The equation of the line that passes through the points (-2,3) and (2,7) is:
x-y=-5
Therefore, option(C) x-y= -5 is correct answer.
Step-by-step solution:
The algebraic representation of a line's equation is the collection of points that make up the line in a coordinate system.
Given the line passes through the points (-2,3) and (2,7)
So, the equation of the line passing through the two points is given by:
[tex]\frac{y-y_{1} }{y_{2}-y_{1} } =\frac{x-x_{1} }{x_{2} -x_{1} }[/tex]
[tex]\frac{y-3 }{7-3} } =\frac{x-(-2) }{2-(-2) }[/tex]
[tex]\frac{y-3}{4} =\frac{x+2}{2+2}[/tex]
[tex]\frac{y-3}{4} =\frac{x+2}{4}[/tex]
[tex]y-3 = x+2[/tex]
Now rearranging the above equation:
x - y + 3 + 2 = 0
x - y + 5 =0
Therefore, the equation of the line passing through the points (-2,3) and (2,7) is: x-y=-5
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The rate of change increased by about _____ bass per a year. Round to the nearest tenth
From the exponential function, the average rate of change from year 1 to year 4 is 62.43, the average rate of change from year 5 to year 8 is 67.57 and the rate of change per year is 65
What is Exponential FunctionAn exponential function is a type of function that involves a variable in an exponent. It is of the form f(x) = a⋅b^x where a and b are constants and b > 0, b ≠ 1. The input to the function, x, is the exponent that the base, b, is raised to. The output, f(x), is the result of raising the base to the exponent.
In this problem, we have to calculate the rate of increase per year.
Data;
rate = 2%
P = 3000
The exponential growth can be calculated by;
A = P(1 + r)ⁿ
In year 1
A = 3000(1 + 0.02)¹
A = 3060
In year 4
A = 3000(1 + 0.02)⁴
A = 3247.3
a)
The average rate of change from year 1 to year 4 will be
A = [3000(1 + 0.02)⁴ - 3000(1 + 0.02)¹] / 4 - 1
A = 62.43
The average rate of change from year 1 to year 4 is 62.43
b)
The average rate of change from year 5 to year 8 is calculated as
A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)⁵] / 8 - 5
A = 67.57
C)
The rate of change increase can be calculated as;
A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)¹] / 8 - 1
A =65
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What is the value of 9x÷y³?
roxanne needs 134,000 three years from now. How much should she deposit at the beginning of each 3 months in order to accumulate the desired amount if money is worth 4% coumpounded quarterly?
what is the missing in the given question?
The amount that Roxanne should deposit at the beginning of each 3 months to accumulate $134,000 at 4% compounded quarterly for three years is $10,461.13.
How is the quarterly deposit determined?The quarterly deposit can be computed using an online finance calculator with the following parameters.
The quarterly deposit shows the periodic investment that must be made to accumulate a future value of $134,000.
N (# of periods) = 12 quarters (3 x 4)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
FV (Future Value) = $134,000
Results:
PMT (periodic deposits) = $10,461.13
Sum of all periodic deposits = $125,533.56
Total Interest = $8,466.44
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Alice is buying a
bicycle that regularly
cost $120. It is on
sale for 25% off and
the tax rate is 9.125%.
is the final amount cheaper or more expensive than the original price?
Answer:
NO
the final amount is 98.21 which is less than 120
Step-by-step explanation:
Price after discount = $120 x (100 - 25%)
$120 x 0.75 = $90
tax = $90 x 0.09125 = $8,21
final amount = $90 + 8.21 = 98.21
I’ll mark brainlist
NO LINKS
Answer:12
Step-by-step explanation: multiply the second fraction by 3 on the top and bottom to equalize the tow fractions denominators
hello i need help with my math question one only pease and thank you
a) The after-tax cost of the vehicle Rachel is buying is $29,368.70.
b) The part of the after-tax cost that Rachel will finance after making the down payment is $25,118.70.
c) The total payments after 5 years are $30,659.60.
d) The total interest Rachel paid is $1,290.90.
What is the interest payment?The interest payment represents the difference between the total monthly payments and the financing part of the after-tax cost of the vehicle.
The total monthly payments ($26,409.60) are obtained by multiplying the monthly payments ($440.16) by the number of payment periods (60).
Value of vehicle = $25,990
Harmonized sales tax (HST) = 13%
After-tax cost of the vehicle = $29,368.70 ($25,990 x 1.13)
Down payment = $4,250
Financing part = $25,118.70 ($29,368.70 - $4,250)
Monthly payments = $440.16
Financing period = 60 months (5 years x 12)
Total monthly payments = $26,409.60 ($440.16 x 60)
The total amount paid for the car = $30,659.60 ($26,409.60 + $4,250)
Total interest = $1,290.90 ($26,409.60 - $25,118.70)
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HELP ASAP!!! IM VERY CONFUSED. THANK YOU!
Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)
As a result, after studying the diagram below of triangle and considering the reasons that follow, the appropriate answers are 1, 2, 3, and 4.
Define triangle.Any three points in a plane can be connected to create triangles, which are polygonal (shapes) with three sides and three angles. They are among the first shapes in geometry that are explored. Since each polygon (with 4, 5, 6, or n sides) may be divided into triangles, triangles are particularly significant.
Here,
A segment bisector in this case is 1)OP.
Since segment LKMN is not divided into two equal sections, NO OP is not a segment bisector.
A perpendicular bisector is
2)OP.
NO,Because a perpendicular bisector creates an angle to the normal and divides a segment into two equal halves, OP is not a perpendicular bisector.
The angle bisector NO is OP.
Due to the fact that OP they do not divide any angles into two equal pieces.
4) The diagram's vertex of a pair of congruent angles is O.
YES Since O lines connect two angles with the same degree ()
5)O is the right angle's vertex.
NO
As a result of things not being at a straight angle.
6) A segment's midway in the diagram
By drawing diagonals across the four vertices LMNK, it is possible to determine where this segment's midpoint lies.
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31 is what percent of 37?
Answer: The total answers count 37 - it's 100%, so we to get a 1% value, divide 37 by 100 to get 0.37. Next- calculate the percentage of 31: divide 31 by 1% value (0.37), and you get 83.78% - it's your percentage grade.
Rahul performed an experiment using 16 windup rubber band single-propeller airplanes. He wound up the propeller a different number of times and recorded the amount of time (in seconds) that the airplane flew for each number of rotations that the propeller was wound. A regression analysis was performed and the partial computer output is given below.
The regression equation is
Time = 0.924 + 0.0462 Rotations
Predictor Coef SE Coef T P
Constant 0.9241 0.6413 1.44 0.172
Rotation 0.04625 0.01565 2.96 0.010
S= 0.5426 ; R-Sq= 38.4% ; R -Sq(adj) =34.0%
Required:
What is a 95 percent confidence interval for the slope of the regression line that relates the number of rotations the rubber band is wound and the plane's flight time?
Answer:
0.0462 ± 2.131(0.01565)
Step-by-step explanation:
The confidence interval for the slope, :
Slope Coefficient = 0.0462
Slope Coefficient ± Margin of error
Margin of Error = Tcritical * standard error
Standard Error (rotation) = 0.01565
We use T distribution, because sample size is small ; n = 16
Tcritical at 95% ; df = n - 1 = 16 - 1 = 15
Tcritical(0.05, 15) = 2.131
Hence,
Margin of Error = 2.131(0.01565)
Slope Coefficient for rotation = 0.0462
95% Confidence interval :
0.0462 ± 2.131(0.01565)
The 95% confidence interval for the slope of the regression line is 0.0462 ± 0.0333 or (0.01284, 0.07955)
What is the margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
Slope coefficient = 0.0462
Slope coefficient ± Margin of error
The margin of error will be given as
[tex]\rm Margin \ of \ error = T_{critical} \times standard \ error[/tex]
Standard error = 0.01565
We use T distribution because the sample size is small
[tex]\rm n = 16 \\\\T_{critical} \ at \ 95\% \ ; df = n-1 = 16- 1 = 15\\\\T_{critical} \ (0.05, 15) = 2.131[/tex]
Then we have
Margin of error = 2.131 × 0.01565
Margin of error = 0.0333
Then the 95% confidence interval will be
0.0462 ± 0.0333
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Which of the following fractions is equivalent to 10/12
Answer:
I don't know what the options are so I'm just gonna list a few and if they aren't on there lmk the options you have to choose from
Step-by-step explanation:
5/6, 15/18, 20/24, 25/30, 30/36, 35/42, 40/48, 45/54, 50/60, 55/66, 60/72, 65/78, 70/84, 75/90, 80/96, 85/102, 90/108, 95/114, 100/120
Answer:
5/6
Step-by-step explanation:
the equivalent fraction of 10/12 is 5/6 because both the numerator and the denominator are divisible by 2.
HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLP
Write a letter to your friend describing your hobbies. (80 words)A2/32, Chengal Nagar
Tambaram
Chennai – 600023
May 5, 2021
Dearest Malu,
I hope this letter finds you in the best of health. I received your letter the other day asking how I am spending my leisure time these days.
I have developed many hobbies over the years but collecting stamps and embroidery have been my favourite so far. Stamp collection is something I started as a kid. I had just taken a few pages off my notebook and made it my stamp book. I get so excited every time I see the postman. I wait to see what kind of stamp I will get. Knowing that I have a liking for collection of stamps, my cousins have been sending it across to me every time they find a different stamp. I can’t wait to show you my collection.
Embroidery is another hobby I picked up recently. I always liked embroidered clothes. I just started trying out different stitching patterns. Slowly, I learned almost everything, and now I am selling embroidered frames and dresses. It is so fulfilling to see a piece of work come out so well. I am sending you a gift along with this letter, something I made, as your birthday is fast approaching.
Hope to meet you soon.
Your dearest friend,
Renitaالسلام عليكماخوي عارض شريطPandemic
You bought a new laptop and paid an initial payment of $150 you will make 12 payments of $69.50 how much would the computer cost if your state tried to 6% sales tax
The cost of the computer if the sales tax is 6% is 924.96 dollars.
How to find the cost of the computer after sales tax?You bought a new laptop and paid an initial payment of $150. You will make 12 payments of $69.50.
The amount the computer cost if the your state charge 6% sales tax can be calculated as follows;
Install mental payment = 12 × 69.50
Install mental payment = 834 dollars
You already made payment of 150 dollars.
Therefore,
total payment including sale tax = 150 + 834
total payment including sale tax = 984 dollars
Sales tax = 6% of 984
Sales tax = 6 / 100 × 984
Sales tax = 5904 / 100
Sales tax = 59.04 dollars
Therefore,
cost of the computer = 984 - 59.04
cost of the computer = 924.96 dollars
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Help PLZZ no files
Jessica's teacher asked her to create a histogram representing students and cell phone use.
Which would be the BEST question to obtain statistical data?
А
Are symbols used in your text messages?
B
How many text messages do you send each day?
с
Do you have an unlimited texting package on your phone?
D
In the past month have you sent over 100 text messages?
I’m
Answer:
B.
Why?
Step-by-step explanation:
"Jessica's teacher asked her to create a "histogram" representing students and cell phone use."
the hint histogram means the history or record of
HOPE IT HELPS
(FROM CROSS)
write the equation of the line that passes through the pointe (-6,1) and (2,5).
Answer:
y=1/2x+4
Step-by-step explanation:
m = y2-y1/x2-x1 = 5-1/2-(-6) = 4/8 = 1/2
since you have the slope, graph the points and find the y-intercept.
y=1/2x+4
Lisa plays soccer 3 out of the 7 days of the week. How many possible schedules are there to play
soccer on Monday or Tuesday or both.
Ex: 5
Answer:
There are 25 possible schedules.
Step-by-step explanation:
The order in which they play soccer is not important(Monday and Tuesday is the same as Tuesday and Monday), and thus the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Monday but not Tuesday:
Monday(1) and 2 out of the remaining 7 - 2 = 5. So
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
Tuesday but not Monday:
Tuesday(1) and 2 out of the remaining 7 - 2 = 5. So
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
Monday and Tuesday:
Monday and Tuesday(1), plus one out of the remaing 5 days. So
[tex]C_{5,1} = \frac{5!}{1!4!} = 5[/tex]
Total:
10 + 10 + 5 = 25
There are 25 possible schedules.
The minute hand of a clock is 7 minutes. How far does the tip of the minute hand move in 50 minutes?
The distance that the minute hand moves in 50 minutes, given that it started at 7 minutes, is 258 degrees.
How to find the distance moved ?A rotatation around the clock by the minute hand, is a full 360 degrees as it begins at 12 and ends at 12 .
If a minute hand is at 7 minutes, then it means that the degrees moved is:
= 7 / 60 x 360
= 42 degrees
At 50 minutes, the degrees moved is :
= 50 / 60 x 360
= 300 degrees
Seeing as the minute hand started at 7 minutes, the distance moved is :
= 300 - 42
= 258 degrees
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A jewelry store has 218.75 ounces of 14-carat gold in stock.
(a) How many custom necklaces can be manufactured if each requires 3 1/8 ounces of gold?
(b) If gold is currently selling for $1,050 per ounce, how much is the gold in each necklace worth (in $)?
Select the best answer for the question.
10. Which one of the following pairs of numbers contains like fractions?
O A.% and 60/70
O B. 12 and 32
O C. 54 and 45
O D. 4 and 12/16
Can someone help me please
Step-by-step explanation: the awnser is 70 because 69 and 71 is in the outside of 70 therefore it's 70 there u go
salve for y √(7-x)²+(9-y)²
The solution for y in the equation √(7 - x)² + (9 - y)² is infinite many solutions
How to determine the solution for yFrom the question, we have the following parameters that can be used in our computation:
√(7-x)²+(9-y)²
Express tthe equation properly
So, we have the following representation
√(7 - x)² + (9 - y)²
The above is an expression, not an equation
This means that the value of the variable y can take any value and the equation will be true
In other words, it means that the variable y has infinite many solutions because it is not an equation but it is an expression
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25 POINTS PLEASE ANSWER!
A fifth grader takes a standardized achievement test (mean = 125, standard deviation = 15) and scores a 104. What percent scored less than a 104? Go to z-table.com
HOPE IT WILL HELP YOU
====================================
====================================
z = 148 - 12515
= 1.53PLEASE LOOK AT THE ATTACHMENT
====================================
PLEASE MARK AS A BRAINLIST====================================
You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house has a market value of $170,000. Your bank requires 1/5
of the market value as a down payment.
(a)
What is the amount (in $) of the down payment?
$
(b)
What is the amount (in $) of the mortgage for which the Bradys are applying?
$
(c)
Your bank offers the Bradys a 30 year mortgage with a rate of 5%. At that rate, the monthly payments for principal and interest on the loan will be $5.37 for every $1,000 financed. What is the amount (in $) of the principal and interest portion of the Bradys' monthly payment?
$
(d)
What is the total amount (in $) of interest that will be paid over the life of the loan?
$
(e)
Your bank also requires that the monthly mortgage payments include property tax and homeowners insurance payments. If the property tax is $1,710 per year and the property insurance is $1,458 per year, what is the total monthly payment (in $) for PITI (principal, interest, taxes, and insurance)?
$
(f)
To qualify for the loan, bank rules state that mortgage payments cannot exceed 1/4
of the combined monthly income of the family. If the Bradys earn $3,750 per month, will they qualify for this loan?
Yes, they will qualify.
No, they will not qualify.
(g)
What monthly income (in $) would be required to qualify for this size mortgage payment?
$
Answer:
West Elm Savings and Loan
a) The amount of the down payment is:
= $34,000
b) The amount of the mortgage for which the Bradys are applying is:
= $170,000.
c) The amount of the principal of $136,000 ($170,000 - $34,000) and the interest portion of the monthly payment by the Brady's is:
= $730.32
d. The total amount of interest that will be paid over the life of the loan is:
= $126,915.20
e) Total monthly payment = $994.32
f) No, they will not qualify.
g) The monthly income that would be required to qualify for this size of mortgage payment is:
= $3,977.28
Step-by-step explanation:
a) Data and Calculations:
Market value of mortgage house = $170,000
Required down payment = 1/5 or 20%
a) The amount of the down payment = $34,000 ($170,000 * 20%)
b) The amount of the mortgage for which the Bradys are applying is = $170,000.
c) Interest on the loan = $5.37 for every $1,000
The amount of the principal of $136,000 ($170,000 - $34,000) and interest portion of the monthly payment by the Brady's = $730.32 ($5.37 * $136,000/$1,000)
d. The total amount of interest that will be paid over the life of the loan is:
= $126,915.20 ($262,915.20 - $136,000)
Sum of all periodic payments = $262,915.20 = ($730.32 * 12 * 30)
e) Annual Property tax = $1,710
Annual Property insurance 1,458
Total additional annual pyts $3,168
Monthly additional costs = $264 ($3,168/12)
Total monthly payment = $994.32 ($730.32 + $264)
f) Bradys' combined monthly income = $3,750
Qualification threshold = $937.50 ($3,750/4)
No, they will not qualify.
g) The monthly income that would be required to qualify for this size of mortgage payment is:
= $3,977.28 ($994.32/0.25)
The correct answers are given below, based on the available information given.
The amount (in $) of the down payment is:
$34,000
The amount of the mortgage for which the Bradys are applying is:
$170,000.
The amount of the principal of $136,000 ($170,000 - $34,000) and the interest portion of the monthly payment by the Brady's is:
$730.32
The total amount of interest that will be paid over the life of the loan is:
$126,915.20
The total monthly payment
= $994.32
No, they will not qualify.
The monthly income that would be required to qualify for this size of mortgage payment is:
$3,977.28
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what values are solutions for inequality -3 < 2x -3
The values that are solutions to the inequality -3 < 2x -3 are all real numbers greater than 0.
What is the solution to the given inequality?Given the inequality in the question;
-3 < 2x -3
Solve for x, by making it the subject of the formula.
Subtract 2x from both sides
-3 < 2x -3
-3 - 2x < -3
Add 3 to both sides
-3 + 3 - 2x < -3 + 3
-2x < -3 + 3
-2x < -3 + 3
-2x < 0
Next, divide both sides by -2
-2x/-2 > 0/2
x > 0/2
x > 0
Therefore, the solution to the inequality is x > 0.
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A savings account increased by $75 is now more than $500. What is the least amount of money that was originally put in the savings account?
The least amount of money that was originally put in the savings account is $426.
What is the least amount of money?The amount of money in the savings account is a function of the money that was originally in the account and the amount by which the account was increased by.
The inequality that represents the total amount of money in the savings account is:
amount originally in the account + amount deposited > 500
x + $75 > $500
x > $500 - $75
x > $425
The least amount would be $426 because this is the smallest number that is greater than $425 that would make the total amount more than $500.
To check:
$75 + $426 = $501
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Refer to the diagram shown.
I need help with this please help me
Answer: Angle-Side-Angle Theorem
Step-by-step explanation:
The two triangles are shown to have congruent angles. By the Reflexive Property of Congruence, Side PM is shared and congruent between the two.
Because the angles are on either side (left and right) of the shared side, the triangles are congruent by the Angle-Side-Angle Theorem.
Mr. Hart recorded the ratio of the minutes spent driving to the miles driven while on a road trip.
Miles Driven
Number of
Minutes Number of Miles
? 40
75 60
100 80
Which graph represents these pairs of values?
The graph representing the given pairs is represented by the equation y = (4/5)x + 40.
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.The general equation of a straight line is → y = mx + c{m} - slope {c} - intercept along the y - axis.
Given is that Mr. Hart recorded the ratio of the minutes spent driving to the miles driven while on a road trip.
The given table is as follows -
Number of Minutes {m} : 75 60
Number of Miles {M} : 100 80
The slope of this graph will be -
m = (80 - 60)/(100 - 75)
m = 20/25
m = 4/5
The equation of the line can be written as -
y = (4/5)x + c
For the point (75, 100) as follows -
100 = 4/5 x 75 + c
100 = 4 x 15 + c
c = 100 - 60
c = 40
The equation of the graph will be -
y = (4/5)x + 40
Refer to the graph attached.
Therefore, the graph representing the given pairs is represented by the equation y = (4/5)x + 40.
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How is the graph of y = −3x^2 − 8 different from the graph of y = −3x^2
a. It is shifted 8 units left.
b. It is shifted 8 units up.
c. It is shifted 8 units down.
d. It is shifted 8 units right.
Answer:
C shifted 8 units down
Step-by-step explanation:
The slope (part with x) lets us know its negative, the second number lets us know the y intercept.
SO since the original has no second number the y intercept is 0 but since the new equation is -8 it means its 8 units lower than 0 hence -8
If the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y intercept of the regression line to three decimal places. X y 2 4101 31029 4 261 5 69 6 21 O A. log(y) = -4.743x+0.575 O B. login) - - 575x +4743 O C. logly) - 4743x+0575 O D. logi) - 0575x+4 743
The equation of the regression line is given as ŷ = -0.5755X + 4.743
How to solve for the regression line
First we have to find the logarithm of the y variables.
Logarithms of y-values:
log 4101 = 3.613
log 1029 = 3.012
log 261 = 2.417
log 69 = 1.839
log 21 = 1.322
We have to plot the ordered pairs to be in order of the table using the log y parameters.
Using a regression analysis calculator online, the equation of the regression line is ŷ = -0.5755X + 4.743.
The graph and the online calculator is contained in the image attached.
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Help me pleaseeeeeee