Find an equation for the perpendicular bisector of the line segment whose endpoints are ( 8 , − 1 ) (8,−1) and ( 4 , − 9 ) (4,−9).

Answer:

3

Step-by-step explanation:

let unknown point (x, -2)

-2(x)+4=-2

-2x=-6

x=3

By completing squares, we will see that the two solutions of the quadratic equaiton are:

m = -7 + √(145)/2

m = -7 - √(145)/2

Here we have the quadratic equation:

m^2 + 7m - 51/4 = 0

If we multiply both sides by 4, we will get

4m^2 + 28m - 51 = 0

Now, remember the relation:

(a + b)^2 = a^2 + 2ab + b^2

Then to complete the squares we can write:

(2m)^2 + 2*14*m + (14)^2 - (14)^2 - 51 = 0

(2m + 14)^2 - 14^2 - 51 = 0

(2m + 14)^2 = 145

We already completed squares, now the solutions are:

2m = -14 ± √145

m = (-14 ± √145)/2

m = -7 + √(145)/2

m = -7 - √(145)/2

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Ratio of length of cell A to the length of cell B will be 20 : 1.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

Length of cell A = 4 x 10⁻⁵

Length of cell B = 0.000002 = 2 x 10⁻⁶.

Now,

Length of cell B into scientific notation = 2 x 10⁻⁶

Hence, The ratio of the length of cell A to cell B =  4 x 10⁻⁵ / 2 x 10⁻⁶

                                                                          = 2 x 10⁻⁵⁺⁶

                                                                          = 2 x 10¹

                                                                          = 20

Thus, Ratio of length of cell A to the length of cell B is 20 : 1.

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∵ There are 142 who prefer carrots

∵ There are 250 all

∴ The fraction represents who prefer carrots is

We must simplify the fraction by divide up and down by the same number until getting the simplest form

∵ 142 and 250 can divide by 2

∵ 71 and 125 can not divide by any number

∴ The fraction is 71/125

∴

∵ There are 97 who prefer peas

∵ There 250 all

∴ The fraction represents who prefer peas is

∵ 97 and 250 can not divide by the same number

∴ The fraction is 97/250

∴ The ratio is 97: 250

Each person will sell 8 shirts if 56 shirts were sold

Mandy and 6 of her teammates each sold an equal number of shirt

Mandy is one person, let add 1 plus six to get the total number

1 + 6

= 7

The total number of shirts sold is 56 shirts

Since there are 7 people, the number of shirt that each person will sell can be calculated by dividing 56 by 7

= 56/7

= 8

Hence 8 shirts will be sold by each person

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The description of the one transformation that maps ∆ABC to ∆A'B'C' is a rotation counterclockwise, 90 degrees, with the center at the origin

A rotation transformation can be described as the angular motion of a rigid, geometric figure around a point

The vertices on the triangle ∆ABC are;

The vertices on the triangle ∆A'B'C' are;

The rotation of a point A(x, y), 90° counterclockwise about the origin gives the point A'(-y, x)

The reflection of a point (x, y) across the y–axis gives the point A'(-x, y)

Therefore;

The coordinates of the vertices of∆ABC following a 90° counterclockwise rotation gives;

A(-5, -2) → A'(2, -5)

B(-7, -4) → B'(4, -7)

C(-5, -5) → C'(5, -5)

Therefore;

The transformation that maps ∆ABC to ∆A'B'C' is therefore a rotation of 90° counterclockwise about the origin

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Answer:

No it's not a function

Step-by-step explanation:

You can use the vertical line test to determine whether it's a function or not. If the vertical line touches the graph at more than one point, the graph is not a function therefore the answer is no.

The most appropriate choice of percentage will be given by-

The store have to increase the price of the item by [tex]11\frac{1}{9}[/tex] %  in order to sell it for the original amount.

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Let the original price be x

Percentage decrease in price due to sale = 10%

Decrease in price due to sale = [tex]\frac{10}{100} \times x[/tex]

                                                  = [tex]\frac{x}{10}[/tex]

New price = ([tex]x - \frac{x}{10}[/tex])

                 = [tex]\frac{10x-x} {10}[/tex]

                 = [tex]\frac{9x}{10}[/tex]

Now,

Increase in price from [tex]\frac{9x}{10}[/tex] to [tex]x[/tex] = [tex]\frac{x}{10}[/tex]

Percentage by which the store have to increase the price of the item in order to sell it for the original amount =

                                                                  [tex]\frac{\frac{x}{10} }{\frac{9x}{10} } \times 100[/tex]

                                                              =[tex]\frac{x}{10} \times \frac{10}{9x} \times 100[/tex]

                                                              = [tex]\frac{100}{9}[/tex]

                                                              = [tex]11\frac{1}{9}[/tex] %

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The slope of the line from the pair of given points would be [tex]m = 5[/tex].

Hope this helps!

Question:

On a circle of radius 6 feet, what angle would subtend an arc of lenght 5 feet?

nswer:

he frormula for the lenght of arc (s) given an angle theta (in radians) and a radius R is:

We'll just have to clear theta from this equation, and convert it to degrees.

Therefore, the angle that would subtend an arc of lenght 5 feet on a circle of radius 6 feet is 47.74°

The predicted distance of the ball is 271.93 feet.

The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time. Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Given Data

The speed, s, is measured in miles per hour, and distance, y, is

measured in yards.

The line of fit is given by ý = 3.98 +53.59s.

When s = 5 sec

y = 3.98 + 53.59(5)

y = 3.98 + 267.95

y = 271.93

The predicted distance of the ball is 271.93 feet.

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Answer: 31,000

Step-by-step explanation: You need to find two  numbers that if you add the two variables will equal 76,000 and i checked 40,000-14,000=A=40,000 which equaled  66,000 and then 50,000-14,000=A+50,000  which equaled 86,000 so i knew the number in between was the one which was 45,000 and 45,000-14,000=31,000

A statistics professor plans classes so carefully that lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes.The Probability that a given class period runs between 51.5 and 51.75 minutes is 0.025.

The density of a place refers to the quantity of things—which may include people, animals, plants, or objects—there are in it. Divide the number of objects by area's measurement to determine density. A country's population density is calculated by dividing its total population by its area, expressed in the square kilometers or miles.

A flat distribution with the same probability density for each number is called a uniform distribution. The area beneath the distribution's graph must be 1. This distribution has a range of 10.0 and runs from 46.0 to 56.0 minutes (56.0-46.0). Since the density must be 1/10, 10.0*0.1 Equals 1.0.

Multiply the range between the numbers by the probability density to get the likelihood of being between two numbers

range: 50.75-50.5 = 0.25

0.25*0.1 = 0.025

P(50.5 < x < 50.75) = 0.025

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The x intercepts are 0, 1, -2, 2.

What is intercepts?

The term "intercept" refers to the x- and y-intercepts of of a given equation. The x-intercept is the point at which a line crosses the x-axis and the y-intercept is the point at which a line crosses the y-axis.

In the linear equation, we have the general form as y=mx+b

where m and b are constants.

We have to find the x intercept of the given function.

Given equation is [tex]x^{4} +x^{3} -4x^{2} -4x[/tex]

put this equation equals to 0

x^{4} +x^{3} -4x^{2} -4x = 0

[tex]x(x^{3} +x^{2} -4x-4)=0[/tex]

from this x = 0

x =1 is also the root of the equation

we get [tex]x^{2} -4=0[/tex]

from this

x = -2, 2

The intercept are 0,1,2,-2.

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Answer:10(x-3)

Step-by-step explanation:

Just divide 10 on both sides and be done with it

10/10x-30/10

move ten to the left

10(x-30/10)

10(x-3)

If you have ​$50 in your bank account and each week you plan to deposit ​$8 from your allowance and ​$20 from your paycheck. The number of  weeks from now that you will have ​$210 in your bank​ account is: 5.71w.

The given equation is:

b=50+​(20+8​)w

Where:

b  is the amount in your account after w weeks.

w = Number of week

Hence,

b = 50+​(20+8​)w

b = 50+28w

b-50 = 28w

(b-$50)/28 = w

(210-$50)/28 = w

160/28 = w

5.71 = w

Therefore we can conclude that you will have the amount of  $210 in your account in 5.71 weeks.

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Answer:

true

Step-by-step explanation:

2.5≤25

Compare 2.5 and 25.

True

The value of x for the given arithmetic sequence is x = 4.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Given,

First three terms of an arithmetic sequence are x, 2x + 4, 5x

The difference of 1 and 2 term equals the difference of 3 and 2 term.

⇒ 2x + 4 - x = 5x - 2x - 4

⇒ x + 4 = 3x - 4

⇒ 2x = 8

⇒ x = 4

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Check the picture below.

Answer:30 in.

Step-by-step explanation:13+5+12

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-9}{3 +2}\implies {\Large \begin{array}{llll} -\cfrac{9}{5} \end{array}}[/tex]

Answer:

A=14

B=pi 7^2

Step-by-step explanation:

All you need to do is put pi symbol on calculator and x by 7 squared to get answer

Answer:

1:20

Step-by-step explanation:

Because it's maths duhh

Answer:

2 apples and 4 bananas

Step-by-step explanation:

Given info:

Question given:

Determine the number of apples, x, and the number of bananas, y, that Juan bought.

Solution:

Since, we know that;

apples = x

bananas = y

Cost of each apple = $1 & Cost of each banana = $ 0.50

Total = 6

The equation that represents the following information:

x + y = 6

x + 0.5y = 4

We can multiply the top equation by -1 so it becomes -x -y = 6

-x - y = 6

x + 0.5y = 4

Now, we can use elimination to cancel out the x.

-0.5y = -2

y = 4

Because y=4, x must be 2 since x+y=6. So,

x = 2 and y = 4

Which means;

Juan bought 2 apples and 4 bananas.

~kavinsky

Answer:

D

Step-by-step explanation:

The line needs to be dotted since the boundary is not included.

The line should be shaded above because of the > sign.

Answer:

Step-by-step explanation:

If its 15000:65000

Then we divide both sides by 1000 first :

15 : 65

Then we divide both sides by 5 :

3 : 13

This is simplified

If K is a unit then it will be 3k : 13k by doing the above steps but skipping the first.

Hope this helped and have a good day

The number of times heavier that the largest dog is when compared with the smallest dog is B. 41.

It should be noted that from the information given, the biggest dig is the St Bernard and it has 145 pounds.

Also, it should be noted that the smallest dog is Yorkie and it had 3.5 pounds. Therefore, it should be noted that the number of times heavier will be:

= Weight of biggest fog / Weight of smallest dog

= 145 / 3.5

= 41.

It is 41 times heavier.

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y = feet in the air

x = seconds it takes

well, what's "y" when x = 3?

[tex]y=-2.7(3)^2 + 30(3) + 6.5\implies y=-2.7(9)+96.5\implies \boxed{y=72.2~feet}[/tex]

now, what's "x" when y = 75?

[tex]75=-2.7x^2+30x+6.5\implies 0=-2.7x^2+30x-68.5 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-2.7}x^2\stackrel{\stackrel{b}{\downarrow }}{+30}x\stackrel{\stackrel{c}{\downarrow }}{-68.5} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]

[tex]x=\cfrac{-30\pm\sqrt{(30)^2 - 4(-2.7)(-68.5)}}{2(-2.7)}\implies x=\cfrac{-30\pm\sqrt{900-739.8}}{-5.4} \\\\\\ x=\cfrac{30\mp\sqrt{160.2}}{5.4}\implies x\approx \begin{cases} 3.2&\textit{on the way up}\\\\ 7.9&\textit{on the way down} \end{cases}[/tex]

The value of the expression given as b(a+1)² -5(a+1) will be a²b + 2ab + 2b - 5a - 5.

It should be noted that based on the information that given, we want to factor out the variables that are given.

This will be illustrated thus:

b(a+1)² -5(a+1)

= b(a + 1)(a + 1) - 5(a + 1)

= b(a² + 2a + 2) - 5a - 5

= a²b + 2ab + 2b - 5a - 5

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