Which of the following equations represents the perpendicular bisector of WX graphed below?
Thank you! :)
Answers
First, we find the midpoint M using the midpoint formula:
[tex]\displaystyle{ M_{WX}= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )= (\frac{-5+5}{2}, \frac{2+(-4)}{2} )=(0, -1).[/tex]
Nex, we find the slope of the line containing M, perpendicular to WX. We know that if m and n are the slopes of 2 parallel lines, then mn=-1.
The slope of WX is [tex]\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}= \frac{2-(-4)}{-5-5}= \frac{6}{-10}= -\frac{3}{5} [/tex].
Thus, the slope n of the perpendicular line is [tex]\displaystyle{ \frac{5}{3} [/tex].
The equation of the line with slope [tex]\displaystyle{ n= \frac{5}{3} [/tex] containing the point M(0, -1) is given by:
[tex]\displaystyle{ y-(-1)=\frac{5}{3}(x-0)[/tex]
[tex]\displaystyle{ y+1= \frac{5}{3}x[/tex]
[tex]\displaystyle{ 3y+3=5x[/tex]
[tex]\displaystyle{ 5x-3y-3=0 [/tex]
Answer: 5x-3y-3=0
Related Questions
Fifty randomly selected individuals were timed completing a tax form. the sample mean was 23.6 minutes; the sample standard deviation was 2.4 minutes. a 99% confidence interval for the mean time required by all individuals to complete the form is about:
Answers
n = 50, sample size
[tex]\bar{x} = 23.6 \, min[/tex], sample mean
s = 2.4 min, sample standard deviation.
The confidence interval is
[tex]\bar{x} \pm t^{*} \frac{s}{ \sqrt{n} } [/tex]
At the 99% confidence level, t* (from the student's t-distribution) is
t* = 2.68
Therefore
t*(s/√n) = 2.68*(2.4/√50) = 0.9096
The confidence interval is
(23.6-0.9096, 23.6+0.9096) ≈ (22.69, 24.51)
Answer: (22.7, 24.5)
The Garcias have $12,000 in a saving account. The bank pays 3.5% interest on saving accounts, compounded monthly. Find the balance after 3 years?
Answers
A=p (1+r/k)^kt
A the balance?
P present value 12000
R interest rate 0.035
K compounded monthly 12
T time 3years
A=12,000×(1+0.035÷12)^(12×3)
A=13,326.49
Hope it helps!
To find the balance after 3 years in a savings account with $12,000 and a 3.5% interest rate compounded monthly, we can use the formula for compound interest.
Explanation:To find the balance after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amountP is the principal amount (initial balance)r is the annual interest rate (as a decimal)n is the number of times interest is compounded per yeart is the number of yearsPlugging in the given values:
P = $12,000r = 0.035n = 12 (monthly compounding)t = 3 yearsThe formula gives us:
A = $12,000(1 + 0.035/12)^(12*3)
Calculating this expression will give us the balance after 3 years.
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A variable is: an instruction for the compiler a location in memory where a value can be stored a description of a value (such as a number or character) none of the above.
Answers
Final answer:
A variable is a name assigned to a quantity that can take on various values, and is used by mathematicians, economists, and statisticians in different contexts to represent data or elements of an equation.
Explanation:
A variable is the name given to a quantity that may assume a range of values. Mathematicians and economists often use variables in equations to represent different aspects of a problem or scenario. For example, in the equation of a line, commonly expressed as y = mx + b, the variables are 'x' and 'y'. Here, 'x' typically represents values on the horizontal axis, and 'y' represents values on the vertical axis, while 'b' is the y-intercept, and 'm' is the slope of the line. To understand how an equation with variables functions, we can look at a numerical example.
In statistics, variables can also refer to characteristics or measurements that can be determined for each member of a population. These variables can be numerical or categorical. A numerical variable, such as 'X' representing the number of points earned by a math student, allows for mathematical calculations like averaging. A categorical variable, like 'Y' indicating a person's political party affiliation, places individuals into categories and doesn't lend itself to mathematical operations like averaging.
Change each fraction to a decimal. If the division doesn’t end, round your answer to the nearest hundredth. a. 3⁄4 b. 7⁄16 d. 3⁄5 e. 7⁄40 f. 51⁄20
Answers
Answer:
a = 0.75
b= 0.4375
d= 0.6
e=0.175
f= 2.55
Step-by-step explanation:
By simple division method, the following answers can be calculated:
a.
=[tex]\frac{3}{4}[/tex]
=0.75
b.
= [tex]\frac{7}{16}[/tex]
=0.4375
d.
= [tex]\frac{3}{5}[/tex]
=0.6
e.
= [tex]\frac{7}{40}[/tex]
=0.175
f.
=[tex]\frac{51}{20}[/tex]
=2.55
Thus, the answer are :
a = 0.75
b= 0.4375
d= 0.6
e=0.175
f= 2.55
Answer:
A.0.75 B.0.4375 C. 14.4 D. 0.6 E. 0.175 F. 2.55
Step-by-step explanation:
Write a quadratic function (f) whose zeros are −8 and 2.
Answers
Marcia can make 5 candles in an hour. Kevin can make only 4 candles in an hour, but he already has 7 completed candles. Explain to Marcia how she can use a system of equations to determine when she will have the same number of candles as Kevin. Use complete sentences.
Answers
k = kevin's total amount of candles
h = amount of hours
so in 1hr she makes 5(1), in 2hrs she makes 5(2) and 3 she makes 5(3), in "h" hours she makes 5h.
kevin makes in 1hr 4(1), in 2hrs 4(2) and 3hrs 4(3), in "h" hours 4h. But kevin already has 7 candles done from the day before, so the 4h is really additional to his 7 candles.
[tex]\bf \begin{cases} m=5h\\\\ k=4h+7 \end{cases}\impliedby \textit{when are they equal?}\qquad \stackrel{m}{5h}~~=~~\stackrel{k}{4h+7}\\\\ -------------------------------\\\\ 5h=4h+7\implies h=7[/tex]
Adam earns a base pay plus a commission for each car he sells at Crazy Carl's Cool Cars. His monthly salary is modeled by the function f(c) = 250c + 500. If Adam doesn't sell a car, how much money does he earn for the month?
Answers
Answer: 500
Step-by-step explanation:
Since, The monthly salary is modeled by the function,
f(c) = 250 c + 500.
According to the question,
Adam earns a base pay plus a commission for each car he sells at Crazy Carl's Cool Cars.
In the given function c is a variable.
Thus, c must show the number of cars.
Thus, the base pay must be free from any variable.
In the above expression 500 is free from the variable c therefore, 500 is the base pay of Adam.
⇒ f(c) is the total earning by Adam after selling a car.
If he Does not sell any car then c=0,
f(0) = 250×0+500 = 500
Therefore, if he does not sell any car then his earning is 500.
Twice the smallest of three consecutive odd integers is nine more than the largest. find the integers.
Answers
2x =9+ x+4 Twice the smallest is nine more than the largest
2x - x= 13
x= 13 the first
the second integer 15 the third 17
The required Integers are 13, 15, 17
What are the Integers?
Integers are the collection of whole numbers and negative numbers.
Given that twice the three consecutive odd Integers is nine more than the largest.
Let the numbers be x , x+2 , x+4
According to question
2x = 9+x+4
x = 13
Hence the Integers are 13, 15, 17
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2. For the circle with equation , answer each question.
(a) What are the coordinates of the center?
(b) What are the radius and diameter of the circle?
(c) Graph the circle.
Answers
You have to recognize this circular equation form.
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the center and r is the radius
------------------------------------------------
What are the coordinates of the center?
Ans: (2,-3)
(B) The Radius is the distance from the center outwards. The Diameter goes straight across the circle, through the center. The Circumference is the distance once around the circle.
(C) Realize that the circle is centered at the origin (no h and v) and place this point there.Calculate the radius by solving for r. Set r-squared = 16. ...Plot the radius points on the coordinate plane. ...Connect the dots to graph the circle using a smooth, round curve.
How many students had a shoe size greater than the mean shoe size?
Answers
HELP!!! I GIVE LOTS OF POINTS!! THE ANSWER IS NOT 3!!!!!!!!
In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in.
Answers
the answer would be 6 i did my calculations on paper then misplaced it but checked answer and it said 6
in triangle RST, m∠R=(2x+10), m∠S=(2x+25), m∠T=(x-5)
what is the value of x
A. 30
B. 28
C. 26
D. 32
Answers
70+85+25=180 which means A.30 is the correct answer
(2(30)+10)+(2(30)+25)+(30-5)= 180
John has six more nickels than dimes in his pocket for a total of 2.25 write an equation to determine the number of dimes, x in his pocket
Answers
Let x = the number of dimes
Let x+6 = the number of nickles
We know that nickles are represented as $0.05 and dimes $0.10...
Together they make $2.25 right? So you have to add them.
0.05(x+6) + 0.10(x) = 2.25 => This is the equation the problem is asking for.
If they ask you how many nickels and dimes does John have in this pocket, then you have to solve for x, like this:
0.05x + 0.3 + 0.10x = 2.25 In this step you apply the ditributive property.
0.15x + 0.3 = 2.25 In this step you combine like terms
0.15x = 2.25 - 0.3 In this step you moved to +0.3 to the other side, but remember to switch the sign!
0.15x = 1.95 In this step you subtract 2.25 and 0.3
x = (1.95) / (0.15) In this step you divide 0.15 in the right because in the left side of the equals sign it was multiplying. You get x by itslef.
x = 13 Latly, you divide and you get 13 as an answer
Now that the value of x is 13. You plug this number into the let statements.
We had:
x and x+6 which would be
x = 13
x+6 = 13+6 = 19
Which means that John has 13 dimes and 19 nickels in his pocket.
Tristan jogs a route that is 7/10 mile. If he wants to jog between 2 and 3 miles, how many times should he plan to run the route? Circle the letter for all that apply.
A. 2 times
B 3 times
C. 4 times
D. 5 times
Answers
Answer:
B 3 times
C. 4 times
Step-by-step explanation:
For Tristan to jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.
Considering the options given
A. 2 * 7/10 = 1.4 miles (this is not within the range)
B. 3 * 7/10 = 2.1 miles (this is within the range)
C. 4 * 7/10 = 2.8 miles (this is within the range)
D. 5 * 7/10 = 3.5 miles (this is not within the range)
If sinθ = -1/2 and θ is in Quadrant III, then tanθ = _____.
Answers
Answer: [tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]
Step-by-step explanation: Given that
[tex]\sin\theta=-\dfrac{1}{2}[/tex] and [tex]\theta[/tex] lies in Quadrant III.
We are to find the value of [tex]\tan \theta.[/tex]
We will be using the following trigonometric identities:
[tex](i)~sin^2\theta+\cos^2\theta=1,\\\\(ii)~\dfrac{\sin\theta}{\cos{\theta}}=\tan \theta.[/tex]
We have
[tex]\tan\theta\\\\\\=\dfrac{\sin\theta}{\cos\theta}\\\\\\=\dfrac{\sin\theta}{\pm\sqrt{1-\sin^2\theta}}\\\\\\=\pm\dfrac{-\frac{1}{2}}{\sqrt{1-\left(\frac{1}{2}\right)^2}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\sqrt{1-\frac{1}{4}}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\frac{\sqrt3}{2}}\\\\\\=\pm\dfrac{1}{\sqrt3}.[/tex]
Since [tex]\theta[/tex] lies in Quadrant III, so tangent will be positive.
Thus,
[tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]
Find the value of the variable.
Answers
And x is 58
Describe how the variability of the x bar distribution changes as the sample size increases
Answers
The standard deviation decreases and the sampling distribution becomes more normal as the sample size increases in x bar distribution.
The variability of the x bar distribution changes as the sample size increases. As the sample size increases, the standard deviation of the sampling distribution of the means will decrease, approaching the standard deviation of X. The sampling distribution of the mean becomes more normal as the sample size grows, showing less variability.
Two buses leave towns 1631km apart at the same time and travel toward each other. one bus travels 17 /kmh slower than the other. if they meet in 7 hours, what is the rate of each bus?
Answers
the first bus travels a total of 7x km, the second bus travels 7(x-17)km, together they travel the total distance of 1631 km
7x + 7(x-17) =1631
7x + 7x -119 =1631
14x=1750
x=125
x-17=108
Witch of the following is closest to 27.8 X 9.6 is it 280, 2800, 300, or 3000
Answers
Hope this helps and thank you for using Brainly!
An is planning a birthday party for her younger sister at a skating rink. the cost of admission is $3.50 per adult and $2.25 per child., and there is a limit of 20 people. jan has $50 to spend. how many adults and how many children can jan invite?
Answers
let y be the number of child
3.5 x + 2.25 y = 50
x+ y =20 y = 20 - x
3.5 (20-y ) + 2.25 y = 50
70 - 3.5 y +2.25y =50
70 -1.25 y = 50
y = 16
and x = 4
Kim drives 378 miles and uses 18 gallons of gasoline. At that rate, how many miles can she go on 24 gallons of gas?
Answers
That equals 21
Then do 21 * 24
That equals 504
Conclusion: It would take 504 miles to go on for 24 gallons of gas.
Brainliest for a math answer
Answers
question 6- is 9
question 7-is 4
question 8-is 21
Question 9-is 2
question 10-not sure sorry :(
Tell me if your right ;)
We know b is 7 and a is 2 so plug it in
7 - 2= 5
5=5
The answer is 5
The second question is b / a = ___
We know b is 18 and a is 2 so plug it in
18/2=9
9=9
The answer is 9
Which equation could generate the curve in the graph below?y=3x^2-2x+1
Answers
Then, the attached file would be the answer.
To check, b^2 - 4(a)(c), for each equation and use these facts:
If b^2 - 4(a)(c) = 0, there is only one real root meaning, the graph touches the x-axis only in one point.
If b^2 - 4ac > 0, there are two real roots meaning, the graph touches the x-axis in two different points.
If b2 - 4ac < 0, there are no real roots then the graph does not touch the x-axis. This would be the case for y = 3x^2 - 2x + 1.
Solution:
(-2)^2 -4(3)(1) = 4 - 12 = -8 < 0 will result in not real roots.
Which property justifies this statement? If 4x=20, then x=5. Division Property of Equality Reflexive Property of Equality Substitution Property of Equality Subtraction Property of Equality
Answers
Answer:
Option 1 - Division Property of Equality
Step-by-step explanation:
Given : If [tex]4x=20[/tex], then x=5.
To find : Which property justifies this statement?
Solution :
The equation is [tex]4x=20[/tex]
To make variable separate we have to remove 4 which is in multiple of variable x.
So, We divide both side by 4,
Applying division property of equality,
We can divide both sides of an equation by the same number and preserve equality.
[tex]\frac{4x}{4}=\frac{20}{4}[/tex]
[tex]x=5[/tex]
Therefore, The property justifies the statement is 'Division Property of Equality'.
So, Option 1 is correct.
How many degrees are in each interior angle of a regular pentagon? 50 72 108 120
Answers
The answer 108 degrees.
Answer: [tex]108^{\circ}[/tex]
Step-by-step explanation:
The sum of all the angles in a regular polygon with sides n , is given by :-
[tex]S_n=180^{\circ}(n-2)[/tex]
Now, the sum of all the angles in a regular pentagon with 5 sides will be :-
[tex]S_5=180^{\circ}(5-2)=180^{\circ}(3)=540^{\circ}[/tex]
We know that all the interior angles of a regular polygon are equal .
Therefore, the measure of each interior angle in a pentagon is given by :-
[tex]x=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]
Hence, the measure of each interior angle in a pentagon=[tex]108^{\circ}[/tex]
Jim’s fundraiser BBQ needs to make at least $1000 in sales on Saturday. He sells hot dogs for $2 each and hamburgers for $3 each, and he wants to sell at least twice as many hamburgers as hot dogs. He brought 300 hot dogs and 800 hamburgers to sell. The graph shows the feasible region, where x represents the number of hot dogs sold and y represents the number of hamburgers sold. Which ordered pairs meet all the constraints for a successful fundraiser and make sense in context of the situation?
Select each correct answer.
(275, 0)
(100.5, 800.5)
(0, 350)
(250, 700)
(200, 350)
Answers
What is the slope of the line perpendicular to the line represented by the equation 2x+4y=12?
Answers
If you have $45 and they take 2.1% of it how much do you have left ?
If you have $765 and they take 2.1% of it how much do you have left ?
If you have $1300 and they take 2.1% of it how much do you have left ?
Answers
100-2.1 = 97.9
97.9/100 = 0.979
Then you multiply all the questions by it:
$45 * 0.979 = $44.055
$765 * 0.979 = $748.935
$1300 * 0.979 = $1272.7
Hope this helps! :)
I need help with this math question!!
Simplify 0.4i−i.
Answers
= i(0.4-1)
= 0.6i
The simplification of the given expression is 0.6i.
What are complex numbers?Complex numbers are those numbers that contain the imaginary and the real part.
A Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
where r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Usually the simplification involves proceeding with the pending operations in the expression.
We need to simpify the 0.4i - i
= i(0.4-1)
= 0.6i
Therefore, the simplification of the given expression is 0.6i.
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A Springer Spaniel weighs 20 kilograms 490grams. A Cocker Spaniel weighs 7,590 grams less than a Springer Spaniel. A Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. What is the difference, in grams, between the weights of the Newfoundland and the Springer Spaniel?
Answers
To find the difference in weight between the Newfoundland and the Springer Spaniel, subtract the weight of the Springer Spaniel from the weight of the Newfoundland.
Explanation:To find the difference in weight between the Newfoundland and the Springer Spaniel, we need to subtract the weight of the Springer Spaniel from the weight of the Newfoundland. The Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. So, we first need to find the weight of a Cocker Spaniel by subtracting 7,590 grams from the weight of the Springer Spaniel. We then add this weight to the weight of the Newfoundland to get the final answer. Let's calculate:
The weight of the Cocker Spaniel = Weight of Springer Spaniel - 7,590gThe weight of the Newfoundland = Weight of Cocker Spaniel + 52kg 656gFinally, the difference in weight between the Newfoundland and the Springer Spaniel is the weight of the Newfoundland - weight of the Springer SpanielWe can now substitute the given values into these equations and solve.
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