8. Laurie graphed two lines, as shown on the right.
One line has a slope of -2 and the other has a slope of
1/2. Laurie noticed that although the slopes are
negative reciprocals of each other, the lines do not
appear to be perpendicular. Explain why this result
occurs, even though she graphed the lines correctly.
It's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle,
What are the slopes of the two lines?
The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter m.
The slopes of the two lines that Laurie graphed, -2 and 1/2, are negative reciprocals of each other, which means that their product is -1.
In a Cartesian coordinate system, lines that are perpendicular to each other will have slopes that are negative reciprocals of each other, and the product of their slopes will be -1.
However, it's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle.
The two lines could be skew lines that never intersect and thus cannot be perpendicular.
Another reason could be that the lines may not be in the same coordinate system or not graphed on the same set of axes.
When working with slope, we always assume that the lines are defined on a 2D Cartesian coordinate system, if that is not the case, it could cause the lines to not appear as perpendicular.
Hence, it's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle, another reason could be that the lines may not be in the same coordinate system or not graphed on the same set of axes.
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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====================================
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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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 range for this set of data? 38, 17, 55, 40 02 38 39 O 72
Answer:
38
Step-by-step explanation:
The range is the difference between the highest value and the lowest value. Here the highest value is 55 and the lowest 17. Therefore, the range is take away 17 from 55 which equals to 38
The range for this set of data is 38.
Option B is the correct answer.
What is range in a set of data?The range is a measure of dispersion or spread in a set of data.
It is defined as the difference between the largest and the smallest values in the data set.
Range provides an idea of how much the data values are spread out or dispersed.
If the range is small, it indicates that the data values are close together, while a large range indicates that the data values are spread over a wider range of values.
We have,
To find the range of a set of data, we need to subtract the smallest value from the largest value.
Here, the smallest value is 17 and the largest value is 55.
So,
The range of the data set is:
55 - 17 = 38
Thus,
The range for this set of data is 38.
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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 $)?
Review the diagram of a locket in the shape of an ellipse.
The major and minor axes are labeled in the diagram.
If the center of the locket is at the origin of a coordinate
plane, which equation represents the locket?
x2
361
+
72
= 1
169
OK
V2
361
+
X2
= 1
169
38 mm
x2
1.444
1
676
26 mm
0 ' '
x2
676
= 1
1,444
Answer:
D
Step-by-step explanation:
If a = 38 and b = 26 then the equation would be y^2/1444 + x^2/676 = 1
also just graph it or smth
The equation of the ellipse in the figure is x^2/676 + y^2/1296 = 1
How to determine the equation?The figure is an ellipse, and it has the following parameters:
Center, (h,k) = (0,0)Major radius = 36Minor radius = 26The equation of the ellipse is then calculated using:
x^2/r^2 + y^2/R^2 = 1
So, we have:
x^2/26^2 + y^2/36^2 = 1
Evaluate the exponents
x^2/676 + y^2/1296 = 1
Hence, the equation of the figure is x^2/676 + y^2/1296 = 1
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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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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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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
Help me pleaseeeeeee
Each other 11 letters of the word mathematics with written on a separate piece of paper and placed in a bowl what is the probability of drawing
Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331
Define Probability.The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Define Statistics.The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
The word "mathematics" has 11 letters, so there are 11 letters in the bowl. The probability of drawing the letter "O" is 1/11, since there is only 1 "O" in the 11 letters. Similarly, the probability of drawing the letter "B" is 1/11, and the probability of drawing the letter "J" is 1/11 as well.
Since the events of drawing the letter "O", "B", and "J" are independent of each other, the probability of drawing all three letters in order is the product of their individual probabilities.
Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331
It is a very low probability, the chances of drawing that sequence are very low.
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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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The number of views for a video on a social media website doubles every day. You begin observing the
number of views 8 days after the video was introduced. The number y of views x days after the video is introduced is
represented by the function = 22(2^x-8). When will there be one million views?
The total number of times social media browsers have been showed your content.
How is social media value calculated?A general, but simplified earned media value formula is: EMV = impressions x cost per 1000 impressions x adjustable variable. The adjustable variable can be anything you are looking to track like engagement or impressions.
Simplifying
22 = 2(x + 8)
Reorder the terms:
22 = 2(8 + x)
22 = (8 * 2 + x * 2)
22 = (16 + 2x)
Solving
22 = 16 + 2x
Solving for variable ‘x’.
Move all terms containing x to the left, all other terms to the right.
Add ‘-2x’ to each side of the equation.
22 + -2x = 16 + 2x + -2x
Combine like terms: 2x + -2x = 0
22 + -2x = 16 + 0
22 + -2x = 16
Add ‘-22’ to each side of the equation.
22 + -22 + -2x = 16 + -22
Combine like terms: 22 + -22 = 0
0 + -2x = 16 + -22
-2x = 16 + -22
Combine like terms: 16 + -22 = -6
-2x = -6
Divide each side by ‘-2’.
X = 3
Simplifying
X = 3
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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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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
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.
help please! include how you did it and i will give you brainilist.
Answer: A' (3, 6)
Step-by-step explanation: It is given that the point at is at the coordinate of (1, 2). In this coordinate, 1 represents the x-coordinate while 2 represents the y-coordinate. All you have to do is plug the values of x and y into (x+2)(y+4); so, it will look like this, (1+2)(2+4). Therefore, the new x-coordinate is 3 and the new y-coordinate is 6, so A'(3, 6).
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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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
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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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
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)
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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Can anyone tell me why this is wrong
Answer:
i, n, e, q, u, a, l, t, y
Step-by-step explanation:
You repeated some letters.
pls give me brainliest and have a nice day! Hope it helps!
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
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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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.
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
What is the value of 9x÷y³?