Perpendicular bisector passes through midpoint of the line joining the given two points so the equation for this perpendicular bisector of the line segment whose endpoint are (7,-1) and (-9,-5) is 4x-y=29.
What is a bisector of a line?To divide a segment or an angle into two congruent sections is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.
Is a bisector always a straight line?A straight line called a bisector divides an angle or a line into two equal pieces. The bisector of a segment always travels through the middle of the segment.
For this problem you have to find the mid point of the line joining
the given points and also the slope of the perpendicular line.
Here, A(7,-1) and B(-9,-5) are the given two points.
let
C is the mid point and CD is the perpendicular through C
Midpoint of AB=[x1+x2)/2,(y1+y2)/2]
C=((7-9)/2,(-1-5)/2)
C=(-1,-3)
Slope of AB=(y2−y1)/(x2−x1)
=(-5+1)/(-9-7)
=4/16
=1/4
Slope of CD=4
Equation of line;
(y−y1)=m(x−x1)
(y+1)=4(x−7)
Y+1=4x-28
4x-y=29
this is our required solution.
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y = 1/4x+1 y =1/4x-1
How many solutions does this system
of equations have?
Answer:
3
Step-by-step explanation:
3 because you have to find x, you have to find x and y and then the overall answer
The given system of equations,
y = 1/4 x + 1
y = 1/4 x - 1
has no solution.
Given a system of equations.
There are two equations in the system.
We have to find the number of solutions for the system if it exists.
Consider the equations,
y = 1/4 x + 1
y = 1/4 x - 1
Since both the equations are in y value, they are equal.
1/4 x + 1 = 1/4 x - 1
1/4 x - 1/4 x = -1 - 1
0 = -2
This is not possible.
This means that the given system has no solution.
Hence the given system of equations has no solution.
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How might you use a perpendicular bisector or an angle bisector in your everyday life?
And why would an orthocenter be the most difficult part of a triangle for someone to identify and use?
You use a perpendicular bisector or an angle bisector in your everyday life and orthocenter be the most difficult part of a triangle.
Everyday life example :
On a clock, the second hand in the middle of the hour hand and minute hand, is working as the angle bisector.
For a perpendicular bisectors, take two ends of a compass needle, with the long end on the North, the short end is pointing South, and the lines of East and West are on the left and right.
Orthocenter :
The orthocenter is the point of intersection of the three altitudes of a triangle. It is the hardest part of the triangle to find because :
It can lie inside a triangle or outside the triangle as it depends on the type of type of the triangle whether it is acute or obtuse. So, in order to identify it we must first know the type of the triangle.
And secondly, the formula for finding orthocenter is quite complicated so it is the hardest part of the triangle to identify and use.
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Need some help with this!
Answer:
4 liters
Step-by-step explanation:
We need to first figure out what the proportional value is.
(Y ×? = X)
10(Y) × 2.5 = 25 (X)
If the capacity of X is equivalent to 10 liters, then we need to use the same proportional value to get the number of liters for Y.
10 ÷ 2.5 = 4
Trough Y can contain 4 liters
Choose the system of inequalities that best matches the graph below.
y
5
4
3
KE
-6-5-4-3-2-1 01 23 4 5 6
-1
IN
03
3
S
X
The inequalities that represent the line in the graph will be y < x - 3 and y = -(2/3)x. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the blue line has a slope of 1 and the y-intercept is at (0, -3), then the inequality is calculated as,
y < x - 3
The red line is passing through the origin and (3, -2), then the equation is given as,
y - 0 = [(-2 - 0) / (3 - 0)](x - 0)
y = -(2/3)x
The disparities that address the line in the chart will be y < x - 3 and y = - (2/3)x. Then the right choice is B.
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Consider the following points on the graphs of y = sin(x) and y = sin(2x), with the added vertical dashed lines:
What are c and d in that order?
From the given graphs the values of c and d are, c = 0.53,
d = 0.95.
What is sinusoidal wave?
A mathematical curve defined in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.
Let the graphs of y = sin(x) and y =sin(2x) are given.
From this graphs we have to find the value of c and d.
First from y = sin(x) to find the value of 'a'.
consider the point [tex](a, -\frac{4}{5})[/tex]
⇒
[tex]sin(a) = -\frac{4}{5} \\a = sin^-^1(-\frac{4}{5})\\ a = -53.13[/tex]
Now to find the value of 'c'.
Plug a = -53.13 in y = sin(2x)
[tex]sin(2a) = c\\sin(2(-53.13)) = 0.52622\\sin2a= 0.53[/tex]
Hence, the value of 'c' is c = 0.53.
Now to find the value of d.
First y = sin(x) to find the value of b.
Consider, the point [tex](b, \frac{5}{13})[/tex]
⇒
[tex]sinb = \frac{5}{13} \\b = sin^-^1(\frac{5}{13})\\ b = 22.62[/tex]
Now to find value of d.
Plug b = 22.62 in y = sin(2x)
[tex]sin(2b) = d\\sin(2(22.62)) = 0.95138\\sin(2b) = 0.95[/tex]
So, the value of 'd' is 'd = 0.95'.
Hence, from the given graphs the values of c and d are, c = 0.53,
d = 0.95.
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How many gallons of rocket fuel containing 80% liquid oxygen must be mixed with 250 gallons containing 40% liquid oxygen to produce a mixture containing 70% oxygen? PLSSSS EXPLAIN!!!!
750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity
We need to find how many gallons of 80%
8x, since we don't know how many gallons
mixed with 250 gall of 40%: 0.40(250)
and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:
8x+0.4(250)=0.7x+0.7*250
Multiply on both sides of the equation
0.8x+100= 0.7x+175 Subtract 100 on both sides
0.8x= 0.7x+75
Subtract 0.7 on both sides
0.1x= 75
Divide both sides by 0.1
x= 750
You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
Hence, 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
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Suppose a sightseeing tour company charges $7.50 for each hour you rent a motorized scooter, plus a non-refundable fee of $45. Write an equation that represents the total cost, y, of renting the scooter in relation to the number of hours, x.
An equation that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45
What is meant by an equation?3x - 5 = 16 is an illustration of an equation. By solving for x, we discover that the variable's value is 7, or x = 7. By deleting parenthesis and merging related terms, you can simplify either side of an equation and obtain the solution. Together with the variables for which the equation must be solved, the values of the variables that must satisfy the equality to compose the answer are referred to as the unknowns. Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
Given,
You must pay a non-refundable $45, plus $7.50 per hour, to rent a motorized scooter from a sightseeing tour company.
The equation is y=7.50x+45
Therefore, a formula that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45.
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A city is building a fence around a rectangular playground. If the perimeter of the playground is 90 feet and the length of one side of the fence is 26 feet, what is the width of the playground?.
We can conclude that the width of the rectangular ground is 19ft.
What is a rectangle?A quadrilateral with all of its angles equal, or right angles, is a rectangle.
In addition to having all equal angles, a square also has all equal sides. Therefore, a special case of a square is a rectangle.
To put it another way, a rectangle can also be a square.
So, we know that:
The perimeter of the rectangular ground is 90ft.
The length of the rectangular ground is 26ft.
Now, the width will be:
Perimeter of rectangle formula: P = 2(l+w)
Now, put the values and substitute as follows:
P = 2(l+w)
90 = 2(26+w)
90 = 52 + 2w
2w = 90 - 52
2w = 38
w = 38/2
w = 19ft
Therefore, we can conclude that the width of the rectangular ground is 19ft.
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After a reflection of the figure, the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1). What is the line of reflection?
After a reflection of the figure, the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1). What is the line of reflection?
y = 2x
y = –x
x = 2
y = 2
Line of reflection for the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) will be x = 2..
What is mean by Reflection?
Reflection is the process of taking the time to think deeply about the experiences, events, and choices that shape our lives. Reflection allows us to consider how our views and opinions have changed over time, and to take stock of our successes and failures. Reflection can also help us understand our personal values and beliefs and how we can use them to make more informed decisions in the future. Reflection involves looking inward and assessing our thoughts and feelings, as well as looking outward and considering our interactions with the world around us. Taking time for reflection can help us gain insight into our behaviors and motivations, as well as identify areas of our lives that need improvement. It can also help us stay mindful of our goals and stay on the path to achieving them. Reflection is an important part of personal growth and development, and can be a valuable tool for gaining self-awareness and increasing our emotional intelligence.
Given that;
After a reflection of the figure,
The image vertices are A'(5, 1), B'(3, –1), and C'(7, –1).
And, In the figure;
The vertices are A(-1, 1), B'(1, –1), and C'(-3, –1).
Now, When we take the reflection about the line x = 2.
Then, we get the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) of the vertices A(-1, 1), B'(1, –1), and C'(-3, –1).
Therefore, Line of reflection for the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) will be x = 2.
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50th term: –9, 2, 13, 24, 35, ... ______________
Answer: :/ listen to the lesson
Step-by-step explanation:
Answer: the 50th term is 530
Step-by-step explanation:
it increases by 11 each time so 11*49
539 subtract by nine since it starts at -9
530
a rhombus has sides of length 51 units each and a shorter diagonal of length 48 units. what is the length, in units, of the longer diagonal?
The length of the longer diagonal of the given rhombus with side length 51units and shorter diagonal 48 units is equal to 90units.
As given in the question,
Side length of the given rhombus 's' = 51 units
Length of the shorter diagonal of given rhombus 'a' = 48 units
Let us consider length of the longer diagonal of the given rhombus be 'b'
As per the property of the rhombus:
Diagonals of the rhombus bisects each other at right angle
Triangle formed by side length bisecting diagonals is right angled triangle.
Using Pythagoras theorem we have,
(Side length)² = (a/2)² + (b/2)²
Substitute the values
⇒ (51)² = (48/2)² + (b/2)²
⇒2601 = 576 + (b/2)²
⇒(b/2)² = 2601 -576
⇒(b/2)² = 2025
⇒b/2 = √2025
⇒ b/2 =45
⇒ b = 90units
Therefore, the length of the longer diagonal of the given rhombus is equal to 90units.
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help asappppp i dont understand graphs
The function that is represented by the graph is defined as follows:
A. f(x) = (x - 1)(x + 2)(x + 4).
How to obtain the function represented by the graph?The function represented by the graph is obtained using the Factor Theorem, as we can identify the roots of the function from the graph.
The Factor Theorem states that the function can be declared according to it's linear factors, as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which:
a is the leading coefficient of the polynomial.[tex]x_1, x_2, \cdots, x_n[/tex] are the roots of the polynomial.From the graph given in this problem, the roots of the polynomial are listed as follows:
-4, -2 and 1.
Hence the function can be defined as follows:
f(x) = (x - 1)(x + 2)(x + 4).
Considering a leading coefficient of 1, option A is correct.
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Mr. Reynolds is a car salesman. He makes a salary of $55,000 a year. He
also earns a commission of of his total sales for the year. This year, Mr.
Reynolds has a sales total of $295,200. Write and evaluate a function to find
Mr. Reynolds's total earnings for the year.
Answer:you speak French pls
Step-by-step explanation:
:::
Evan saved $30 on a new TV. If the percent of discount was 20%, how much money did the
TV originally cost?
Answer:
$150
Step-by-step explanation:
we can make a ratio
20/100=30/x
cross multiple
20x=30(100)
20x=3,000
/20 /20
x=150 hopes this helps
Write the following expression using an exponent. (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
For the given expression the exponent would be [tex](2y-9)^5$[/tex].
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = [tex](2y-9)^5$[/tex]
Hence, for the given expression the exponent would be [tex](2y-9)^5$[/tex].
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For the given expression the exponent would be (2y-9)⁵.
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = (2y-9)⁵
Hence, for the given expression the exponent would be (2y-9)⁵.
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seasonality causes comparability problems in ratio analysis. a common solution is to use an average account balance as opposed to an ending account balance. t or f
The given statement is true.
Seasonal inventory or revenue fluctuations that are not based on sales can artificially inflate or deflate the value of the company's assets.
What is Seasonal inventory ?
Products with a seasonal inventory are those that sell more frequently at particular times of the year. Weather, events, and holidays can affect how much demand there is for these products.
Holiday merchandise was probably your first thought when thinking about seasonal inventory. Labor Day weekend, Halloween, and Christmas are a few examples of holiday inventory. Every one of them sells particular goods that people only purchase around the holidays.
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An item on sale costs 45% of the original price. The original price was $39.
Use the ALEKS calculator to find the sale price.
$0
X
S
The sales price of the item is $17.55
How to determine the sales priceFrom the question, we have the following parameters that can be used in our computation:
Sales price = 45% of the original price
The original price = $39
The above parameters mean that
Sales price = 45% * original price
Substitute the known values in the above equation, so, we have the following representation
Sales price = 45% * $39
Evaluate
Sales price = $17.55
Hence, the sales price is $17.55
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If a researcher wants to use a control group whose participants receive a placebo pill as well as an experimental group whose participants receive a new treatment medication, which type of statistical test is most appropriate for analyzing the results and why?.
The t-test is appropriate because it can handle small sample sizes and is robust to violations of normality assumptions.
What are Statistical Tests?Mathematical statistical tests are techniques for data analysis and drawing conclusions about a population from a sample. These tests employ mathematical formulae and probability theory to assess if a participant's result is statistically significant, implying that it is unlikely to have happened by chance. Comparing two or more groups, figuring out how variables relate to one another, and assessing the accuracy and validity of data may all be done using statistical tests. They are frequently used to derive inferences from experimental or observational data in disciplines including psychology, economics, and sociology.The outcomes of these tests are used to determine whether to accept or reject a hypothesis and can offer important insights into the underlying patterns and relationships in data.
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Solve each system by elimination: 2x+y=5 3x-2y=4
Answer: 2x+y +5 we know that because if u get 2x+y we do 2xxy and get 2xy
Step-by-step explanation:
What is 1+1
A. 2
B. 3
C. -24,000
D. Some ridiculous number
Answer:
a
Step-by-step explanation:
ik my math
The Morgan family and the Collins family each used their sprinklers last summer. The Morgan family's sprinkler was used for 35 hours. The Collins family's sprinkler was used for 40 hours. There was a combined total output of 1725 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 45 L per hour?
Answer:
you have to multiply 45^2
2025
help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
Answer:
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
What are the domain and range of the function f(x)= x^2-3x-28/x+4?
The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
f(x) = (x² - 3x - 28) / (x + 4)
Simplify the function, then we have
f(x) = (x² - 7x + 4x - 28) / (x + 4)
f(x) = [x(x - 7) + 4(x - 7)] / (x + 4)
f(x) = [(x + 4)(x - 7)] / (x + 4)
f(x) = x - 7
The Domain of the function is all real numbers except 4. And the range of the function is all real numbers except 11.
The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.
The diagram is given below.
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Hello factor the polynomial completely with steps please
The factor form of the cubic equation y = x³ + 3 · x² + x + 3 is y = (x² + 1) · (x + 3).
How to factor a cubic equation
In this problem we find a cubic equation, that is, a polynomial of the form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are the real coefficients of the polynomial. Herein we must use algebra properties to find the factor form of the expression:
y = a · Π (x - rₙ) for n = {1, 2, 3, ..., m - 1, m}
Where:
a - Lead coefficient.m - Grade of the polynomial.First, write the entire equation:
y = x³ + 3 · x² + x + 3
Second, use distributive property of real mumbers:
y = x² · (x + 3) + 1 · (x + 3)
Third, use distributive property of real numbers once again:
y = (x² + 1) · (x + 3)
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In which choice is y a function of x?
A (-2, 3), (0, 2), (-1, 1), (0, 0)
B. (4, 1), (1, 4), (-4, 1), (1, 4)
C. (4, 1), (4, 2), (4,3), (4,4)
D. (0, 2), (1, 1), (3, 0), (0, -2)
Answer:
B. (4, 1), (1, 4), (-4, 1), (1, 4)
Step-by-step explanation:
A mixed number is a number consisting of a whole number and a proper fraction.
It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 4 = 4. In the following intermediate step, it cannot further simplify the fraction result by canceling. In other words - four minus one quarter is fifteen quarters.
not allowed
a) Find the mode shown below.
15, 8, 21, 2, 12, 22, 19, 8, 19, 8
Answer:8
Step-by-step explanation: Mode is the value or values in the data set that occurs most frequently.
Order these numbers from least to greatest: 0, 1,
1
2
8
610
9
49
100
11
20
1
13
Answer:
100
Step-by-step explanation:
I did the test
Which relation is not a function?
Answer: C, the table.
Step-by-step explanation:
In a function, there can only be one output (y) per input (x), but you can have multiple inputs (x) per one output (y).
Using this logic, we see that the answer is;
C
one year, the population of a city was 359,000. several years later it was 420,030. find the percent increase.
Answer:
17%
Step-by-step explanation:
Which one doesn't belong?
1. 5 + 7 = 7 + 5
2. 5 * 7 = 7 * 5
3. 2 = 7 - 5
4. 5 - 7 = 7 - 5
Write a post sharing which equation you think doesn't belong and why.
Answer:
3 does not belong because its not long enough