R'Find the composition of transformationsthat map APQR to APQ'R'.QT RRotate [?] degrees aboutthe origin and then translate(unit(s) [ ].90180
![R'Find The Composition Of Transformationsthat Map APQR To APQ'R'.QT RRotate [?] Degrees Aboutthe Origin](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/errDd6f0AooClPAZBtQ683GCFoYZdxyE.jpeg)
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For a transformation like the one shown in the graph, note that the points have switched as follows;
[tex]P(x,y)\Rightarrow P^{\prime}(-y,x)[/tex]This is a 90 degree anticlockwise rotation about the origin.
That means point P would now be translated as follows;
[tex]\begin{gathered} P(1,1)\Rightarrow P^{\prime}(-1,1) \\ Q(2,1)\Rightarrow Q^{\prime}(-1,2) \\ R(2,3)\Rightarrow R^{\prime}(-3,2) \end{gathered}[/tex]After this rotation, the coordinates have now moved from their position one unit upwards. That now makes the final coordinates;
[tex]undefined[/tex]Related Questions
(3x10⁴) (2x10⁵)Find the answer by simplifying
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The given expression (3x10⁴) (2x10⁵)
we seperate the terms and collect like terms:
[tex]\begin{gathered} \mleft(3\times10^{4}\mright)(2\times10^{5})\text{ = 3}\times10^{4}\times2\times10^{5} \\ =\text{ 3}\times2\times10^{4}\times10^{5} \end{gathered}[/tex]When multiplying exponent (power) of the same base, the exponenet of the two numbers (base) are added together.
[tex]\begin{gathered} \text{Base = 10 , exponent = 4 and 5} \\ =3\times2\times10^{4+5} \\ =\text{ 6}\times10^9 \end{gathered}[/tex]
Find the set An B.
U = {1, 2, 3, 4, 5, 6, 7, 8)
A = {1, 2, 3, 4)
B = {1, 2, 6}
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Step-by-step explanation:
I assume A n B means the intersection of the sets A and B.
that means all the elements that are in A and in B.
that is the set {1, 2}
help meeeeeeeeee pleaseee !!!!!
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For the given functions, the two compositions are:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3*x² + 15
How to find the compositions of the functions?Here we have two functions which are:
f(x) = x² + 5
g(x) = 3x
Now we want to find the compositions:
(f o g)(x) = f( g(x) )
So we just need to evaluate f(x) in g(x), we will get:
f( g(x) ) = g(x)² + 5
f( g(x) ) = (3x)² + 5 = 9x² + 5
The other composition is:
(g o f)(x) = g(f(x))
And we can get this in a similar way:
g(f(x)) = 3*f(x) = 3*(x² + 5) = 3*x² + 15
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For the point P(24,14) and Q(31,17), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ.
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STEP 1
Identify what is given and establish what is required.
We are given the coordinates of two points P and Q on the cartesian and are asked to find their midpoint M assuming a straight line is drawn from P and Q
Midpoint between two points is given as:
[tex]\begin{gathered} M=\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2_{}}{2} \\ \text{Where} \\ x_1,y_{1\text{ }}are\text{ the coordinates of point 1} \\ x_2,y_{2\text{ }}are\text{ the coordinates of point }2 \end{gathered}[/tex]STEP 2
Employ formula while putting the appropriate variables.
We select point P as our point 1 as in the formulae and
We select point Q as our point 2 as in the formulae
This gives us:
[tex]\begin{gathered} M=\frac{24+31}{2},\frac{14+17}{2} \\ M=\frac{55}{2},\frac{31}{2} \\ M=27.5,15.5 \end{gathered}[/tex]Therefore, our midpoint M is(27.5, 15.5)
what is the surface area of the rectangular prism? 1.8 ft 2/5 ft 1/2 ft
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Each face of a rectangular prism has a rectangle shape. To calculate the surface area we need to calculate the area of all the faces. Each face appears twice on the prism, on opposite sides so we only need to make three calculations. These are done using the formulas below:
[tex]\begin{gathered} A_1=height\cdot width_{} \\ A_2=length\cdot width_{} \\ A_3=length\cdot height_{} \end{gathered}[/tex]Using the data from the problem we can calculate these areas.
[tex]\begin{gathered} A_1=\text{ 1.8}\cdot\frac{2}{5}=0.72\text{ square ft} \\ A_2=\frac{1}{2}\cdot\frac{2}{5}=0.2\text{ square ft} \\ A_3=1.8\cdot\frac{1}{2}=0.9\text{ square ft} \end{gathered}[/tex]The surface area of the prism is the sum of the areas above multiplied by two.
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(A_1+A_2+A_3) \\ A_{\text{surface}}=2\cdot(0.72+0.2+0.9)=2\cdot1.82=3.64\text{ square ft} \end{gathered}[/tex]on the coordinate plane below
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As we can see by the picture below, the school is on the point (5, -2).
For which equation would x = 12 not be a solution?96 ÷ x = 89 x - 7 = 101x + 4 = 105 + 4 x = 53
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Notice that:
1)
[tex]\frac{96}{12}=8.[/tex]Therefore x=12 is a solution to
[tex]96\div x=8.[/tex]2)
[tex]9*12-7=108-7=101.[/tex]Therefore x=12 is a solution to:
[tex]9x-7=101.[/tex]3)
[tex]12+4=16\ne10.[/tex]Therefore x=12 is not a solution to:
[tex]x+4=10.[/tex]4)
[tex]5+4*12=5+48=53.[/tex]Therefore x=12 is a solution to:
[tex]5+4x=53.[/tex]Answer: Third option:
[tex]x+4=10.[/tex]See attached pic for problem. Only need help with #2
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SOLUTION
Part 1
The independent variable are the predicting varaible for which other variable are depends on. The are the x- values
Hence
The indepedent varibles is school year
The dependent variable are the responses variables. They are the y-values for which depends on othere values,
Hence
The dependent variable for the data given is
The Tution
Part 2
To find the function, we need to set up the data as given in the table below.
The years has an interval of 1 and each fees difer by 4, the to obtain the x-values we use the mid-point
[tex]x=\frac{\text{lower}+\text{higher}}{2}\text{ for each }[/tex]Hence
The data plot will be
The linear is given by the form
[tex]\begin{gathered} y=ax+b \\ \text{Where }^{} \\ a=561.043,\text{ b=-0.0000}010994 \\ \text{Hence } \\ y=561.043x-0.0000010994 \end{gathered}[/tex]THerefore
The linear regression is y = 561. 043x -0.0000010994
Then for exponenetial we have
[tex]\begin{gathered} y=e^{ax+b} \\ \text{Where } \\ a=0.0286229,b=-47.2727 \\ \text{Hence } \\ y=e^{0.029x-47.27} \end{gathered}[/tex]Hence
The exponential regression is y = e^(0.029x-47.27)
For the power represion we have
[tex]\begin{gathered} y=ab^x \\ \text{Where } \\ a=2.9495\times10^{-21,}b=1.02904 \\ \text{Hence } \\ y=2.9495\times10^{-21,}(1.02904)^x \end{gathered}[/tex]Hence
The power regression is
y= 2.9495 x 10^-21 (1.02904)ˣ
Part 3
The graoh lot for linear function is given below
The graph for the exponential plot is
The graph for the power regression plot is given below as
The surface area of the solid cone requiring paint rounded to the nearest whole number is how many square centimeters?
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In order to calculate the surface area of the cone, first let's calculate its slant height.
If the diameter is 5 cm, the radius is 2.5 cm. Now, using the Pythagorean theorem, we can calculate the slant height s:
[tex]\begin{gathered} s^2=h^2+r^2 \\ s^2=11.4^2+2.5^2 \\ s^2=129.96+6.25 \\ s^2=136.21 \\ s=11.67\text{ cm} \end{gathered}[/tex]Now, we can calculate the surface area using the formula below:
[tex]\begin{gathered} S=\pi rs+\pi r^2^{} \\ S=\pi\cdot2.5\cdot11.67+\pi\cdot2.5^2 \\ S=29.175\pi+6.25\pi \\ S=35.425\pi \\ S=111.29\text{ cm}^2 \end{gathered}[/tex]Rounding to the nearest square centimeter, we have a surface area of 111 cm².
if cos ∅=sin 46° find ∅
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Answer:
∅ = 44°
Step-by-step explanation:
cos∅ = sin46°
∅ = (90 - 46)°
∅ = 44°
Hope this helps
If I complete this review, then I will do well on the test. If I do well on the test. If I do well on the test, then I will get an “A” on my progress report. Make a conclusion using the law of syllogism
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Law of syllogism:
If p, then q
If q, then r
Conclude:
If p, then r
Given situation:
p: complete this review
q: do well on the test
r: get an “A” on my progress report
If p, then q: If I complete this review, then I will do well on the test
If q, then r: If I do well on the test, then I will get an “A” on my progress report
Conclusion:
If p, then r: If I complete this review, then I will get an “A” on my progress report
PLS HELP ASAP WILL GIVE BRAINLIST
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Answer:
65
Step-by-step explanation:
[tex]-4a + 65 = 2a + 5\\60 = 6a\\a = 10\\[/tex]
KJN = 25 degrees
MJN = 25 degrees
KJM = KJN + MJN = 25 + 25 = 50 degrees
total angles = 360 degrees
JKL = (360 - 50 - 50 )/2 = 130 degrees
LKN is half of JKL = 130/2 = 65
What is the answer for 5p+10 = 8p+1
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The equation is given to be:
[tex]5p+10\: =\: 8p+1[/tex]We can solve for p using the following steps:
Step 1: Subtract 10 from both sides of the equation
[tex]\begin{gathered} 5p+10-10=8p+1-10 \\ 5p=8p-9 \end{gathered}[/tex]Step 2: Subtract 8p from both sides of the equation
[tex]\begin{gathered} 5p-8p=8p-9-8p \\ -3p=-9 \end{gathered}[/tex]Step 3: Multiply both sides by -1
[tex]\begin{gathered} -1\times(-3p)=-1\times(-9) \\ 3p=9 \end{gathered}[/tex]Step 4: Divide both sides by 3
[tex]\begin{gathered} \frac{3p}{3}=\frac{9}{3} \\ p=3 \end{gathered}[/tex]ANSWER:
[tex]p=3[/tex]There is a stack of plates in the backyard. There are 4 plates in the 1st layer, 8 in the second, 16 in the third, 32 in the fourth, and so on. There are total 10 rows/layers. How many total plates are in the stack?
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Given that
[tex]\begin{gathered} layer1=4plates \\ layer2=8plates \\ layer3=16plates \\ layer4=32plates \end{gathered}[/tex]Explanation
From the above, it is easy to see that the arrangement of the layers follows a geometric sequence where
[tex]\begin{gathered} first\text{ term = 4} \\ common\text{ ratio = }\frac{second\text{ }term}{first\text{ term}}=\frac{8}{4}=2 \end{gathered}[/tex]Since r>1, therefore the sum of 10 terms, which implies would give the total number of plates that are in the stack can be seen below.
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ therefore; \\ S_{10}=\frac{4(2^{10}-1)}{2-1}=\frac{4(1024-1)}{1}=4(1023)=4092 \end{gathered}[/tex]Answer: 4092
Dunoga cycled 15.26 kilometres and then ran 740 metres. What was the total distance he covered in kilometres?
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Answer:16 Kilometers
Step-by-step explanation:15.26km+.74km
Dunoga covered a distance of 16 km in total.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement.
For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.
Given that, Dunoga cycled 15.26 kilometers and then ran 740 meters. We need to find the distance he covered in kilometers,
To find the total distance, we will add the distance he covered by cycle and by running,
But the units of both the distances are not same and to add we need to convert the units,
Since, the answer required in kilometers, so we will convert meter into kilometers,
1 km = 1000 m
Therefore,
740 m = 740 / 1000 = 0.74 km
Therefore, the distance he covered in kilometers = 0.74+15.26
= 16 km
Hence, Dunoga covered a distance of 16 km in total.
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que es el producto para (x+5) (2x-1)?
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the given expression is,
(x+ 5) (2x -1)
so the answer is
[tex]\begin{gathered} \mleft(x+5\mright)(2x-1)=2x^2-x+10x-5 \\ \end{gathered}[/tex][tex]=2x^2+9x-5[/tex]so the answer is
2x^2 + 9x - 5
Marco is a newspaper boy who received a total piecework paycheck of $169.12. He receives 56 cents for every newspaper he delivers. How many newspapers did he deliver?
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if he receives 56 cents for each period it means that the multiplication must give the total paid
[tex]0.56\times P=169.12[/tex]where P is the number of newspapers
then, solve for p
[tex]P=\frac{169.12}{56}=302[/tex]he delivered 302 newspapers
Why might It be more useful to have a square root in simplest form rather than a large number under the root or the approximate Value?
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Problem
Why might It be more useful to have a square root in simplest form rather than a large number under the root or the approximate Value?
Solution
One possible answer is that if we have the square root in the simplest form we can simplify expression add, subtract and multiply/divide by other quantities. Also with the simplification is easire to understand the value of interest.
A business woman buys a new computer for $4000. for each year that she uses it the value goes depreciates by $400 the equation below gives the value y of the computer after x years. What does the x intercept mean in this situation? Find the x intercept. After how many years will the value of the computer be $2000Y=-400x+4000
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Step 1: Write the equation
y = -400x + 4000
Step 2:
The intercept in the equation represents time in years.
x-intercept represents the total length of time taken in years for the computer to values to depreciate to $0.
step 3: Find the x-intercept
To find the x-intercept, you will have to find the time taken for the computer value to depreciate to $0.
y = $0
[tex]\begin{gathered} \text{From the equation.} \\ y\text{ = -400x + 4000} \\ 0\text{ = -400x + 4000} \\ 400x\text{ = 4000} \\ x\text{ = }\frac{4000}{400} \\ x\text{ = 10} \end{gathered}[/tex]The x-intercept = 10 years
Step 4:
To find the number of years take for the computer value to depreciate to $2000.
You will substitute the value of y = $2000 and find the value of x.
Therefore
[tex]\begin{gathered} y\text{ = -400x + 4000} \\ 2000\text{ = -400x + 4000} \\ 400x\text{ = 4000 - 2000} \\ 400x\text{ = 2000} \\ x\text{ = }\frac{2000}{400} \\ \text{x = 5 years} \end{gathered}[/tex]It will take 5 years for the value of the computer to depreciate to $2000.
Solve for w.4w+6= -22Simplify your answer as much as possible.W8DDХ5?
Answers
w= -7
Explanation
[tex]\begin{gathered} 4w+6=-22 \\ \end{gathered}[/tex]
Step 1
The addition property of equality and subtraction property of equality are similar. Adding or subtracting the same number to or from both sides of an equation keeps both sides equal, so we can use this fact to isolate w
a) subtract 6 in both sides of the equation
[tex]\begin{gathered} 4w+6=-22 \\ 4w+6-6=-22-6 \\ 4w=-28 \\ \end{gathered}[/tex]Step 2
The division property of equality states that when we divide both sides of an equation by the same number, the two sides remain equal.so
b) divide both sides by 4
[tex]\begin{gathered} 4w=-28 \\ \frac{4w}{4}=\frac{-28}{4} \\ w=-7 \end{gathered}[/tex]therefore, the answer is
w= -7
I hope this helps you
Suppose the cost per ton f(x) to build an oil platform of x thousand tons is approximated byf(x)= 62,500 ______ x+125What is the cost per ton for x=30?
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Given that
The cost per ton f(x) to build an oil platform of x thousand tons is approximated by
[tex]f(x)=\frac{62500}{x+125}[/tex]The cost per ton for x = 30, i.e f(30) will be
[tex]\begin{gathered} f(x)=\frac{62500}{x+125} \\ f(30)=\frac{62500}{x+125}=\frac{62500}{30+125}=\frac{62500}{155} \\ f(30)=\frac{62500}{155}=403.226\text{ (3 d.p)} \\ f(30)=403.226\text{ (3 d.p)} \end{gathered}[/tex]Hence, the answer is 403.226 (3 d.p)
0.4(2-) 0.2(9 + 7) A)-3 B - 1 C) 3 D) all real numbers
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Let us solve the equation to arrange the steps
[tex]-3(4+3x)+5x=-16[/tex]In the first step, we must multiply the bracket by -3 (distributive property)
[tex](-3)(4)_{}+(-3)(3x)=-12-9x[/tex]Then the equation is
[tex]-12-9x+5x=-16[/tex]Now add the like terms on the left side
[tex]\begin{gathered} -12+(-9x+5x)=-16 \\ -12x+(-4x)=-16 \\ -12-4x=-16 \end{gathered}[/tex]Next step, add 12 to both sides
[tex]undefined[/tex]This season, the probability that the Yankees will win a game is 0.59 and theprobability that the Yankees will score 5 or more runs in a game is 0.43. Theprobability that the Yankees lose and score fewer than 5 runs is 0.3. What is theprobability that the Yankees win and score 5 or more runs? Round your answer to thenearest thousandth.
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From the information given we conclude that the probability that the Yankees win and score 5 or more scores is 0.43
It is because of the description given in the problem.
How many values does the expression 6+ (7 + 3)² have? Write down the values.
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Answer:
3
Step-by-step explanation:
6
7
3
The values are the number that compose the expression
Solve the System of Equations8x + 15y = -1174x + 9y=-75Write your answer as an ordered pair: (x,y)
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We have to solve the system of linear equations:
[tex]\begin{gathered} 8x+15y=-117 \\ 4x+9y=-75 \end{gathered}[/tex]We can substract 2 times the second equation for the first equation and solve for y:
[tex]\begin{gathered} (8x+15y)-2(4x+9y)=-117-2(-75) \\ 8x+15y-8x-18y=-117+150 \\ 0x-3y=33 \\ y=\frac{33}{-3} \\ y=-11 \end{gathered}[/tex]Now, we can solve for x:
[tex]\begin{gathered} 4x+9y=-75 \\ 4x+9(-11)=-75 \\ 4x-99=-75 \\ 4x=-75+99 \\ 4x=24 \\ x=\frac{24}{4} \\ x=6 \end{gathered}[/tex]Answer: (x,y)=(6,-11)
what is 5x6 I need help
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Thus, the required solution is 30.
Answer: 30
Step-by-step explanation: 30
You buy a new commercial stove for $9,000 and estimate that it will enable you to deliver 20 additional meals per night at an average price of $20. Assuming 25% food cost and no additional costs to using the new stove, how long will it take the stove to pay for itself?
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Assuming 25 % food cost and no additional costs to using the new stove, The time it will take the stove to pay for itself is 30 days.
Determining the number of daysProfits per meal = $20 - ( 0.25 x20)
Profits per meal = $20 -$5
Profits per meal = $15
Profits for 20 meals = $15 x 20
Profits for 20 meals =$300
Now let determine the number of days
Number of days =$9000 / $300 days
Number of days =30 days
Therefore we can conclude that 30 days is the days that it will take.
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An earthquake in California measured 3.6 on the Richter scale. Use the formula R=log(A/Ao) to determine approximately how many times stronger the wave amplitude of the earthquake was than .
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The correct option regarding how many times stronger the wave amplitude of the earthquake was than the standard wave Ao is given by:
A = 3981Ao.
Ratio of A and AoTo find the ratio of A and Ao, measuring how many times a earthquake measuring R in the Richter scale was than Ao, we have to solve the following logarithmic function:
R=log(A/Ao)
The power of 10 in inverse to the logarithm, hence it is applied to both sides of the expression, as follows:
10^R = 10^log(A/Ao).
Since they are inverses, we can remove the power and the logarithm as follows:
A/Ao = 10^R
Hence the formula for how many times stronger and earthquake is than Ao is given as follows:
A = 10^R Ao
In this problem, the Richter measure of the earthquake was of:
R = 3.6.
Hence the ratio is:
A = 10^(3.6)Ao
A = 3981Ao.
Missing informationThe problems asks how many times stronger the earthquake was than Ao.
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write a quadratic equation in the form of ax²bx+c=0
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The general form of a quadratic equation is expressed as
ax^2 + bx + c = 0
In order to write the equation, we would substitute values for a, b and c. If a = 3, b = 8, c = 25, the equation would be
3x^2
Solve 2x - 8 < 7...........................................................................
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
2x - 8 < 7
Step 02:
inequality:
2x - 8 < 7
2x - 8 + 8 < 7 + 8
2x / 2 < 15 / 2
x < 15 / 2
The answer is:
x < 15 / 2
(-oo , 15/2)