotenuse is AC.

For angle C the opposite side is AB, the adjacent side is CB and the hypotenuse is AC.

[tex]sinC = \frac{\text{Opposite side }}{Hypotenuse} = \frac{4}{5} =0.80\\ \\ cosC = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{3}{5} = 0.60\\\\tanA =\frac{\text{Opposite side }}{Adjacent side} = \frac{3}{4} = 0.75\\\\tanC= \frac{\text{Opposite side }}{Adjacent side} =\frac{4}{3} = 1.33\\\\cosA = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{4}{5} = 0.80\\\\sinA= \frac{\text{Opposite side }}{Hypotenuse}=\frac{3}{5} =0.60[/tex]

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Carman buy the video game in the cost of $45.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Carman has saved 80% of the money she needs to buy a new video game.

And, she saved the cost $36.

Let total cost of the video game = x

So, We can formulate;

⇒ 80% of x = $36

⇒ 80/100 × x = 36

⇒ 8x = 360

⇒ x = $45

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The area of the window that lets in the most light will be the one that causes the window to transmit the most light overall.

To find the proportions of the window that will admit the lightest, we need to maximize the total area of the window while keeping the perimeter fixed. The total area of the window is the sum of the area of the rectangle and the area of the semicircle. The area of the rectangle is the product of its length and width, and the area of the semicircle is half the product of its radius and the area of a full circle with the same radius.

Since the perimeter is fixed, the length and width of the rectangle are also fixed. The radius of the semicircle can be found using the perimeter and the length and width of the rectangle.

Once we have the radius of the semicircle, we can find the area of the rectangle, the area of the semicircle, and the total area of the window. Since the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does, we will have to multiply the area of the semicircle by 0.5 to find the total amount of light transmitted by it.

Finally, we will have to compare the total amount of light transmitted by the window for different values of the length and width of the rectangle. The proportion of the window that admits the most light will be the one that results in the maximum total amount of light transmitted by the window.

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Logical Error: In computer programming language, a logic error is a bug or in a program or code that causes it to operate incorrectly, but not to terminate abnormally (or crash).

A logic error developed unintended or undesired output or other behavior, although it may not immediately be recognized as such.

For example, assigning a value to the wrong variable may cause a many of unexpected program errors.

These errors can be programmer mistakes or sometimes machine less memory to load the code.

if(x>=5) {

// program

}

else if(x==5) {

//program

}

else(x<=5) {

//program

}

they all do not give any error.

x=5 gave an error because it is value assigning to 5.

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Answer:

20x²

-5xy

14y²

Step-by-step explanation:

17x² + 3x² = 20x²

-3xy - 2xy = -5xy

14y²

The length of each piece of the sandwich is 0.3125 feet.

A unitary approach is a mathematical technique for finding the value of a single unit and then multiplying it by any number of other units to derive the value of the given units.

Given, Zachary's art club ordered a giant sub sandwich for a party.

Therefore, t6o obtain the length of each piece we have divide the total length of the sandwich by the total number of pieces which is,

= (5/16) feet.

= 0.3125.

So, The length of each piece is 0.3125 feet.

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Answer:

B) -9 + 4 2/3

Explanation:

The answer is B because -9 - (-4 1/3) is -4 2/3 which is equal to -14/3, so that means B also has the same sum.

I hope this helps you! :)

Jackie spends 15 minutes running every day.

Part A: The relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day can be represented by the following pair of linear equations:

Equation 1: x + y = 55 (This equation represents the total amount of time Jackie spends running and dancing every day, which is 55 minutes)

Equation 2: y = x + 25 (This equation represents the relationship between the number of minutes Jackie runs and the number of minutes she dances, which is that she dances 25 minutes longer than she runs)

Part B: To find out how much time Jackie spends running every day, we can substitute the second equation into the first equation:

x + (x + 25) = 55

2x + 25 = 55

2x = 30

x = 15

Therefore, Jackie spends 15 minutes running every day.

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Answer:

16

Step-by-step explanation:

16 is a positive multiple of 8, in which 16²=256>100 and 16<20 are true statements.

Answer:

[tex]$x=\boxed{16}$[/tex]

Step-by-step explanation:

Since $x$ is a positive multiple of 8, it must be at least 8. Since $x^2>100$ and $x$ is at least 8, the only solution is $x=16$.

To verify this, note that $x=8$ does not satisfy the inequality $x^2>100$, but $x=16$ does, so $x=16$ is the only solution that works.

Therefore, $x=\boxed{16}$.

Answer:

10 students are wearing shirts other than blue or white.

Step-by-step explanation:

1 10 of the students in the classroom are wearing blue shirts, which is 1/1020 = <<1/1020=2>>2 students.

2 5 of the students in the classroom are wearing white shirts, which is 2/5*20 = 8 students.

Altogether, 2+8 = <<2+8=10>>10 students are wearing either blue or white shirts.

There are 20 students in the classroom, so 20-10 = <<20-10=10>>10 students are wearing shirts other than blue or white.

$21,500  this would be cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)

EMV 1 = 0.2*10,000 + 0.3*2,000 + 0.5*-5,000 = $100EMV 2 = 0.2*6,000 + 0.3*4,000 + 0.5*-0 = $2,400.

Comparing both funds based on EMV calculations, Fund B shows a higher EMV. Therefore, to maximize expected value, we should invest in Fund B with an expected value of $2,400. First, his EMV for Fund A is not the same as Fund A's return being higher or lower in good economic conditions. Therefore, the EMC can also be higher or lower. But obviously the economy changes quickly sometimes. You don't always get the same return. So relying solely on returns is risky. Relying heavily on favorable economic conditions makes Fund A vulnerable to change and increases investor risk, so investors need to be more diversified. We can do the calculation:

Fund A return in good economy = Difference between A and B: EMV (Fund A) = EMV (Fund B) 0.2*X + 0.3(2,000) + 0.5(- 5,000) = 2 4,000.2X = 4,300X = $21,500.

Therefore, if the economy is good, Fund A's return should be $21,500 for there to be indifference between Fund A and the fund B.

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Answer:

Step-by-step explanation:

slope is the coefficient of x when the coeficient of y is 1.

we need change the form.

2y=x+8

y=[tex]\frac{1}{2}[/tex]x+4

so, the slope of a line parallel to the line is 1/2