Applying the transformation rule (x - 2.y + 4) and using the scale factor k = 3 for dilation gives
preimage translation image Dilation image
A (1.-2) A' (-1, 2) A'' (-3, 6)
B (4,-1) B' (2, 3) B'' (6, 9)
C (5.-3) C' (3, 1) C'' (9, 3)
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
Applying the transformation rule (x - 2.y + 4 ) gives
A (1.-2) = (1 - 2, -2 + 4) = (-1, 2)
B (4,-1) = (4 - 2, -1 + 4) = (2, 3)
C (5.-3) = (5 - 2, -3 + 4) = (3, 1)
preimage image
A (1.-2) A' (-1, 2)
B (4,-1) B' (2, 3)
C (5.-3) C' (3, 1)
Dilation involves making the image bigger or smaller. In this case K > 1 hence the image is bigger
Using the scale factor k = 3 for dilation rule (kx, ky) gives
A' (-1, 2) = (-1 * 3, 2 * 3) = (-3, 6)
B' (2, 3) = (2 * 3, 3 * 3) = (6, 9)
C' (3, 1) = (3 * 3, 1 * 3) = ( 9, 3)
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Reid's Hardware discounts all riding lawnmowers 9% to customers paying in cash. If Trey paid $1,517.74 in cash for a riding lawnmower, which of the following equations can be used to determine the original price of the lawnmower?
(Let x represent the original price of the lawnmower and y represent the discounted price.)
A.
y = 1.09x
B.
y = 0.91x
C.
y = 1.9x
D.
y = x - 9x
An equation to determine the original price of the lawnmower discounted at 9% to $1,517.74 is B. y = 0.91x.
What is an equation?An equation summarizes a mathematical statement that equates two or more mathematical expressions.
Equations operate with values, numbers, and variables, using the equation symbol (=) and mathematical operands to establish the equality of values.
Discount offered = 9%
Amount paid for a lawnmower = $1,517.74
Original price = x
Discounted price, y = 0.91x
Y = 0.91x
1,517.74 = 0.91x
x = 1,667.85
Thus, the original price of the lawnmower is determined by Equation B.
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
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Answer:
Step-by-step explanation:
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
What is proportionality?
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
a fence is to be built to enclose a rectangular area of 310 square feet. the fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 14 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
The dimension for the enclosure that is most economical to construct will be length=11.13 feet and width=27.85 feet.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
A=l*b
=310
b=310/l
total cost=(8b+4l+16l)
=8b+20l
=8*310/l+20l
t=2480/l+20l
t'=20-2480/l²
t'=0
20l²=2480
l²=124
l=11.13 feet
b=310/11.13
b=27.85 feet
The enclosure's length and width, which add up to 11.13 feet and 27.85 feet respectively, will be the most cost-effective dimensions to build.
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Solve the equation by completing the square. x2 + 6x = 9
What is the constant of variation, k of the direct variation, y=kx,through (5,8)
Constant of variation, k of the direct variation is 8/5.
Equation -> y = kx
Point (x,y) = (5,8)
Putting the value in the equation,
8 = 5k
k = 8/5
Hence, k = 8/5.
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if f(x) = 2x - 4 find f(k+1)
Answer: [tex]f(k+1)=2k-2[/tex]
Step-by-step explanation:
Substituting [tex]k+1[/tex] for [tex]x[/tex],
[tex]f(k+1)=2(k+1)-4\\\\f(k+1)=2k+2-4\\\\f(k+1)=2k-2[/tex]
7.69 to the nearest whole number.
Answer: 8
Step-by-step explanation:
7.69 to the nearest whole number is 8
a bank auditor claims that credit card balances are normally distributed, with a mean of $2870 and a standard deviation of $900. a) what is the probability that a randomly selected credit card holder has a credit card balance less than $2500? b) you randomly select 25 credit card holders. what is the probability that their mean credit card balance is less than $2500? c) compare the probabilities from a) and b).
(a) -0.255 is the probability that a randomly selected credit card holder has a credit card balance less than $2500. (b) You randomly select 25 credit card holders. 0.0228 is the probability that their mean credit card balance is less than $2500.
Let us pull out the critical elements
Population: Normally distributed with mean of 2870
population standard deviation = 900 standard deviation of the sample mean (standard error) is 900 / √25. or 180
As population sigma is known, we do not have apply any corrections
P(xbar < $2500) = ?
Since μ and σ are known (population mean and standard deviation) we can use a simple Z test.
Ztest = (2500-2870 )/ 180 or -370/180 = -2.055
As this is very close to -2 one can use the rule of thumb for probability within ± 2 sigma being 95.44% to get a close estimate. If the area between -2 and 2 sigma = .9544 then the area outside = .0456. Half of this (the amount under the curve LESS THAN -2) would be .0228
Using a calculator or computer for an exact answer we find (using a TI-83/86):
nmcdf(-9E6,2500,2870,180) = .0199
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Given the linear function f(x) = -4x+8, what is the value of x if f(x) = 24?
Answer:
[tex]f(x) = - 4x + 8 = 24 \\ \\ = > - 4x + 8 = 24 \\ \\ => - 4x = 24 - 8 = 16 \\ = > - 4x = 16 \\ = > x = \frac{ - 16}{4} = - 4 \\ \\ [/tex]Step-by-step explanation:
Sᴏ ᴛʜᴇ value of x= -4
x = -4
Step-by-step explanation:
Solution:-
[tex]{ \blue{ \sf{f(x) = - 4x + 8}}}[/tex]
In order to find the value of x, put 24 in the place of f(x) (given) then,
[tex]{ \blue{ \sf{24 = - 4x + 8}}}[/tex]
[tex]{ \blue{ \sf{24 - 8 = - 4x}}}[/tex]
[tex]{ \blue{ \sf{16 = - 4x}}}[/tex]
We should find the value of x. So divide bith the sides by -4. then,
[tex]{ \blue{ \sf{ - \frac{16}{4} = \frac{ - 4}{ - 4} x}}}[/tex]
[tex]{ \bold{ \boxed{ \red{ \sf{ -4 = x}}}}} \: (or) \: { \bold{ \boxed{ \red{ \sf{x = - 4}}}}}[/tex]
javieretta earned $9.50 each hour she works at camp clap happy during summer vacation. she earned $304 one week in june and $247 during a week in july. how many hours did she work that week in june? please help
Javieratta worked for a total of 32 hours in the week of June to earn an amount of 304 dollar.
Javieretta earns $9.50 each hours she works at camp clap happy.
She earned $304 in week of june and $247 during a week in july.
Let us assume that she works X hours.
So, using unitary method, we can write,
X times the amount she earns in one hour = Earning in the week of june.
X(9.50) = 304
X = 304/9.50
X = 32 hours.
So, she worked for a total of 32 hours in the camp clap happy summer vacation.
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The ones digit is 2 less than the tens digit, and the sum of this number and its reversed number is 154.
Answer:
Step-by-step explanation:
the answer is 86
hope it helps!
(-_-)
Brian loves to bake blueberry muffins for his friends and family.
there is a proportional relationship between the volume of flour brian uses (in cups), x, and
the number of muffins he bakes, y.
10
9
8
7
9
s
s
3
2
2
s
9
00
9
10
For a proportional relationship between the volume of flour used (in cups), x, and the number of baked muffins, y, the constant of proportionality is 4.
Constant of proportionality, also known as constant ratio or constant rate, refers to is the ratio that relates two given values in a data set that is represented as a proportional relationship. When two parameters are proportional, either directly or indirectly, the relationship is expressed as a = kb or a = k/b, where k indicates the relationship between the two variables and is known as the proportionality constant. In the given data, the proportionality constant is:
k =b/a = 8/2 =12/3 = 16/4 = 20/4 = 4
Hence, the proportionality constant for the given data is 4.
Notes: The question is incomplete. The complete question is: Brian loves to bake blueberry muffins for his friends and family. There is a proportional relationship between the volume of flour brian uses (in cups), x, and the number of muffins he bakes, y. What is the constant of proportionality. (Refer to the table).
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Translation rule:
(x, y) (x + 2, y – 4)
Either draw in the translated image or write down the new coordinates for the translated image
Step-by-step explanation:
it is really simple :
every x is increased by 2, every y is decreased by 4.
C = (-4, 2) -> C' = (-2, -2)
R = (-5, -1) -> R' = (-3, -5)
T = (-1, 1) -> T' = (1, -3)
Please help!!!!!!!!!!
Answer: 81
Step-by-step explanation:
Let's start with what we know:
Time spent each evening = 1/3 of an hour
Time spent: 27
We need to turn the time spent into minutes so We will do
27 * 60 = 1620 minutes
As well as we need to turn the 1/3 of an hour into minutes so we will do
1/3 * 60 = 20 minutes
So now we have these numbers
You can pick any letter but I will pick x
We can do 20x = 1620 (Time spent times number of evenings equals time spent)
Then after that you just divide 20x/20 and 1620/20
Then getting x = 81.
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i have an algebra 2 question asking about this: is there any pair of numbers that multiply to 36 and add up to -7? the factors of 36 are (1, 36) (2, 18) (3, 12) (4, 9) (6, 6)
There are no pair of numbers that multiply to 36 and add up to -7
How to find the factors of 36?The factors of number refers to any of various numbers multiplied together to form some whole. For instance, 3 is a factor of 12, as are 2, 4 and 6.
36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.The pairs of factors of 36 that multiply to 36 are:
(1, 36) (2, 18) (3, 12) (4, 9) (6, 6)From the pair of numbers above, none add up to -7
Therefore, there is no pair of numbers whose product is 36 and sum is -7
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Bert keeps honeybees on his farm. When he first started, he used a six frame beehive that have 40 pounds of honey. Now, he uses a 30 frame we have. It has the same ratio of frames to honey it’s a smaller behive.
How much honey does Burt‘s new beehive hold?
The amount of honey that Bert’s new beehive hold would be; 200.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given data that the Number of frame beehive = 6
The Pound of honey = 40
The Current Frame beehive = 30
First step is to formulate an equation and then use the formulated equation;
40 × 30 ÷ 6
Hence, 40 × 5
= 200 honey
Therefore, the number of honey would be; 200.
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3y minus 27 i have no idea
3(y-9)
Step by step explanation:3y-27
Factorizing
3(y-9)
Suppose that y varies directly with x, and y=-4 when x=10. what is
y when x=2.
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em}\textit{we know that} \begin{cases} y=-4\\ x=10 \end{cases}\implies -4=k(10) \\\\\\ \cfrac{-4}{10}=k\implies -\cfrac{2}{5}=k\hspace{10em}\boxed{y=-\cfrac{2}{5}x} \\\\\\ \textit{when x = 2, what is "y"?}\qquad y=-\cfrac{2}{5}(2)\implies y=-\cfrac{4}{5}[/tex]
a survey of a congressional race finds 52 percent of voters supporting candidate a and 48 percent supporting candidate b, with a 5 percent margin of error. given this information, we can say that:
Answer:
When you round the number to 5
Step-by-step explanation:
The function f(x) = (x + 5)(x-3) is dilated by x to produce
the function g(x) = x f(x). How many x-intercepts does
3. the function g(x) have?
Function g(x) have 3 x intercepts.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The function f(x) = (x + 5)(x-3) is dilated by x to produce the function
the function g(x) = x f(x).
A dilation is a transformation which preserves the shape and orientation of the figure, but changes its size
g(x)=x(x + 5)(x-3)
=x(x²-3x+5x-15)
=x(x²+2x-15)
x=0, x=-5 and x=3
The function g(x) have 3 x intercepts.
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each day for five days, you collect a sample of 200 buns coming out of a commercial oven. you record the number of burned buns in the table below. the standard deviation (sigma) is 0.025. what is the upper control limit? state your answer to two decimal places, for example 0.12
The upper limit is 0.79
The class interval's upper limit is its highest value. Similarly, the lower limit is the class interval's smallest value.
Given that n = 200 and standard deviation σ = 0.025
σ = (√n/√n) = 0.025
Now calculate p
P = defectives/total inspected
= 145/200
P = 0.72
Q= 1-p
= 1- 0.72
= 0.18
Now calculate the upper limit
UCL = p – (-3 x σ)
= 0.72 – ( -3 x 0.025)
= 0.72 – (-0.075)
= 0.72 + 0.075
= 0.795
= 0.79
Therefore the upper limit is 0.79
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7x=8x+12
How do I solve this
Answer:
x = -12
Step-by-step explanation:
Get X all on one side
7x - 8x = 8x - 8x + 12
-x = 12
x = -12
Answer:
x = -12
Step-by-step explanation:
To solve this, you will need to get all of the variables on one side, and the 12 on the other. You will subtract 8x from both sides to get the equation -x = 12. You can then divide both sides by -1 to get the x alone, and thus you get x = -12.
a scout group has a raffle to rasie money for charity there is 1 prize to be won in the raffle
laura buys 12 raffle tickets a total of 350 raffle tickets are sold
find the probability that laura does not win the prize
The probability that Laura does not win the prize is 119 / 175.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
Total number of raffle rickets to be sold is 350.
The number of tickets bought by Laura is 12.
Since, the probability of an event is defined as the ratio of favorable outcome to the total outcomes, the probability of winning the prize is,
P = 12 / 350
Thus, the probability of not winning the prize is,
1 - 12 / 350
= 338 / 350
= 119 / 175
Hence, the probability of not winning a prize is 119 / 175.
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what finding the range of possible values for the length of missing side of a triangle means
Answer:
range
Step-by-step explanation:
An element with a ma and of 200 gram decay by 12. 6% per minute. To the nearet minute, how long will it be until there are 30 gram of the element remaining
The time taken, to the nearest minute, by the element to decay until only 30 grams of it are left is 14 minutes.
An element with an initial mass of 200 gram, decays by 12.6% per minute. We need to find out, to the nearest minute, how long it took for the element to decay until only 30 grams were left.
In exponential decay, a quantity diminishes slowly at first and then rapidly. The exponential decay formula is used to calculate population decay (depreciation), and it may also be used to calculate half-life (the amount of time for the population to become half its size).
Let the initial mass, remaining mass, decay rate, and time taken be represented by the variables M, m, d, and t, respectively. We can form the equation given below.
m = M(1 - d)^t
30 = 200(1 - 0.126)^t
3/20 = (0.874)^t
Take the logarithm on both sides of the equation.
log(3/20) = t × log(0.874)
t = log(3/20)/log(0.874)
t = 14.087
t ≈ 14
Hence, the time taken, to the nearest minute, by the element to decay until only 30 grams of it are left is 14 minutes.
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Is -97 prime or composite?
Answer:
Prime
Step-by-step explanation:
Because this number is only divisible by itself and no other number.
The pages of a book are numbered consecutively from 1 to 100. What is the sum of all the digits used in numbering the pages of the entire book?
5050
Step-by-step explanation:
1+2+3+.....+100 add all the numbers and u get that
Solve the following equation for y. 3y - 7(y + 5) = y - 35 Also Show your work Describe and show each step taken.
A. y = 0
B. y = 1
C. y = 2
D. All real values for y are correct solutions.
Answer:
a) y = 0
Step-by-step explanation:
Given equation,
→ 3y - 7(y + 5) = y - 35
Now the value of y will be,
→ 3y - 7(y + 5) = y - 35
→ 3y - 7y - 35 = y - 35
→ -4y - y = -35 + 35
→ -5y = 0
→ y = 0/-5
→ [ y = 0 ]
Hence, the value of y is 0.
please answer this question (answer is needed as a fraction)
Answer:
4/6 means 2/3 it is most likely 0, 67 or 0, 66.
Step-by-step explanation:
Determine whether each statement is always, sometimes, or never true.
13. For a 0, the value of a¹ is positive. ●
14. If n is an integer, then 3" 3" equals 1.
15. If 6P 0, then p > 0. 16. 4* equals 1. 4*
17. If m is an integer, then the value of 2m is negative
Problem 13
Answer: Sometimes trueReason:
If a > 0, then the statement would always be true. However, if 'a' was negative, then the statement is false.
For example, if a = -2 then:
[tex]a^{-1} = (-2)^{-1} = \frac{1}{(-2)^1} = -\frac{1}{2} = -0.5[/tex]
In short,
[tex]a^{-1} = -0.5 \ \ \text{ when } a = -2[/tex]
This is one of infinitely many counter-examples to prove the original statement isn't always true.
===================================================
Problem 14
Answer: Always trueReason:
The rule to use here is [tex]a^b*a^c = a^{b+c}[/tex]
We add exponents b and c, while the base 'a' stays the same the whole time.
In this problem we have: [tex]3^n*3^{-n} = 3^{n+(-n)} = 3^{n-n} = 3^0 = 1[/tex]
Therefore [tex]3^n*3^{-n} = 1[/tex] is always true regardless of what you replace n with. The variable n doesn't have to be an integer.
===================================================
Problem 15
Answer: Sometimes trueReason:
Let's say p = -1 is plugged into the expression
[tex]6^p = 6^{-1} = \frac{1}{6^1} = \frac{1}{6} \approx 0.1667[/tex]
which is a positive outcome showing that [tex]6^p > 0[/tex] doesn't automatically guarantee that p > 0. Feel free to try other negative values as counter-examples. Also p = 0 works as well. It turns out that [tex]6^p[/tex] is always positive regardless of what real number you use for p.
===================================================
Problem 16
Answer: Always trueReason:
The rule used here is [tex]a^{-b} = \frac{1}{a^b}[/tex]
An equivalent rule is [tex]\left(\frac{a}{b}\right)^{-c} = \left(\frac{b}{a}\right)^c[/tex]
The idea is to flip the fraction to turn the exponent positive.
Examples: [tex]2^{-5} = \frac{1}{2^5} \ \ \text{ and } \ \ \left(\frac{7}{9}\right)^{-3} = \left(\frac{9}{7}\right)^{3}[/tex]
===================================================
Problem 17
Answer: Never trueReason:
This is similar to problem 15 in that [tex]2^m[/tex] is always positive regardless if m is negative, zero, or positive. It might help to graph out [tex]y = 2^x[/tex] and see that the curve never dips below the x axis.
