The rate of change is 7 more of function A than the slope of function B.
What is meant by slope?Slope is calculated as the ratio of "vertical change" to "horizontal change" between any two points on a line, or any two points. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.
Since y=8x+3,
The rate of change in equation A is equal to the slope m m=8.
The rate of change, m=1, is given in equation B.
y=mx+ is the solution to equation B.
By substituting the values we get,
y=x+4
Calculate the difference between the rates of change of function A and function B.
8-1=7
Therefore, the rate of change is 7 more of function A than the slope of function B.
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Find the equation of the curve passing through(1,4)if the slope is given by the following. Assume thatx>0
Hence, we get the curve, [tex]$$\mathrm{y}(\mathrm{x})=\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\frac{23}{4}$$[/tex].
What is slope of function ?
Algebra. Finding the rate at which the value of y (the dependent variable) changes in relation to x is what this process entails. The slope itself identifies the line's slope and direction.
Given the slope of function is,
[tex]$$\begin{aligned}\frac{\mathrm{dy}}{\mathrm{dx}} & =\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1 \\\Rightarrow \mathrm{dy} & =\left(\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1\right) \mathrm{dx}\end{aligned}$$[/tex]
Taking integration both side, we get
[tex]$$\begin{aligned}\int \mathrm{dy} & =\int\left(\frac{3}{\mathrm{x}^5}+\frac{7}{\mathrm{x}}-1\right) \mathrm{dx} \\\Rightarrow \mathrm{y} & =3 \int \mathrm{x}^{-5} \mathrm{dx}+7 \int \frac{1}{\mathrm{x}} \mathrm{dx}-\int \mathrm{dx} \\& =\left[3 \cdot \frac{\mathrm{x}^{-5+1}}{-5+1}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c} \\& =\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c}\end{aligned}$$[/tex]
( where, [tex]$\mathrm{c}=$[/tex] constant)
Now. given that the curve is passing through point (1,4). So, putting $x=1$ and, y=4 into the curve,
[tex]$$\begin{aligned}\mathrm{y} & =\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\mathrm{c} \\\Rightarrow 4 & =\left[-\frac{3}{4}+7 \ln 1-1\right]+\mathrm{c} \\\Rightarrow 4 & =-\frac{7}{4}+\mathrm{c} \\\Rightarrow \mathrm{c} & =\frac{23}{4}\end{aligned}$$[/tex]
Therefore,
[tex]$$\mathrm{y}(\mathrm{x})=\left[-\frac{3}{4 \mathrm{x}^4}+7 \ln (\mathrm{x})-\mathrm{x}\right]+\frac{23}{4}$$[/tex]
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The diagram below shows a sketch of the graph y=f(x). The graph passes through the points (-2,0),(0,8),(4,0) and has a maximum point at (1,9).
Consider a sketch of the graph y=2 f(x+3), indicate the coordinates of the stationary point and the points where the graph crosses the x-axis below.
Input note: write your coordinates in the form (x, y) with no spaces.
The coordinates of intersection with the x-axis are _________
and ________
The maximum point is ________
The coordinates of the intersection with the x-axis are (-2,0), and (4, 0) and the maximum point is (1,9).
What are the coordinates of the axis?
A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.
We have,
The graph shows the sketch of y=f(x).
The graph passes through the points (-2,0), (0,8), (4, 0), and (1,9).
The coordinates of the intersection with the x-axis are
(-2,0), and (4, 0).
The maximum point is (1,9).
Hence, the coordinates of the intersection with the x-axis are
(-2,0), and (4, 0) and the maximum point is (1,9).
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I lowkey need help like immediately
The answers to all the parts are given below.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.
[A] -
For [x] = 1000ft, we can write -
1000 = -16t² + 1800
16t² = 800
t² = (800/16)
t² = 50
t = 7.07 seconds
[B] -
For [x] = 950ft, we can write -
950 = -16t² + 1800
16t² = 850
t² = 53.125
t² = √(53.125)
t = 7.29 seconds
[C] -
The domain of the function will be -
0 ≤ x ≤ 10
[D] -
The range of the function will be -
0 ≤ h ≤ 1800
Therefore, the answers to all the parts are given above.
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What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places. x y 2 2 5 9 7 20 12 19 16 30
y = -1.893x + 31.901
Detailed explanation:
We are given the following values in a table:
x y
2 30
5 19
7 20
12 9
16 2
It is now abundantly evident from the set of values that when x increases, the y-value decreases, indicating a negative connection.
Therefore, the line of best fit will have a negative slope.
Consequently, a scatter plot is used to display the data values.
As can be seen, the line of best fit equation
y = -1.893x + 31.901T
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Evaluate the expression for the given variable
w = 288
36w - w
The expression for the given variable is -276
What is variable?
A variable is anything that can take on any one of a number of values. A variable is a symbol. A variable is something that can change in an experiment.An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are often employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 Equals 10. "X" in this case is a variable.
[tex]\sqrt[3]{6 \times 288}-288[/tex]
[tex]\sqrt[3]{6 \times 288}=12[/tex]
[tex]=12-288[/tex]
[tex]Subtract the numbers: $12-288=-276$$$=-276$$[/tex]
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the sum of 9 and the quotient of x and 7
The equation for line s can be written as y+9=–9(x–8). Perpendicular to line s is line t, which passes through the point (9,9). What is the equation of line t?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
Line t: y = 1/9x + 8
Step-by-step explanation:
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
The formula for finding the slope the line perpendicular to line s is:
[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we don't know (in this case, line t) and m1 is the slope of the line we're given (in this case, line s).
Currently line s is in point-slope form or
[tex](y-y_{1})=m(x-x_{1})[/tex]. Since m is the slope, we know that the slope of line s is -9.
By plugging in -9 for m1 in our equation, we have:
[tex]m_{2}=-\frac{1}{-9}\\ m_{2}=-\frac{1}{9}[/tex]
Since we know -1/9 is the slope of line t, we can plug this in for m and (9,9) for x and y in the slope-intercept equation to find b:
[tex]9=1/9(9)+b\\9=1+b\\8=b[/tex]
Thus, the equation of line t in slope intercept form is y = 1/9x + 8
W 5. Suppose that 40% of the cars in a certain town are white A person stands at an intersection waiting white car. Let X= the number of cars that must drive by until a white one drives by. What is the exp value of X?
The no. of cars that must drive by until a white one drives by is 40.
What is a binomial distribution in probability?In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is
[tex]^nC_xp^Xq^{n-x}[/tex].
We know the expected value of a binomial distribution E(x) = np.
Given, Suppose that 40% of the cars in a certain town are white.
Therefore 50% of cars in the town are not which.
Let, The no. of cards in the town be 'n'.
So, p = 40/n and q = 60/n
Therefore from the formula E(x) = np we get,
E(x) = n×40/n
E(x) = 40.
So, The expected value of X is 40.
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Answer: We expect 2.5 cars to
The expected value of X is 2.5.
Step-by-step explanation:
In this case, it is a geometric distribution because we do not have a fixed number of trials.
We use the formula of a geometric distribution to find the mean (the expected value) such that mu_x = 1/p.
In this case:
mu_x=1/0.4 = 2.5
In this case, we do not round up or down even if we cannot have half a car because we want the expected value (mean).
A water tank initially contained 65 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 109 seconds? Round answers to the nearest whole liter.
(p-124) / 9 min many liters of water are in the tank after 109 seconds.
for 4 min = 65 + (6.5x4) = 91 lit
for 109 sec = 65 + (9x 109/60) = 81.35 lit
for m min = 65 + (9m) lit
how long time
for 151 lit = (151 - 124)/9 = 3 min
for 191.5 lit = (191.5-124) /9 = 67.5/9 = 7.5 min means 7 min 30 sec
for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 means 16 min 15 sec
for p lit = (p-124) / 9 min
What is liters ?
The water must be measured and expressed in the same unit for all of the containers. The litre is the name of that common unit for measuring liquid. Liquids are measured in litres, millilitres, centilitres, kiloliters, etc., including water, milk, gasoline, and oil.
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Two Truths & One Lie: Which of the 3 statements below is a lie? Explain how you made your decision.
x=2 y=5 z=7
Answer:
The 3rd statement is a lie and other two are truth.
Step-by-step explanation:
when two same numbers with power are divided their respective powers are subtracted.
1.
[tex] {b}^{a } \div {b}^{c} = {b}^{a - c} [/tex]
Using this formula for
[tex] {b}^{9} \div {b}^{y} = {b}^{4} [/tex]
[tex] {b}^{9 - 5} = {b}^{4} [/tex]
Here RHS =LHS
so the equation is true
2.
[tex] {b}^{z} \div {b}^{x} = {b}^{5} [/tex]
[tex] {b}^{7 - 2} = {b}^{2} [/tex]
Here RHS=LHS,
so the equation is true
3.[tex] {b}^{8} \div {b}^{x} = {b}^{8} [/tex]
[tex] {b}^{8 - 2} = {b}^{8}[/tex]
Here RHS is not equal to LHS
so the equation is false
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Find how long it takes $2500 to double if it is invested at 6% interest compounded semiannually. Use the formula A=P(1+r/n) to solve the compound interest problem.
It will take approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $2500
Total amount = $5000
Compounded semi -anually,so formula becomes,
Total amount = amount (1+r/200)^2t
T = A[tex](1+r/200)^{2t[/tex]
5000 = 2500 (1+3/100)^2t
2 =(1+ 0.03)^2t
2 =(1.003)^2t
taking log on both sides
log 2 = 2t *log 1.03
0.3/0.012 = 2t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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The height / (in feet) of a badminton birdie t seconds after it is hit can be modeled by the function h = -16^2t+32t+ 4.
a. Find the maximum height of the birdie.
The maximum height of the birdie is ___ feet.
b. How long does it take for the birdie to hit the ground?
About ___seconds
The ball may rise up to a height of 20 feet. and it will strike the ground in 1 second.
Describe height.Height is the vertical measurement from an object's top to its base. On sometimes, it has the designation "altitude."
The vertex at point (h,k) of a parabola, y = ax2 + bx + c, is first determined using the equation h = -b / 2a, and then that point is entered into the equation to determine k.
Let's now solve for h in this issue. We know that a = -16, b = 32, and c = 4 in the equation y = -16t2 + 32t + 4.
h = -b/2a
h = -(32) / 2(-16) (-16)
1 second is equal to h = -32/-32.
This means the the ball will reach it's maximum height after 1 seconds. But the problem is asking is for what that height is. So for our final step, let's plug in t=1 to our equation:
y = -16t^2 + 32t + 4
y = -16*(1)^2 + 32*(1)+ 4
y = -16 + 36
y = 20 feet
which means that the final answer is that the maximum height of the ball is 20 feet. and it will take 1sec to hit the ground.
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There were 700 colonies of bacteria on day 1 of culturing. With a growth rate of 2.3, determine how many days it will take the bacteria to multiply to 10 000 000 colonies.
Round your answer to four decimal places.
Use A = Pert
The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
There were 700 provinces of microbes on day 1 of refined. With a development pace of 2.3. Then the equation is given as,
[tex]\rm A = 700 \times (2.3)^{t - 1}[/tex]
Then the number of days it will take the bacteria to multiply to 10,000,000 colonies will be given as,
[tex]\rm 10,000,000 = 700 \times (2.3)^{t - 1}\\[/tex]
Take log on both sides, then we have
(t - 1) × log 2.3 = 14,285.71
t - 1 = 39,492.99
t ≈ 39,493 days
The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.
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What % of 780 shirts is 46
Answer:
i think the answer will be 6%
Answer:
below
Step-by-step explanation:
46 / 780 * 100% = 5.9 %
A rubber bouncy ball is dropped from a height of 106.00 inches onto a hard flat floor
Answer:
explain m ore
Step-by-step explanation:
A ball is thrown directly upward from a height of 5 ft with an initial velocity of 24 ft/sec. The function s(t)=−16t2+24t+5 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.
Answer:
The ball reaches 14 ft in 0.75 seconds
Step-by-step explanation:
[tex]h(t) = -16t^2+24t+5\\h'(t) = -32t+24\\[/tex]
The highest point occurs when the derivative is equal to 0, because the tangent line is horizontal at that point
[tex]-32t + 24 = 0\\24 = 32t\\t = \frac{24}{32}=\frac{3}{4}=0.75s\\[/tex]
plug t back into h(t) to get height
[tex]h(0.75) = -16(0.75)^2+24(0.75)+5\\=(-16)(9/16)+23\\=-9 + 23\\= 14 ft[/tex]
Note: If you are not familiar with the concept of derivatives yet, you can find the time of the highest point using the equation [tex]t =-\frac{b}{2a}[/tex] where [tex]h(t) = at^2 + bt + c[/tex]
The selling price of an item is $. It is marked down by %, but this sale price is still marked up from the cost of $. Find the markup from cost to sale price.
The markup from cost to sale price is $135.
What is the cost price?
Cost price, for instance, equals selling price plus profit ( when selling price and profit are given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).
Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)
Given the selling price of the item = $650
The cost = $450
Therefore,
10% × $650 = $585
$585-$450=$135
Hence, the markup from cost to sale price is $135.
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Complete question:
The selling price of an item is $650 It is marked down by 10%, but this sale price is still marked up from the cost of $450.Find the markup from cost to sale price.
Write the statement "the sum of a number and 10.7 is at most −3.2" as an inequality.
100 PTS HURRY
−3.2 + b > 10.7
−3.2 + b < 10.7
b + 10.7 ≥ −3.2
b + 10.7 ≤ −3.2
The given statement can be written in terms of inequality as b + 10.7 ≤ 3.2. The correct option is (d).
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
The given statement can be written in terms of inequality as follows,
The statement is, "the sum of a number and 10.7 is at most −3.2".
Suppose the number be b.
The following expression can be written,
b + 10.7 ≤ 3.2
Hence, the required inequality expression for the given problem is b + 10.7 ≤ 3.2.
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A cola company decides to test 7 different brands of soft drinks. The company
decides to compare each brand with the other brands by pairing them together.
How many different pairs will result from selecting two different brands at a time?
Please fast it’s for finals
the anwser is 14 degrees for angle 1
What expression is an equivalent expression of 12x+10+4y
The expression that is an equivalent expression of 12x+10+4y is D 2(6x + 5 + 2y).
How to illustrate the expression?In Mathematics, expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, the expression that is an equivalent expression of 12x+10+4y is 2(6x + 5 + 2y). The correct option is D.
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Which expression is an equivalent expression of 12x + 10 + 4y?
A.) 2(6x + 2y + 6)
B.) 3(4x + y + 10)
C.) 2(6x + 4y + 8)
D.) 2(6x + 5 + 2y)
please help me plsssssssss
Find the equation of the line with slope 5 that passes through (2, 8). Write the
equation in slope-intercept form.
Answer:
y = 5x - 2
Step-by-step explanation:
y-8 = 5(x-2)
y-8 = 5x - 10
y = 5x - 10 + 8
y = 5x -2
You are offered a job in sales where you can choose to
either make a salary $500 (constant) every week or
commission of $20 per sale. Write 2 equations that
represent this scenario and solve the system
Dollars
600
400-
-300-
200-
-100-
(0, 500)
(1,500)
(0, 0) (1, 20)
20
Sales
20
The equations will be 20x and 500w.
How to express the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, when offered a job in sales where you can choose to either make a salary $500 (constant) every week or commission of $20 per sale. This will be:
Let the sales be x
The equation will be:
= 20 × x
= 20x.
The second equation will be:
= 500 × w
where w = number of weeks.
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What is the total surface area of the rectangular prism?
Answer:
256 feet.
Step-by-step explanation:
The equation for the surface area of a rectangular prism is lw x lh x hw. That means it would be 12x4, 12x5, and 4x5. In total that is 256.
Please help me and explain. Thanks so much in advance
The area of the given figure is 48 [tex]ft^{2}[/tex].
What is area?Area is a measurement of the space inside a two-dimensional shape. It is determined by multiplying the length and width of the shape together. Area is most commonly measured in square units, such as square feet, square meters, or square kilometers. When measuring curved shapes, the area is determined by measuring the space inside the shape and applying a mathematical formula to calculate the total area. Area is an important concept in mathematics and is used to measure surface area, volume, length, and other measurements. It can also be used to compare the sizes of different shapes.
Firstly, to calculate the area assume the figure as two separate rectangles. Think that you a drawing an imaginary line in the gap between the two 4-ft segments to make a line of 12ft in length.
To solve, multiply to find individual areas then add together to get the total area.
Given: The first rectangle is 5ft by 4ft.
We know, the area of a rectangle = Base × Height
[tex]4ft[/tex] × [tex]3ft[/tex] = [tex]12ft^{2}[/tex] .....(1)
The next rectangle is 12 by 3ft, as you have to add the missing length in the middle to accurately calculate the length of the line.
[tex]12ft[/tex] × [tex]3ft[/tex] = [tex]36ft^{2}[/tex] .....(2)
Adding (1) and (2) we get,
[tex]12ft^{2} +36ft^{2}[/tex] = [tex]48ft^{2}[/tex]
Hence, the area is [tex]48ft^{2}[/tex].
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The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 70000 miles and a standard deviation of 7000 miles.
A) The probability that the tyre wears out before 60000 miles is 0.4221
B) The probability that the tyre lasts more than 83000 miles is 0.49534
The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = the distance the tyres can run until wear-out
u = mean distance
s = standard deviation
From the information given,
u = 70000 miles
s = 7000 miles
A) We want to find the Probability that the tyre wears out before 60000 miles. It is expressed as
P(x lesser than 60000)
For x = 60000,
z = (60000 - 70000)/7000 = - 1.42
Looking at the normal distribution table, the corresponding z score is 0.4221
B)We want to find the probability that the tyre lasts more than 83000 miles. It is expressed as
P(x greater than 83000) = 1 - P(x lesser than or equal to 83000)
For x = 83000,
z = (83000 - 70000)/5000 = 2.6
Looking at the normal distribution table, the corresponding z score is 0.49534
P(x greater than 83000)
= 1 - 0.49534 = 0.50466
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Write the equation x^2 - 10x + 17 = 0 in the form (x+p)^2 = q (50 points!)
Answer: (x-5)²=8
Step-by-step explanation:
x²-10x+17=0
x²-2(x)(5)+5²-5²+17=0
(x²-2(x)(5)+5²)-25+17=0
(x-5)²-8=0
(x-5)²-8+8=0+8
(x-5)²=8
Answer:
(x - 5)² = 8
--------------------------
Given
Expression x² - 10x +17.
Convert this to vertex form by completing the square.
Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:
x² - 10x + 17 =
x² - 2*5*x + 5² - 5² + 17 =
(x - 5)² - 25 + 17 = (x - 5)² - 8
(x - 5)² = 8
The scatterplot shows x, the high temperature in degrees Fahrenheit (°F), and y, the aquifer level in feet, for ten days in the same area.
Based on the scatterplot, which equation best represents these data?
y = 656 − 0.1 x
y=661−0.1x
y = 656 − 0.5 x
y=661−0.5x
Therefore, the equation that best fits these facts as the answer to this problem is y=661-0.1x.
Describe a scatter plot.The term "scatter plot" refers to a particular sort of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that arise indicating any association between the data.
Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.
y=661-0.1x is the equation whose solution best fits this data.
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Which translation maps the graph of the function f(x) = x² onto the function g(x) = x² - 6x + 6?
left 3 units, down 3 units
Right 3 units, down 3 units
Left 6 units, down 1 unit
Right 6 units, down 1 unit
Answer: Based on the information you provided, it seems that the correct answer is "left 6 units, down 1 unit." This translation will map the graph of the function f(x) = x² onto the graph of the function g(x) = x² - 6x + 6.
To understand why this is the case, it helps to understand what the different parts of the function g(x) represent. The term x² represents the original function f(x) = x², the term -6x represents a horizontal translation of the graph of f(x) by 6 units to the left, and the constant term 6 represents a vertical translation of the graph of f(x) by 1 unit downward. Together, these transformations map the graph of f(x) onto the graph of g(x).
Note that if we were to apply the other translations you listed, they would not produce the correct graph. For example, if we were to apply a translation of "right 3 units, down 3 units," this would produce a graph that is shifted 3 units to the right and 3 units down, which is not the same as the graph of g(x). Similarly, if we were to apply a translation of "right 6 units, down 1 unit," this would produce a graph that is shifted 6 units to the right and 1 unit down, which is also not the same as the graph of g(x).