Answer:
The transformation that map line RS to line R"S" is " rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1)" ⇒ B
Step-by-step explanation:
Let us revise some transformationIf the point (x, y) rotated about the origin by angle 180° counterclockwise, then its image is (-x, -y) ⇒ R(180, O) (x, y) → (-x, -y) If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)If the point (x, y) translated vertically up by k units then its image is (x, y + k) ⇒ T (x, y) → (x, y + k)∵ The coordinates of the point R = (-2, 4)∵ The coordinates of point R" = (3, -3)→ Both coordinates in R" have opposite signs then R∴ R rotated 180° about the origin ⇒ using the 1st rule above∴ R' = (2, -4)→ Find the difference between the x-coordinate of R" and x-coordinate of R'∵ xR" - xR' = 3 - 2 = 1→ By using the 2nd rule above∴ R' translated 1 unit to the right → Find the difference between the y-coordinate of R" and y-coordinate of R'∵ yR" - yR' = -3 - (-4) = -3 + 4 = 1→ By using the 3rd rule above∴ R' translated 1 unit up∴ The rule of translation is T(x, y) ⇒ (x + 1, y + 1)Let us use these 2 rules on S to find S"∵ The coordinates of the point S = (-4, -1)∵ S is rotated 180° around the origin→ By using the 1st rule above, opposite the signs of its coordinates∴ S' = (4, 1)∵ S' translated 1 unit right→ By using the 2nd rule above, add its x-coordinate by 1∵ S' translated 1 unit up→ By using the 3rd rule above, add its y-coordinate by 1∴ S" = (4 + 1, 1 + 1)∴ S" = (5,2)→ That means the rules of transformation of point R is rightThe transformation that map line RS to line R"S" is " rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1)"
Translation
Explain Explain Explain Explain
[tex] \rm \int_{ \infty }^{ - \infty } \frac{ { {e}^{ { - x}^{2} } }(5 {x}^{2} + 2 {x}^{4} )}{ {x}^{2}( {x}^{2} + 1)} dx \\ [/tex]
Consider the integral
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx[/tex]
which is the negative of yours. Bit strange to integrate over [tex](\infty,-\infty)[/tex], but if that's what you actually intended, just multiply the final result by -1. Of course, I've already canceled the superfluous factors of [tex]x^2[/tex].
Expand the integrand into partial fractions.
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = \int_{-\infty}^\infty \left(2 + \frac3{1+x^2}\right) e^{-x^2} \, dx[/tex]
Recall that for [tex]\alpha>0[/tex],
[tex]\displaystyle \int_{-\infty}^\infty e^{-\alpha x^2} \, dx = \sqrt{\frac\pi\alpha}[/tex]
Now let
[tex]\displaystyle I(a) = \int_{-\infty}^\infty \frac{e^{-ax^2}}{1+x^2} \, dx[/tex]
Together, these give
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = 2\sqrt\pi + 3I(1)[/tex]
Differentiate [tex]I(a)[/tex] under the integral sign with respect to [tex]a[/tex] to obtain a simple linear differential equation.
[tex]\displaystyle \frac{dI}{da} = -\int_{-\infty}^\infty \frac{x^2 e^{-ax^2}}{1+x^2} \, dx \\\\ ~~~~~~~~ = - \int_{-\infty}^\infty \left(1 - \frac1{1+x^2}\right) e^{-ax^2} \, dx \\\\ ~~~~~~~~ = -\sqrt{\frac\pi a} + I(a)[/tex]
Solve for [tex]I(a)[/tex] with the initial value [tex]I(1) = \sqrt\pi[/tex]. Using an integrating factor,
[tex]\displaystyle \frac{dI}{da} - I(a) = -\sqrt{\frac\pi a} \\\\ e^{-a} \frac{dI}{da} - e^{-a} I(a) = -\sqrt{\frac\pi a}\,e^{-a} \\\\ \frac{d}{da}\left[e^{-a} I(a)\right] = -\sqrt{\frac\pi a}\,e^{-a}[/tex]
By the fundamental theorem of calculus,
[tex]\displaystyle e^{-a} I(a) = e^{-a}I(a)\bigg|_{a=0} - \sqrt\pi \int_0^a \frac{e^{-\xi}}{\sqrt\xi} \, d\xi \\\\ I(a) = \pi e^a - \sqrt\pi \, e^a \int_0^a \frac{e^{-\xi}}{\sqrt\xi} \, d\xi[/tex]
so that
[tex]\displaystyle I(1) = \pi e - \sqrt\pi\,e \int_0^1 \frac{e^{-\xi}}{\sqrt\xi} \, d\xi[/tex]
Substitute [tex]t=\sqrt\xi[/tex].
[tex]\displaystyle I(1) = \pi e - 2\sqrt\pi\,e \int_0^1 e^{-t^2} \, dt[/tex]
Recall the error function,
[tex]\mathrm{erf}(x) = \displaystyle \frac2{\sqrt\pi} \int_0^x e^{-t^2} \, dt[/tex]
which we can use to write
[tex]I(1) = \pi e - 2\sqrt\pi e \cdot \dfrac{\sqrt\pi}2\,\mathrm{erf}(1) = \pi e - \pi e \,\mathrm{erf}(1)[/tex]
Finally, we arrive at
[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = \boxed{2\sqrt\pi + 3\pi e - 3\pi e \, \mathrm{erf}(1)}[/tex]
a box of cereal has a volume of 1250 cubic cm with a length of 20cm and a width of 5cm. what is the height of the box?
Define in words variables for the unknown values
create an equation
solve using algebra
The height of the box that has a volume of 1250 cubic cm with a length of 20cm and a width of 5cm will be 12.5cm.
How to calculate the height?It should be noted that the formula for the volume will be:
= Length × Width × Height
Therefore the height will be:
Volume = LWH
where
L = length = 20cm
W = width = 5cm
H = height = unknown
1250 = (20 × 5 × H)
1250 = 100H
Height = 1250/100
Height = 12.5 cm
Therefore, the height is 12.5cm.
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If you spend 3.5 hours a week studying for English and 7.5 hours studying for math what is the ratio of time
spent studying in math to studying for English?
Answer:
7.5 : 3.5
Step-by-step explanation:
ratio of time spent studying in math to studying for English is ;
time spent studying in math. / time spent in studying English
[tex] \frac{7.5}{3.5} [/tex]
= 7.5 : 3.5
PLS ANSWER THIS QUESTION FAST
WILL MARK BRAINLIEST
Answer: x=18 ==> C
Step-by-step explanation:
19+15+11=14+15+?
19+11=14+?
30=14+?
?=16
?+11+x=19+15+11
x+?=19+15
x+16=34
x=18 ==> C
Question 7 of 20:
Select the best answer for the question.
7. Percent means "per
O A. 100
OB. 1000
O C. 1
O D. 10
11
K
OMark for review (Will be highlighted on the review p
Will mark u brainliest Question
Question
What is the turning point of the graph of f(x)=|x−2|+3?
(2, 3)
(−3, 2)
(3, 2)
(2, −3)
The turning point of the function f(x) = |x-2| + 3 will be (3, 2).
Here,
We have to find the turning point of the graph of function,
f(x) = |x−2|+3
What is an absolute function?
The non-negative value of real number without regard to its sign is known as its absolute value.
Now,
The absolute function is;
f(x) = |x+3| -2.
Since, When we plot the graph of the absolute function f(x) = |x+3| -2,
it will give two straight lines which is shown in the graph.
Clearly, The graph of the function changes its position at the coordinate
(3, 2).
Therefore, The absolute function having its turning point at the coordinate ( 3, 2).
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13x + 5 + 17x -4.5 + x
Answer:
31x+0.5
Step-by-step explanation:
In this problem, we must combine like terms to simplify the expression. We can begin by writing out the expression:
13x + 5 + 17x - 4.5 + x
Now that we have rewritten the expression, we can combine like terms to simplify the expression. This would look like:
13x + 17x + x = 31x
5 - 4.5 = 0.5
The answer would be “31x + 0.5” when simplified.
QUESTION 94
Percentages
In January 2021, a study by the Bureau of Transportation statistics found that 12 out of 35 flights arrived
on time. What percent of the flights were on time?
Choose one 4 points
O 72%
O 34.3%
O 34%
O 27%
Answer: 34.3%
Step-by-step explanation:
[tex]Given:\ 12/35\ flights\ on\ time[/tex]
To find the percent, divide then multiply by 100:
[tex]\frac{12}{35} = 0.343\times100=\large\boxed{34.3}[/tex]
At the beginning of each of her four years in college, Miranda took out a new Stafford loan. Each loan had a principal of $5,500, an interest rate of 7.5% compounded monthly, and a duration of ten years. Miranda paid off each loan by making constant monthly payments, starting with when she graduated. All of the loans were subsidized. What is the total lifetime cost for Miranda to pay off her 4 loans? Round each loan's calculation to the nearest cent.
a.
$23,650.00
b.
$29,481.08
c.
$7,834.32
d.
$31,337.27
The total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27.
What is interest?Interest is the sum of money paid for using someone else's funds. You must pay interest when you borrow money from lenders. You receive interest when you lend money to borrowers. It could be stated in terms of money or the rate of payment. You will learn more about interest in this article, including the different sorts of interest, what they are, and how to determine how much interest will be charged on a loan or a loan amount.
Given that,
At the beginning of each of her four years in college
Miranda took out a new Stafford loan.
Each loan had a principal of $5,500,
An interest rate of 7.5% compounded monthly
A duration of ten years.
Miranda paid off each loan by making constant monthly payments, starting with when she graduated.
All of the loans were subsidized.
The total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27
Therefore, the total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27
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Answer: D 31,337.27
Step-by-step explanation:
6. A household spend 120 on purchase of a commodity when it price is 6 per unit. When the rises to 10 per unit his total expenditure on this commodity becomes 180.calculate price elasticity of demand by percentage change method.
Therefore, the price elasticity of demand by percentage change method is -0.025.
Given the price of a first commodity (p₁) = 6 rs
the price of a second commodity (p₂) = 10 rs
Expenditure on first commodity (s₁) = 120
Expenditure on second commodity (s₂) = 180
We need to find the quantity as
120 = 6 * Q₁. 180 = 10 * Q₂
Q₁ = 120 / 6 Q₂ = 180 / 10
Q₁ = 20 Q₂ = 18
price elasticity of demand by percentage change method as
Eₐ = P / Q * ΔQ /ΔP
ΔQ = Q₂ - Q₁ = 18 -20 = -2
ΔP = p₂ - p₁ = 10 - 6 = 4
Eₐ = 6 / 120 * -2 / 4
Eₐ = - 0.025
Therefore, the price elasticity of demand by percentage change method is -0.025.
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i really need help! please
Approximate √10 to the nearest tenth
XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.
What is the numerical value of K?A bisector divides a segment or angle into two equal halves.
Given the data in the question;
XZ is the perpendicular bisector of segment WYSegment WX = 3k + 17Segment XY = 7k - 7Value of k = ?Since XZ is a perpendicular bisector of segment WY,
Segment WX is equal to Segment XY
Segment WX = Segment XY
Plug in the given values and solve for k.
3k + 17 = 7k - 7
Collect like terms
3k - 7k = -7 - 17
-4k = -24
Divide both sides by the coefficient of k
-4k/-4 = -24/-4
k = 6
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.
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Draw the image of
ΔDEF
∆DEF
under the dilation with scale factor
−1/2
and the origin as the center of dilation. Label the image
ΔD'E'F'
∆D′E′F′
. Make sure to include the coordinates of D’, E’, and F’.
The image of triangle DEF after the dilation with a scale factor of -1/2 is given at the end of the answer.
What are transformations on the graph of a function?Transformations in the graph of a function involve operations in the vertices of the image, such as addition, subtraction, division or multiplication.
The transformation used in this problem is a dilation, in which the coordinates of the vertices of the original figure are multiplied by the scale factor.
For this problem, the vertices of the triangle are given as follows:
D(3,6), E(3,2) and F(5,4).
The dilation has a scale factor of -0.5 = -1/2, hence the coordinates of the image are given as follows:
D': (3 x -0.5, 6 x -0.5) = (-1.5, -3).E': (-1.5, -1).F': (-2.5, -2).The dilated triangle is given by the graph at the end of this answer.
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The blueprint specifications for a machined part calls for its thickness to be 3.145 in.
with a tolerance of +-0.010 in. Find the limit dimensions of the part?
The limit dimensions of the part are 3.135 inches and 3.155 inches
How to find the limit dimensions of the part?The given parameters are
Thickness = 3.145 inchesTolerance = 0.010 inchesThe limit dimensions of the part are calculated as
Limit = Thickness +/- Tolerance
So, we have
Limit = 3.145 inches +/- 0.010 inches
Expand the above expression
So, we have
Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)
Evaluate the sum
Limit = (3.135 inches, 3.155 inches)
Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches
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Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of $10.50 each, but later decreased the price of each by $2.00. If they sold all 98 pieces and took in $893.00
find how many they sold at the original price and how many they sold at the reduced price.
Answer:
See work below.
30 sold for full price and 68 sold for a discount.
Step-by-step explanation:
Need help with D pls will give brainly
The length of the pen is 2√3 feet
Area of a triangleThe formula for calculating the area of a rectangle is expressed according to the formula below:
Area of a right triangle = 1/2 * base * height
A = 1/2 bh
Given the following parameters
Area = 20 square feet
If the height is five times the length, then;
h = 5b
Substitute
A = 1/2 bh
A = 1/2(b)5b
30 = 1/2(5b²)
60 =5b²
b² = 12
b = 2√3
Hence the length of the pen is 2√3 feet
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Find the unit tangent vector for the following parameterized curves.
r(t)=cos(t)i+sin(t)j+sin(t)k, 0≤t<2π.
The unit tangent vector for the parametrized curve is [tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex].
How to determine the unit tangent vector of a parametrized curveIn this question we know a three-dimension parametrized curve, of which we must derive its unit tangent vector in accordance with the following formula:
[tex]\vec T(t) = \frac{\vec R'(t)}{\|\vec R'(t)\|}[/tex]
Where:
[tex]\vec T(t)[/tex] - Tangent vector.[tex]\|\vec R'(t)\|[/tex] - Magnitude of the first derivative of the parametrized curve.First, determine the first derivative of the parametrized curve:
[tex]\vec R'(t) = -\sin t \,\hat{i} + \cos t \,\hat{j} + \cos t \,\hat{k}[/tex]
Second, derive the magnitude of the parametrized curve:
[tex]\|\vec R'(t)\|[/tex] = √[(- sin t)² + (cos t)² + (cos t)²]
[tex]\|\vec R'(t)\|[/tex] = √(1 + cos² t)
Third, substitute every term in the unit tangent curve formula:
[tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex]
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solve the equation by performing two operations on both sides. State the operation in order of use
Answer:
C. Multiply by 5, then subtract 7.
Step-by-step explanation:
You want to know the two steps required to solve this 2-step linear equation.
SolutionThe variable x has 7 added to it, and the sum is divided by 5. To find the value of x, we must undo these operations in reverse order.
To undo division by 5, we must multiply by 5.
Then, to undo the addition of 7, we must subtract 7.
Here is the "work":
[tex]\dfrac{x+7}{5}=10\qquad\text{given}\\\\x+7 = 50\qquad\text{multiply both sides by 5}\\\\x=43\qquad\text{subtract 7 from both sides}[/tex]
The operations in order of use are ...
Multiply both sides by 5 first, then subtract 7 from both sides.
__
Additional comment
The properties of equality tell you that you must do the same operation to both sides of the equation.
solve the equation for x (3x/4)+2=4x-1
Answer:
Step-by-step explanation:
Use the diagram to find the value of the following. what is the value of x.
Angle A-
Angle B -
Angle C-
Answer:
x=29 angle a=63 Ang b=46 and c=71
Step-by-step explanation:
2x+5+x+17+3x-16=180 (sum of angles in triangles)
value of x is 29 substitute it in angle a b c
a=2*29+5
=63
b=29+17 = 46
c=3*29-16 = 71
Which number below is NOT equal to the others?
1/8
18/10
1.8
1 4/5
Answer:
1/8
Step-by-step explanation:
When worked out, all numbers are equal to 1.8 except 1/8. (1/8 is equal to .125)
1/8) 1 divided by 8 is .125
18/10) 18 divided by 10 is 1.8
1.8) 1.8=1.8
1 4/5) 4 divided by 5 is .8, and when you add the 1 it ends up as 1.8
Point A appears on the number line as shown below:
Answer:
C) x² + y²Step-by-step explanation:
According to the graph, point A has a negative value, between - 1 and zero.
All the expressions could result in negative value apart from the sum of the squares, which is never negative.
Correct choice is C.
A dressmaker needs to cut 18-inch pieces of ribbon from rolls of ribbon that are 3 feet in length. How many 18-inch pieces can the dressmaker cut from 15 of these rolls of ribbon?
Professor Cramer determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 7%, each paper is worth 9%, each test is worth 14%, and the final is worth 33%, (a) What is the average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam? (Round your answer to one decimal place.) (b) Compute the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance. (Round your answer to one decimal place.)
The average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam is 77.31% and the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance is 73.23%.
Averagea. Average:
Average: 82(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33
Average=5.74+5.49+10.08+8.96+13.02+27.06÷0.91
Average=70.35÷0.91
Average=77.31%
b. Average
Average= 29(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33
Average=2.03+5.49+10.08+8.96+13.02+27.06÷0.91
Average=66.64÷0.91
Average=73.23%
Therefore the average for both a and b is 77.31% and 73.23%.
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Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Learn with an example
Susan is going to ship some gifts to family members, and she is considering two shipping
companies. The first shipping company charges a fee of $20 to ship a medium box, plus an
additional $1 per pound. A second shipping company charges $5 for the same size of box,
plus an additional $4 per pound. At a certain weight, the two shipping methods will cost tre
same amount. How much will it cost? What is that weight?
The two shipping methods both cost $
Submit
at a weight of
pounds.
The first company shipping charge is 5 $
the second company shipping charge is 2 $
let the size of the box be 'x'
Given the first company charged as below
20$ for medium-sized and an extra 1$ for one pound
= 20x + 1
The second company charged as below
$5 for the same size of the box, plus an additional $4 per pound
= 5x + 4
The price of the two shipping options will be same.
20x + 1 = 5x + 4
20x - 5x = 4- 1
15x = 3
x= 3 / 15
x = 1/5
x = 0.2
∴ 20x+1 = 20 * 0.2 +1 = 5
5x + 4 = 5 * 0.2 + 1 = 2
Therefore, The first company's shipping fee is $5, whereas the second company's fee is $2.
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if 2/5 kilogram of soil fills 1/3 of a container,can1 a kilogram of soil fit in the container? Explain or show your reasoning
Answer:
Yes
Step-by-step explanation:
1 kilogram of soil will fill:
1/3 ÷ 2/5 = 5/6 (of a container)
Because 5/6 < 1
=> 1 kilogram of soil will fit in the container
The system of equations graphed below has how many solutions?
y = 2x + 2
y= 2x
The given system has zero solutions.
Lines that never cross one other are said to be parallel. Hence, a pair of parallel lines must have the same slope but distinct intercepts. (On the other hand, identical lines have same intercept).
In the general equation of a line, y = mx + b, m represents the slope of the line.
The general equations of parallel lines would be of the form:
(1) y = mx + b
(2) y = mx + c
where b and c are any constants.
Now, we observe that the given equations are of the above form with m=2, b=2 and c=0, therefore, they are parallel lines. Since, parallel lines never intersect each other, they have no solution.
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television and DVD player cost a total of $1242. The cost of the television is two times the cost of the DVD player. Find the cost of each item.
Answer: TV costs $828 and DVD player costs $414.
Step-by-step explanation: let x represent the cost of tv while y represents the cost of the player. x+y = 1242. since the tv costs twice as much as the dvd player, we can say that 2y=x. now replace x with 2y in our equation and we get 2y+y= 1242, 3y = 1242. now divide both sides by 3 and y = 414. Now that we now the value of y, just sub it into our original equation, x+y = 1242. x + 414 = 1242. x = 828.
Find the measure of the missing angles.
Answer:
x=26, y=90
Step-by-step explanation:
This is what I did,
I knew that y = 90 because it is a Right Angle. I subtracted 90 - 64 and that got me = y 26