Answer:
[tex]y = \frac{2}{5}x[/tex]
Step-by-step explanation:
Concepts⭐Perpendicular bisector of a segment
another line or segment that splits the segment in half and forms 90 degree anglesthe perpendicular bisector cuts through the midpoint of the segmentthe perpendicular has a slope that is the opposite reciprocal of the segment⭐Midpoint formula
[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex][tex](x_1,y_1)[/tex] is one coordinate on the line[tex](x_2,y_2)[/tex] is another coordinate on the line⭐Point-slope form
[tex]y-y_1 = m(x-x_1)[/tex]m is the slope[tex](x_1,y_1)[/tex] is a coordinate on the linea way to write the equation of a line⭐Slope
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex][tex](x_1,y_1)[/tex] is a coordinate[tex](x_2, y_2)[/tex] is another coordinate⭐Slope-intercept form
[tex]y = mx + b[/tex]m is the slopeb is the y-intercept (the y-value for when x=0)StrategyFind the midpoint of the given segmentFind the slope of the given segmentWrite the equation of the bisector equation in point-slope formSubstitute the opposite-reciprocal of the given segment's slope into the bisector equationSubstitute the midpoint of the given segment into the bisector equationExpand & simplify the bisector equation to convert it into slope-intercept formWorking1. Find the midpoint of the given segment
[tex]midpoint = (\frac{(x_1+x+2)}{2}, \frac{(y_1+y_2)}{2})[/tex]
[tex](x_1,y_1)[/tex] = (3,7)
[tex](x_2,y_2)[/tex] = (7,-3)
∴ midpoint [tex](\frac{3+7}{2}, \frac{7+(-3)}{2})\\= (\frac{10}{2}, \frac{4}{2})\\= (5,2)[/tex]
2. Find the slope of the given segment
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1,y_1)[/tex] = (3,7)
[tex](x_2,y_2)[/tex] = (7,-3)
∴ slope [tex]m = \frac{-3-7}{7-3}\\= \frac{-10}{4}\\= \frac{-5}{2}[/tex]
3. Write the equation of the bisector equation in point-slope form
[tex]y - y_1 = m(x-x_1)[/tex]
4. Substitute the opposite-reciprocal of the given segment's slope into the bisector equation
The slope of the given segment is -5/2.
Therefore, the opposite-reciprocal of the given segment's slope is 2/5.
[tex]y - y_1 = \frac{2}{5}(x-x_1)[/tex]
5. Substitute the midpoint of the given segment into the bisector equation
midpoint = (5, 2)
[tex]y -2 = \frac{2}{5}(x-5)[/tex]
6. Expand & simplify the bisector equation to convert it into slope-intercept form
We need to convert [tex]y -2 = \frac{2}{5}(x-5)[/tex] into [tex]y = mx + b[/tex] form.
[tex]y -2 = \frac{2}{5}x - \frac{2 * -5}{5}[/tex] . . . . . . . distribute the 2/5 into the parentheses
[tex]y -2 = \frac{2}{5}x - 2[/tex] . . . . . . . compute
[tex]y = \frac{2}{5}x[/tex] . . . . . . add 2 to the LHS and RHS to isolate y
⭐if this response helped you, please mark it the "brainliest"!⭐
Condos in Georgetown go up in value by 10% each year. If the Sutton family's condo is now worth $120,000, what will it be worth in 8 years? If necessary, round your answer to the nearest cent.
The Sutton family's condo's worth in 8 years will be $216000.
What is exponential function?An exponential function is a mathematical function in the form f(x) = aˣ, where {x} is a variable and {a} is a constant which is called the base.
Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.
We can write the function to calculate the worth after {T} years as follows.
A{T, R} = A{i} {1 + RT}
A{T, R} = {120000} {1 + (10/100) x 8}
A{T, R} = {120000} {1 + 0.1 x 8}
A{T, R} = {120000} {1 + 0.8}
A{T, R} = {120000 x 1.8}
A{T, R} = 216000
Therefore, the Sutton family's condo's worth in 8 years will be $216000.
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Which value of xis
the domain of f(x) = Vx – 8?
O A. X = -8
O B. x = 0
O C. X= 7
O D. x = 10
Answer:
the anser is a
Step-by-step explanation:
The domain of the function f (x) = √x - 8 is,
⇒ Domain = [8, ∞)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The function is,
⇒ f (x) = √x - 8
Now, We can find the domain of the function as;
The function is,
⇒ f (x) = √x - 8
Domain is,
√ x - 8 ≥ 0
x - 8 ≥ 0
x ≥ 8
Thus, The domain of the function f (x) = √x - 8 is,
⇒ Domain = [8, ∞)
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help me please.!!!..
Answer:
m = 3
Step-by-step explanation:
Answer:
m=3
Step-by-step explanation:
Tim has an irregularly shaped garden, as shown below. What is the area of his garden (in square feet)?
58 ft2
174 ft2
not enough information provided
198 ft2
Similar figures review
The width for the second rectangle which is HIJK will be A. 24 inches.
How to illustrate the relationship?From the diagram, it should be noted that rectangle ABCD is similar to rectangle HIJK. Therefore it should be noted that the relationship between the width and length is expressed as:
= Width / Length
= 12/16
= 3/4
Therefore, the width for the second rectangle will be:
= 3/4 × 3.2
= 2.4
In conclusion, the correct option is A.
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Kylie ran 7/10 of a mile and walked 2/5 of a mile. How much farther did Kylie run than walk?
Write your answer as a fraction or as a whole or mixed number.
The farther distance run by Kylie is 3 /10 miles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Kylie ran 7/10 of a mile and walked 2/5 of a mile. The distance will be calculated as,
Distance = ( 7/10 ) - ( 2 / 5)
Distance = ( 7 - 4 ) / 10
Distance = 3 / 10 miles
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When graphing the function on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function
The most appropriate viewing window for determining the domain and range of a function when graphing it on a graphing calculator would depend on the specific function and what information you are trying to gain from the graph.
DETERMINING THE DOMAIN AND RANGE OF THE FUNCTIONWhen graphing a function, it is important to set the viewing window correctly so that the full behavior of the function is visible. The domain of a function is the set of all input values for which the function is defined. The range of a function is the set of all output values that the function can produce. To determine the domain and range of a function from its graph, you need to be able to see all of the points where the function is defined, as well as any asymptotes or singularities.
To set the appropriate viewing window, you should start with a wide window that includes the x- and y-values where the function is defined. For example, if the function is defined for all real numbers, you would want to set the x-min and x-max to a large negative and positive number respectively, and y-min and y-max to a large negative and positive number respectively. This will ensure that all of the function's behavior is visible on the graph.
Once you have a general idea of the function's behavior, you can adjust the viewing window as needed.
Also, it is a good idea to check the graph for symmetry or periodicity, which can help to narrow down the domain or range. For example, if the graph is symmetric about the y-axis, you know that the domain includes all real numbers. If the graph is periodic, you know that the domain includes all real numbers and the range is limited.
By adjusting the viewing window and looking for symmetry or periodicity, you should be able to determine the domain and range of the function from its graph.
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Two functions are given below. How does the graph of
a compare with the graph of b?
PLEASE HELP!!!
Which represents “4 more than one half a number”?
Answer:
i think it is D
Answer:
D
Step-by-step explanation:
It is D because it divides n by 2 and adds on 4 to it.
[tex]\frac{n}{2}+4[/tex]
PLEASE LOOK AT PHOTO AND ANSWER QUESTION!!!
Answer:
A
Step-by-step explanation:
the exact number is 1,000 miles per hour
so the closest answer is A
An auditorium has 28 seats
in the front row. Each row
behind the front has three
more seats than the row
directly in front of it.
How many seats are in the
eleventh row?
Answer:
11 x 3 = 33
28 x 11 = 308
308 + 33 = 341
[tex]\huge\boxed{Answer\341}
(341) is the answer
heyy! i’ll give brainliest help asap pls
Answer: the answer is B
Step-by-step explanation:
Kate bought a circular swimming pool with a diameter of 50 feet. She wanted to know about how
many feet the circumference of her pool is. Which of these is the closest number to the
circumference?
The closest number to the circumference of the circle is 157 feet.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more generally referred to as the perimeter.
Given:
Kate bought a circular swimming pool with a diameter of 50 feet.
We have to find the closest number to the circumference of the circle.
Since,
Circumference = 2πr
where r is the radius of circle.
Here diameter of circle = 50 feet.
⇒ Radius of circle = 25 feet.
⇒ Circumference = 2*π*25 = 157.08
Hence, the closest number to the circumference of the circle is
157 feet.
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A wedding cake weighed 8 kg .If of its weight was flour , was sugar, 2 5 ℎ 5 16 ℎ 1 4 ℎ was cream and the rest were nuts ,find the weight of the nuts
Answer:
300G
Step-by-step explanation:
Here is the complete question
A wedding cake weighed 8kg. If 2/5th of its weight was flour, 5/16th was sugar,1/4th was cream and the rest were nuts, find the weight of nuts.
fraction of the cake that was nuts = 1 - (2/5 + 5/16 + 1/4)
1 - [tex]\frac{32 + 25 + 20}{80}[/tex] = 3/80
wight of nuts = 3/80 x 8 = 0.3 kg = 300g
2.4 liters of water is poured into a pitcher that now contains 10.1 liters of water. Which equation represents this?
Solve for m/IGH if m/FGH = 141° and m/FGI = 72°.
F
Answer: m/IGH =
O
G
Submit Answer
H
attempt 1 out of 2/ problem 1 out
Answer:
Step-by-step explanation:
m∡IGH = ? m∡FGH = 141 degrees and m∡FGI = 72 degrees
therefore, m∡IGH = m∡FGH - m∡FGI = 141 - 72 = 69 degrees
What is the length of the 3rd side?
The length of the 3rd side cannot be determined without at least one more side length.
In order to calculate the length of the third side of a triangle, we must also have the lengths of the other two sides. This is because the sum of the three sides of a triangle must equal 180°, so the length of one side can be determined from the other two. For example, if two sides have lengths of 4 and 8, then the third side must have a length of 8, as
4 + 8 + 8 = 180°.
Without knowing the lengths of the other two sides, it is impossible to calculate the length of the third side.
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If Jenny earns $375 when she works 5 hours, how much will she earn if she
works 12 hours?
Answer:
She will earn $900.00 in 12 hours.
Step-by-step explanation:
Her unit rate is 75 dollars per hour.
375/5 = $75
75 x 12 = 900
Answer: $900
Step-by-step explanation: 375/5x12.
What do you think that negative distances and velocities could mean in this situation?
Answer:
what situation?
Step-by-step explanation:
A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $26. Option B is a commission rate of 5% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
The total amount of sales he must make should be of $20800.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $26. Option B is a commission rate of 5% on weekly sales
Assume that the amount of sales he needs to make is of ${x}. So, for same amount, we can write -
(26 x 40) = 5% of {x}
(26 x 40) = (5/100) x {x}
{x} = (26 x 40 x 100)/5
{x} = (26 x 40 x 20)
{x} = 26 x 800
{x} = 20800
Therefore, the total amount of sales he must make should be of $20800.
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Estimate a 15% tip on a dinner bill of $43.17 by first rounding the bill amount to the nearest ten dollars.
Estimated tip: s1
Pls hurry
Answer:
The tip is 6 dollars
Step-by-step explanation:
Which is the product of 15 [tex]\frac{5}{12}[/tex]
( 100 POINTS )
Answer:
[tex] \sf \: \frac{75}{12} \: (or) \: 6.25[/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]
[tex] \sf \rightarrow \: \frac{(15 \times 5)}{12} [/tex]
[tex] \sf \rightarrow \: \frac{75}{12} = 6.25[/tex]
Hence, the product is 6.25.
Write an equation of the line that passes through the given point and is perpendicular to the given line.
(2, 5); x = -6
well, since the given line is a horizontal line, a perpendicular line to that will just be, yeap, you guessed it, a vertical line, Check the picture below.
What is y = - 1/4x + 4 in written standard form?
Answer:
x + 4y = 16
Step-by-step explanation:
Answer:
1/4x+y = 4
Step-by-step explanation:
Standard form is just X+Y=N
That means we have to get X and Y on the same side. For this problem we just add 1/4x to both sides of the equation.
Patrick wants to prepare a salad. He needs 3 cups of cooked macaroni, 3 cups of sliced oranges, 2 cups of sliced apple, 1 cup of chopped celery and 2 cups of mayonnaise. What is the total amount of ingredients in ratios?
Answer:
s
Step-by-step explanation:
. If a population of college student ages is skewed right, then this indicates: a. there are a greater number of older students b. the modal age is greater than the median age c. as the age of a student increases, the frequency of the student ages increases. d. there are more younger students within the population e. not enough information
The correct answer is c. as the age of a student increases, the frequency of the student's ages increases.
A skewed right population means that the data is distributed in such a way that the majority of the values are on the right side of the data set. In the case of a population of college students, this would mean that there is a greater frequency of older students (those in their late twenties or older) than younger students. As the age of a student increases, the frequency of the student's ages increases.
Option a. there are a greater number of older students is also correct, but it is not complete.
Option b. the modal age is greater than the median age is not correct, as the modal age is the most common age in the population and the median age is the middle value of the population, and there is no relationship between them.
Option d. there are more younger students within the population is not correct as a skewed right population indicates the opposite.
Option e. not enough information is not correct as the question is providing enough information to make a conclusion.
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four-part spinner is spun once. spinner with four parts labeled Q, R, S, and T List the sample space for the experiment. S = {Q, R, R, T} S = {Q, R, S, T} S = {R, A, T} S = {S, Q, Q}
The list of the sample space is s = {Q, R, S, T}. Option B is the correct option.
What is the sample space?
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.
The random experiment's sample spaces are written in curly brackets, "{ } ".
Given that a spinner wheel has four parts. It is labeled with the names Q, R, S, and T.
The elements of sample space are Q, R, S, and T.
The sample space is a set, thus write the elements in curly brackets.
The sample space is s = {Q, R, S, T}.
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Mrs. Thompson was asked to provide at least 180
bagels for a workshop. She already has 3 dozen bagels.
Mrs. Thomson will buy the remaining bagels in
packages of 6. Which inequality shows all the values of
x if x equals the number of packages of bagels she
could buy, beginning with the minimum value of x?
A. x < 24
B. XS 12
C. x 24
D. X 2 12
Answer: c
Step-by-step explanation:
Which of the following sets of angle measurements determines a triangle? Select all that apply.
60, 80
90, 110
70, 90
100, 80
50, 70
James made 7 identical bags using 5 yards of fabric. How much fabric did James use for each bag?
Answer:
James used 5 yards of fabric to make 7 identical bags, so he used 5/7 yards of fabric per bag.
Step-by-step explanation: