Find the equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)

Answers

Answer 1

Solution

Since it is a perpendicular bisector, hence point M is the midpoint

[tex]\begin{gathered} \therefore Mid\text{ point AB}=(\frac{-2+5}{2},\frac{7+2}{2}) \\ mid\text{ point=(}\frac{3}{2},\frac{9}{2}) \end{gathered}[/tex]

Slope

[tex]\text{Slope (m)=}\frac{2-7}{5--2}=-\frac{5}{7}[/tex]

Since they are perpendicular

[tex]\begin{gathered} m_1\times m_2=-1 \\ -\frac{5}{7}\times m_2=-1 \\ m_2=\frac{7}{5} \end{gathered}[/tex]

The equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)

[tex]\begin{gathered} y-y_1=m(x_{}-x_1) \\ y-5=\frac{7}{5}(x-2) \\ y-5=\frac{7}{5}x-\frac{14}{5} \\ y=\frac{7}{5}x-\frac{14}{5}+5 \\ y=\frac{7}{5}x+\frac{11}{5} \end{gathered}[/tex]

The final answer

[tex]y=\frac{7}{5}x+\frac{11}{5}[/tex]

Find The Equation Of The Perpendicular Bisector Of The Line AB With A(-2,7) And B(5,2)
Find The Equation Of The Perpendicular Bisector Of The Line AB With A(-2,7) And B(5,2)

Related Questions

You have learned about quadratic and linear function in earlier grades. Explain in a variety of ways how you can distinguish the exponential function
f(x)=2^x
from the quadratic function
f(x) = x^2
and linear function
f(x) = 2x
. (Hint: compare the rate of change using finite differences in tables of values, and identify a constant ratio in the table of values).

Answers

We can distinguish between the linear, exponential function and quadratic functions graphically. The graph of the functions is as follows:

linear function f(x) = 2x will be straight line,

for exponential function f(x) = 2^x will rise or fall quickly in one direction

and for quadratic function f(x) = x^2 will be a parabola.

What is an exponential function?An exponential function is a type of mathematical function expressed in the form f(x) = a^x. where "x" is a variable and "a" is a constant  called the base of the function, which must be greater than 0. The most commonly used exponential  base is the transcendental number e, which is approximately equal to 2.71828. The exponential function is defined by the formula f(x) = ax. where the input variable x is displayed as an exponent. Exponential curves grow or fall exponentially. A quantity that increases or decreases at a  regular rate should exhibit either an exponential increase or an exponential decay.

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Consider the series. 16+24+36+54+...Does the series converge or diverge?

Answers

Explanation

We are asked to determine if the given series converge or diverge

A series is said to be convergent when it approaches a certain value as the series approaches infinity.

To check, we will have this re-written as

[tex]\sum _{n=0}^{\infty \:}16+24+36+54+\ldots \quad :\quad \sum _{n=0}^{\infty \:}-32\left(1-\left(\frac{3}{2}\right)^n\right)[/tex]

Every infinite sum of a non-zero constant diverges

Therefore, the series diverges

the side length of 11

Answers

A perfect square means that the given value is the result of the multiplication of an integer with itself, for example 2*2=4 →√

solve for x……………………..

Answers

Answer:

7.5/3

Step-by-step explanation:

7x-7.5 = 4x

-7.5 = -3x

x= 7.5/3

Could you help me with these two questions? 20 points !

1 ) Create an equation in point-slope form that has a slop of 5 passing through the points (3,5)

2) Create an equation in point slop form that has a slop of 2 and passes through the points (-1, 6)

Answers

The equation of line are given as y = 5x - 10 and y = 2x + 8 respectively

Point-Slope Formula

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The equation of a line is an equation that is satisfied by each and every point on the line. This means that a linear equation in two variables represents a line. The equation of a line can be found through various methods depending on the available information.

In this case, we have can proceed to write the equation of a straight line which is given as y = mx + c

m = slopec = y-intercept

Let's find the y - intercept and write the equation.

y = mx + c

5 = 5(3) + c; c = 5 - 15 = -10

y = 5x - 10

2) We have the slope as 2 and the points are (-1, 6)

The equation of the line can be written in form of y = mx + c

6 = 2(-1) + c

6 = -2 + c; c = 8

The equation is given as y = 2x + 8

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Find the axis of symmetry for the parabola that has the points (-2.5, 3) and (-4.5, 3) Justify your answer

Answers

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.

The axis of symmetry always passes through the vertex of the parabola.

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

A general graph of a vertical parabola is shown below:

Note there are two points x1 and x2 that have the same y-coordinate. These points are equidistant from the axis of symmetry. So, if we are given the coordinates of the points, we can find the axis of symmetry by calculating their average.

We are given the points (-2.5, 3) and (-4.5, 3).

Since they have the same y-coordinate, we calculate the average of the x-coordinates as follows:

[tex]x_s=\frac{-2.5-4.5}{2}=-3.5[/tex]

Thus, the axis of symmetry of the parabola is x = -3.5

HELP PLEASE HELP PLEASE NEED IT NOW!!
You run m miles on Monday, the same amount on Tuesday, and 3 miles on Wednesday. Write an expression in the simplest form that represents the total amount in each situation.
(please show work)

Answers

The expression that represents the given situation is 2x + 3 = T.

What do we mean by expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

So, the expression to represent the given situation is:

Since the miles run on Monday and Tuesday are the same, then let the miles run be 'x'.

Miles run on Monday is x.Miles run on Tuesday is x.Miles' run on Wednesday is 3.

Let, the total mile be T.

Now, the expression will be:

x + x + 3 = T2x + 3 = T


Therefore, the expression that represents the given situation is 2x + 3 = T.

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in a video store,a DVD that usually sells for $15 is marked 10% OFF that price. How much does the DVD cost now that it's on sale?

Answers

Answer

The cost of the DVD now that it's on sale will be $13.5​

Explanation

DVD actual price = $15

10% off the price will be (10/100 x $15) = $1.5

The selling price of the DVD now will be $(15 - 1.5) = $13.5

The cost of the DVD now that it's on sale will be $13.5​

Assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $1000. What percent of day care costs are more than $7100 annually?Click here to view page 1 of the standard normal distribution tableClick here to view page 2 of the standard normal distribution table,% (Round to two decimal places as needed.)

Answers

Answer:

81.59%

Explanation:

To find the percentage, we first need to standardize $7100. To standardize, we subtract the mean and then divide by the standard deviation. So, $7100 is equivalent to:

[tex]\begin{gathered} z=\frac{x-\operatorname{mean}}{std\text{ deviation}} \\ z=\frac{7100-8000}{1000}=-0.9 \end{gathered}[/tex]

Now, the percentage of day care costs that are more than $7100 is equivalent to the probability that z is greater than -0.9, so:

P(x > $7100) = P(z > -0.9)

Finally, we can use the standard normal distribution table to get:

P(z > -0.9) = 0.8159

So, the answer is 81.59%

Find the length of RS.A.73 unitsB.11 unitsC.About 8.5 unitsD About 3.3 units

Answers

Let,

[tex]\begin{gathered} R=(x_1,y_1)=(-4,1) \\ S=(x_2,y_2)=(-1,9) \end{gathered}[/tex]

The expression to calculate the distance between two points is,

[tex]\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(-1-(-4))^2+(9-1)^2} \\ D=\sqrt[]{(3)^2+(8)^2} \\ D=\sqrt[]{9+64} \\ D=\sqrt[]{73} \\ D=8.5\text{ units} \end{gathered}[/tex]

Thus, the length of the line RS is 8.5 units, and the correct option is option C.

can you guys s show work for graph inequality for

-2<x<5​

Answers

The graph of the inequality is a straight line on the x-axis

from -2 to 5 also, -2 & 5 are not included in the graph.

Given, an inequality

-2 < x < 5

we have to draw a graph for the given inequality,

as the value of 'x' is from -2 to 5.

So, the graph of the inequality is a straight line on the x-axis

from -2 to 5 also, -2 & 5 are not included in the graph.

Hence, the graph of the inequality is a straight line on the x-axis

from -2 to 5 also, -2 & 5 are not included in the graph.

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Julias frogs are 2/5 of the amount of Remus frogs. If Remus gives a half of his frogs to Julia, what will the ratio of Julia's frogs to Remus frogs be ?

Answers

Let:

Rf = Remus frogs

Jf = Julias frogs

[tex]Jf=\frac{2}{5}Rf[/tex]

If Remus gives a half of his frogs to Julia, what will the ratio of Julia's frogs to Remus frogs be ? so:

[tex]\begin{gathered} Rf=\frac{5}{2}Jf \\ Jf=\frac{2}{5}Rf+\frac{1}{2}Rf=\frac{9}{10}Rf \end{gathered}[/tex]

Therefore, the ratio will be:

[tex]\frac{\frac{9}{10}Rf}{Rf-\frac{1}{2}Rf}=\frac{9}{5}[/tex]

what is the sum of the expression 2/12 + 2/4

Answers

EXPLANATION:

In the exercise we have to perform the sum of two improper fractions which are heterogeneous because they have different denominators.

The procedure is the next:

[tex]\begin{gathered} \frac{2}{12}\text{ }+\frac{2}{4};=\frac{8+24}{48}=\frac{32}{48};\text{here }we\text{ simplify} \\ \\ \frac{32}{48}=\frac{16}{24}=\frac{8}{12}=\frac{4}{6}=\textcolor{#FF7968}{\frac{2}{3}} \\ \text{the answer is }\frac{2}{3} \end{gathered}[/tex]

Solve this equation for N. 3N + 5 = 38

Answers

ANSWER

N = 11

EXPLANATION

Given:

3N + 5 = 38

Desired Outcome:

Value of N

Solve for N

[tex]\begin{gathered} 3N+5=38 \\ subtract\text{ 5 from both sides} \\ 3N+5-5=38-5 \\ 3N=33 \\ divide\text{ both sides by 3} \\ \frac{3N}{3}=\frac{33}{3} \\ N=11 \end{gathered}[/tex]

Hence, the value of N is 11.

(8u^2+3u-4)+(8u^2+3u-1)-(3u^2-3u-8)

Answers

Simplify the expression

[tex]\mleft(8u^2+3u-4\mright)+\mleft(8u^2+3u-1\mright)-\mleft(3u^2-3u-8\mright)​[/tex]

Removing all the parentheses, taking special care to change the signs of the last three terms:

[tex]8u^2+3u-4+8u^2+3u-1-3u^2+3u+8​[/tex]

Now collect like terms:

[tex]8u^2+8u^2-3u^2+3u+3u+3u-4-1+8​[/tex][tex]13u^2+9u+3​[/tex]

hi, I'm supposed to write a exponential equation for the graph but I'm not sure how to do it

Answers

d)

To determine the type of function, we would compare the y values. If the ratio of consecutive y values is the same, then the function is exponential. We have

2/1 = 4/2 = 8/4 = 2

Thus, it is an exponential function. The general formula for an exponential function is

y = ab^x

We would find a and b

Substituting x = 0 and y = 1 into the formula, we have

1 = ab^0

1 = a

Substituting x = 1 and y = 2 into the formula, we have

2 = ab^1

2 = ab

Substituting a = 1 into 2 = ab, then

2 = 1 * b = b

By substituting a = 1 and b = 2 into the original formula, the equation would be

y = 2^x

Write the equation of the line parallel to x+7y=21 that passes through the point (–14, 4).

Answers

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

First, rearrange x + 7y = 21 into y = mx + c form.

x + 7y = 21

7y = - x + 21

y = -1/7x + 3

Parallel lines have the same gradient so gradient of line is -1/7.

Equation of line is now y = -1/7x + c.

Substitute (-14,4) into the equation to find c.

4 = -1/7(-14) + c

4 = 2 + c

c = 2

Hence, equation of line is y = -1/7x + 2.

help meeeeeeeeeeeeeee pleaseeeeeee

Answers

Answer: Width = 5.7 feet, Length = 10.5 feet

Step-by-step explanation:

Let the width be w. Then, the length is 2w-0.9.

[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]

Determine whether the following sequence is geometric. If so, find the common ratio. 1, -4, 16, -64, . . .

Answers

Given:

Geometric sequence is:

1,-4,16,-64

Sol:

For geometric sequence is:

[tex]a_n=a_1r^{n-1}[/tex][tex]\begin{gathered} a_1=1 \\ a_2=-4 \end{gathered}[/tex][tex]\begin{gathered} a_n=a_1r^{n-1} \\ -4=1r^{2-1} \\ -4=r \end{gathered}[/tex]

Common ratio is -4.

How does the allusion to the Pied Piper in “Pan: God of the Wild” contribute to the meaning of the myth?


i need help

Answers

The allusion to the pied piper in "Pan: God of the wild" contributes to the meaning of the myth by B. showing that Pan is a god that leads others to  destruction.

What's the story of the pied piper about?

The story goes that the pied piper went into a town infested with rats and made a deal with the people of the town to drive the rats away for a token. The town agreed and the pied piper drove the rats into the river. When the piped piper asked for his money, they refused to pay up. The pied piper took his revenge on the town by leading children of the town away from the town and they were never discovered.

The myth only shows that Pan is a god that leads others to destruction.

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Given MK is a median use the figure below to answer the questions below.



If JM = 23, then JL =

If LJ = 20, then ML =

Answers

Answer:

[tex]46, 10[/tex]

Step-by-step explanation:

A median is the segment drawn from the vertex of a triangle that bisects the opposite side.

find the unit rate. round to the nearest hundredth, if necessary $200 for 15 ft

Answers

EXPLANATION

The unit rate is given by the following relationship:

Unit rate= $200/15ft = $13.3333.../ft

Then, rounding to the nearest hundreth:

Unit rate = $13.33/ft

12__-15 = -3
divide
multiply
add
subtract

Answers

Answer:

multiply 1 is the correct answer

12×1 - 15 = -3

the radius of a semicircle is 5 kilometers. what is the semicircles diameter

Answers

The semicircles diameter is 10km

What is diameter?

The diameter is defined as twice the length of the radius of a circle.

From the relation diameter of a circle is given as d= 2r

Radius of the semicircle is 5km

Substitute the radius in to d=2r

diameter= 2 x 5= 10km

Therefore, the semicircles diameter is 10km

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Use distributive property and combining like terms to simplify.
5x-4y+2(y+x)

Answers

The simplified form is 7x - 2y.

Distributive property: What Is It?

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

According to question,

5x-4y+2(y+x)

5x-4y+2y+2x

7x-2y

Hence, simplified form is 7x - 2y.

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If f(x) = x2 and g(x) = 3x - 1, find f(g(x))

Answers

Given the following functions:

[tex]\begin{gathered} f(x)=x^2 \\ g(x)=3x-1 \end{gathered}[/tex]

To compose then, is basically use the inside function as the argument.

[tex]f(g(x))=f(3x-1)[/tex]

If we call '3x-1' as 'u'

We know the following

[tex]\begin{gathered} f(u)=u^2 \\ u=3x-1\Rightarrow f(3x-1)=(3x-1)^2 \end{gathered}[/tex]

And this is our answer.

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

8. Draw the graphs described below and answer the question for each.A. Draw the graph of a line with undefined slope. Write the equation of the line youdrew.B. If you wrote the first letter of your LAST NAME (upper-case letter) on a coordinateplane, would it be a function? Make a sketch and provide an explanation as to how youdetermined whether it is a function or not.

Answers

Question:

Draw the graphs described below and answer the question for each.

A. Draw the graph of a line with an undefined slope. Write the equation of the line you drew.

B. If you wrote the first letter of your LAST NAME (upper-case letter) on a coordinate plane, would it be a function? Make a sketch and provide an explanation as to how you determined whether it is a function or not.

Solution:

A.

Remember that any line that has an undefined slope is a vertical line, that has no y-intercept. Therefore the equation of a line with an undefined slope is x = a, where a = x-intercept.

we can conclude that the correct answer is:

According to this information, we can take the following equation for a line with an undefined slope:

[tex]x=5[/tex]

and its graph would be:

B. Remember that a simple visual way to determine if a particular graph is a function is by imagining vertical lines passing through it. If the vertical line touches more than once, it is not a function.

For example, consider the curve that represents the letter O:

And notice that the above curve is a circle and note also the following fact:

We can conclude that the correct answer is:

The curve of the letter O is not a function, since a line intersects at two points of this line.

Point D (8,2) is reflected across the y-axis to form point E.

What are the coordinates of point E?

Answers

Point E would be (-8,2) Due to the reflection, Whenever you reflect on the y or x axis you move the original coordinates to the quadrant that you reflected on, Also The X axis coordinates go first then the Y axis coordinates go last in the ordered pair I have no idea if this helped but yw :D.

Show that the equation is not an identity by finding a value of x for which both sides are defines but not equal.

Answers

We are given the expression:

[tex]\cos (x-\pi)=\cos (x)[/tex]

We, simply replace the values of solution given and then determine in which it is not a solution, but we can see that when we replace x = 0, we will get:

[tex]\cos (\pi)\ne\cos (0)[/tex]

So, this proves that the function is not an identity.

10, 15, 24, 24, 25, 30 What is the mode?

Answers

Mode means the number that appears most.

The answer is 24 since it appears twice.

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High Incomes Don't Bring You HappinessBased on the information in the article, which of the following would improve the happiness of the median U.S. household.A. keeping their income below $52,000B. keeping their income at exactly $52,000C. increasing their income to no higher than $75,000D. increasing their incomes to be greater than $75,000 Turn the following word equation into a symbolic equation: potassium hydroxide and hydrobromic acid react to form potassium bromide and water. you are in class listening to the instructor, but the students on both sides of you are having separate quiet conversations. even though these conversations are distracting, you are able to maintain your focus and attention on the lecture. what skill are you utilizing? a.divided attention b.selective attention c.ignoring d.focused attention Explain when 'p or q' is true. Select all that apply.A. 'p or q' is true when both p and q are false.B. 'p or q' is true when p is true and q is false.C. 'p or q' is true when p is false and q is true.D. 'p or q' is true when both p and q are true. 14 in 8 in 5 in 7 in 9 in 15 in The mass of a bike and cyclist is 75.0 kg. The rider starts at rest at a height of Om. She speeds up to 6.00 m/s. What is the mechanical energy of thebike?The answers would be one of the four choices in the pictures. Outline alpha, betta and gamma radiation in terms of depth of tissue penetration, ionizing effect and speed of radiation. Find the midpoint M of the line segment joining the points C=(8,7) and D= (4,-5) 1. Write an equation for a polynomial with the following properties: it has even degree, it has at least 2 terms, and, as the inputs getlarger and larger in either the negative or positive directions, the outputs get larger and larger in the negative direction. Determine whether the statement is true or false.2 {x | x N and x is even}Is the statement true or false? True False Determine the slope of the line represented by the equation: -5x - 7y = -9DO NOT USE 1 AS THE DENOMINATOR! Solve for a side in right triangles A transformation is a nonrigid transformation if it does not preserve what? Can you name anonrigid transformation? What is the rule for the nonrigid transformation?Nonrigid transformationRule (x,y) In the figure, RS is 24 units long. What is the length of WV ? For which function is f(-x) = f(x)? (A) f(x) = sqaure root x(B) f(x) = 2x (C) f(x) = x2 (D) f(x) = x2 (E) f(x) = 2^x 12 times a number g Graph the line. I am only able to use 2 points on this graph. Find the area of this trapezoid. Be sure to include the correct unit in your answer. Continue 13 cm 20 cm 8 cm 5 cm 0 0/0 08 cm cm X cm ? LUULIO AUnicht Decopied Terms of Use | Priva let f(x)=3x+5 and g(x) =3x^2 -x-10. find (f/g)(x) and state its domain What are the three components of an attitude? Give an example of an attitude and distinguish each of these three components for those components.