1. A rectangular prism is defined as the drawing shows. Note B at (0, 5, 0) and F (0, 0, 4). The prism is reflected over the xz-plane. The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
a.) Show the results of your calculations for points A, B, C and D from the reflection.
b.) Show the results of your calculations for points A, B, C and D from the translation.
Answers
A (0,0,0)
B (0,5,0)
C (3,5,0)
D (3,0,0)
E (3,0,4)
F (0,0,4)
G (0,5,4)
H (3,5,4)
a.) The prism is reflected over the xz-plane.
Reflection Point P(x,y,z) over the xz-plane is P'(x,-y,z):
Reflection P(x,y,z) over the xz-plane → P'(x,-y,z)
Reflection A(0,0,0) over the xz-plane → A'(0,-0,0) = A'(0,0,0)
Reflection B(0,5,0) over the xz-plane → B'(0,-5,0)
Reflection C(3,5,0) over the xz-plane → C'(3,-5,0)
Reflection D(3,0,0) over the xz-plane → D'(3,-0,0) = D'(3,0,0)
b.) The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
Translation P'(x,-y,z) 2 units back, 3 units left, and 1 unit up is P''(x-2,-y-3,z+1):
Translation P'(x,-y,z) → P''(x-2,-y-3,z+1)
Translation A'(0,0,0) →A''(0-2,0-3,0+1) = A''(-2,-3,1)
Translation B'(0,-5,0) →B''(0-2,-5-3,0+1) = B''(-2,-8,1)
Translation C'(3,-5,0) →C''(3-2,-5-3,0+1) = C''(1,-8,1)
Translation D'(3,0,0) →D''(3-2,0-3,0+1) = D''(1,-3,1)
Related Questions
How can you find the surface area of a composite solid made up of prisms
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For what value of xis the square of the binomial 3x+1 is 9 times greater than the square of the binomial x–2?
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First, we expand the parentheses on both sides using FOIL (Firsts, Outers, Inners, Lasts) :
(3x+1)(3x+1)=9(x-2)(x-2)
9x²+3x+3x+1=9(x²-2x-2x+4
Simplify:
9x²+6x+1=9(x²-4x+4)
Now expand the RHS (right-hand side) expression - multiply all the terms inside the parentheses by 9:
9x²+6x+1=9x²-36x+36
Now solve as you normally would to isolate x. Start off by subtracting 9x² on both sides:
6x+1=-36x+36
Add 36x on both sides:
42x+1=36
Minus 1 on both sides:
42x=35
Divide both sides by 42:
[tex]x= \frac{35}{42} [/tex]
which simplifies to
[tex]x= \frac{5}{6} [/tex]
I double checked this by substituting x back into the question and it worked, you can try doing this too for verification.
Final answer:
The value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2 is obtained by equating (3x + 1)² to 9(x − 2)², which simplifies and solves to x = 5/6.
Explanation:
To find the value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2, we need to formulate and solve an equation based on the given conditions:
(3x + 1)² = 9(x − 2)²
Expanding both sides gives us:
9x² + 6x + 1 = 9x² − 36x + 36
Now, by simplifying and solving for x, we find:
42x = 35
x = 35 / 42
x = 5 / 6
Therefore, the value of x is 5/6.
The diagonal of rectangle ABCD measures 2 inches in length What is the length of line segment AB?
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In the diagram, we already have the angles given so we just need to find the length of one side. Let's first find the length of segment CD since we are given the angles on that side of the rectangle.
We can find its length by applying SOHCAHTOA. We can either use the 60 or 30-degree angle but for this solution let's make use of 60 degrees. From SOHCAHTOA we know that sine of 60 is equal to the length opposite it (CD) over the hypotenuse which is the diagonal that is equal to 2 inches. Knowing this we can solve for CD:
[tex]sin(60)= \frac{CD}{2} [/tex]
[tex] \frac{ \sqrt{3}}{2}= \frac{CD}{2} [/tex]
[tex] \sqrt{3}=CD [/tex]
Since we have a rectangle, the measure of segment CD will just be equal to the measure of segment AB.
ANSWER: The length of line segment AB is √3 or 1.73 inches.
Answer:
Step-by-step explanation:
B on edge
C=
5\9
(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I.) A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5\9 degree Celsius.
II.) A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III.) A temperature increase of 5\9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
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If changes are made to a signature while using version 5.x signature files, are they visible in the router running the configuration?
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What is the circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm?
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10^2 + 24^2 = 676
sqrt(676) = 26
The formula for circumference is: diameter times pi.
C = 26pi
Find the equation of the plane through the point p=(5,5,4)p=(5,5,4) and parallel to the plane 5x+2y−z=−6.
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Π : 5x+2y-z=-6
then they both have the normal vector <5,2,-1>
Given the required plane passes through the point (5,5,4), the new plane is defined by
5(x-5)+2(y-5)-1(z-4)=0
=>
plane: 5x+2y-z=31
a rectangle that is 2 inches by 3 Inches has been scaled by factor of 7 suppose you want to scale the copy back to its original size what scale factor would you use?
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This is about transformation of objects.
Scale factor back to original size = 1/7
We are told that the rectangle was scaled by a factor of 7.What this means is that if the length and width are x and y respectively, then the new scaled measurements will be;
7x and 7y.
Now,for us to scale back to the original size, all we need to do is to divide the new scale measurements by a factor of 7.This means the original size will be;
Length = 7x × 1/7
Width = 7y × 1/7
Thus,the scale factor will be 1/7 back to the original size.Read more at; https://brainly.com/question/17292295
A school sold small and large boxes of fruit as a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Let x represent the price of a small box and y represent the price of a large box. Solve the system to determine the price of each size box of fruit.
A The price of a small box of fruit is $10 and the price of a large box of fruit is $14.
B The price of a small box of fruit is $8 and the price of a large box of fruit is $14.
C The price of a small box of fruit is $10 and the price of a large box of fruit is $16.
D The price of a small box of fruit is $14 and the price of a large box of fruit is $16.
Answers
5(10)+13(14)=232
50 + 182 =232
12(10)+7(14)=218
120 + 98 =218
The answer is y=14 and x= 10
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218.
Then we have 5x+13y=232
12x+7y=218
Solving these two equations here we get y=14 and x= 10
Hence, The answer is y=14 and x= 10
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The classroom encyclopedia set seems to fill a shelf that is 24 in long each book is 3/4 in thick how many books are in the classroom set
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Shoe store A is having a sale in which every pair of shoes is 40% off the regular price.
Shoe store B is having a sale in which $40 is deducted from the regular price.
Richard is comparing the price of the same pair of shoes in both shoes in both stores.In both stores, the shoes normally sell for $120. Which store has the better bargain?
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A swimmer swam 49 kilometers in d days. what is the value of d if the swimmer swam an average of 3.2 kilometers daily?
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Because d= 49/ 3.2= 15 days
William runs 5 meters in 20 steps. How many kilometers will he run if he takes 1,000 steps ?
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in 3/4 identify the role of 3. Then explain how to read tbis number
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But how to read the number I’m not sure.
Answer:
The 3 is the numerator, To read the number is "three-fourths"
Step-by-step explanation:
I hope this helps!
2 to the x power equals 512
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Please make brainliest! ☺
a triangle has an area of 54 m2 and a height of 9m how long is the base of the triangle entered your answer in the box
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base of the triangle = 12 m
Explanation:
Area of the triangle = 1/2 * base * height
We are given that:
area = 54 m^2
height = 9 m
Substitute in the equation to get the base as follows:
Area of the triangle = 1/2 * base * height
54 = 1/2 * base * 9
108 = 9*base
base = 12 m
Hope this helps :)
A =(1/2)* b * h
Where,
b: base
h: height.
Clearing the base we have:
b = 2*A / h
Substituting the values
b = 2*(54) / (9) = 12 m
Answer:
The base of the triangle is 12m long
which number produces an irrational number when multiplied by 0.5
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pi symbol
which equation is the inverse of y=100-x2
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Answer:
Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].
Step-by-step explanation:
Given : f(x) = y = 100 - x²
To find : Find inverse.
Solution : We have given that :
f(x) = y = 100 - x²
Step1) : Replace every x with a y and replace every y with an x .
x = 100 - y².
Step 2): Solve for y
On subtracting 100 from both sides
x - 100 = -y²
On multiplying both side by -1
100 -x = y²
Taking square root both sides and switching sides
y = ± [tex]\sqrt{100-x}[/tex].
Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Answer:
A on edge
Step-by-step explanation:
Enrique charges $5 for every 1/5 hour he spends walking dogs.in the morning he walks buttons for 2/5 hour bruno for 1/5 hour and pepper for 3/5 hour. Monday thru friday. On saturdays he takes mimi diva and coco to the dog park for 4/5 of an hour. On wendsday this week it rained and pepper wanted to stay out for only 1/5 hour. How many hours did enrique spend with the dogs this week. Explain your method
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In a rhombus MPKN with an obtuse angle K the diagonals intersect each other at point E. The measure of one of the angles of a ∆PKE is equal 16°. Find the measures of all angles of ∆PKE and ΔPMN.
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The second is that all the sides are congruent. That's actually the key to the problem (or one of them.
The third is that the diagonals are line segments that bisect the angles where the vertex of the angle is.
So just to make sure you understand what that last statement means <PKM = <NKM
K is the vertex of angle PKN
Now the really heavy duty stuff about your question.
Given
K is obtuse. Therefore <PKM can't be 16o because MKN would also have to be 16 degrees and together they don't add up to anything over 90o.
So the 16o angle is at <EPK
Remember that the diagonals meet at right angles. <PEK = 90o
Finally all triangles have 180o
< PKE = 180 - 16 - 90 = 74. So to review
<PKE = 74o
<EPK = 16o
<PEK = 90o That's one half the problem.
Moving on to triangle PMN
By the properties of parallel lines and a rhombus and isosceles triangles, that since PKN is bisected (rhombus property) Then PKN = 2* PKM =2*74 = 148o
The angle opposite <PKN is equal to <PKN so <PMN = <PKN
Since PKN = 148 then PMN = 148
Since KPN = 16o then PMN = 16o
Since triangle <PMN is isosceles <PNM = 16o
Summing up
PMN = 148o
MPN = 16o
MNP = 16o
That's both triangles solved. This is a really nice little problem. If you google properties of a rhombus, you will find all the properties I have used proven.
Answer:
m∠KEP = 90°
m∠EKP = 74°
m∠EPK = 16°
m∠N PM= 16°
m∠MNP = 16
m∠M = 148°
Step-by-step explanation:
If you do RSM those are the answers
There are fewer than 8 gallons of gas in the tank how do I write an inequality for that
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for a rectangular solid with length 12 in width 2 in in height 15 in state the appropriate formula for volume and also find the volume
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Margaret wants to call her friend overseas. There is a connection fee of $2 and a charge of $1.50 per minute. So the cost of the call is 2 + 1.5t dollars for t minutes.
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A vegetable farmer fills 2/3 of a wooden crate with 5/7 pound of tomatoes. How many pounds of tomatoes can fit into one crate?
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x= number of pounds of tomatoes that will fit in one crate
x=5/7 ÷ 2/3
multiply by the reciprocal
x=5/7 * 3/2
x=(5*3)/(7*2)
x=15/14
change to mixed fraction
x=1 1/14 or 1.07 pounds of tomatoes
1 1/14 pounds of tomatoes will fit in one crate.
Hope this helps! :)
what is the rate of decay, as a percent, for the following function n(x)=7(0.067)^x
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Answer: The rate of decay is 93.3%.
Step-by-step explanation:
Since we have given that
The exponential function is given by
[tex]n(x)=7(0.067)^x[/tex]
As we know the general equation of exponential function that is given by
[tex]n(x)=a(1-b)^x[/tex]
Here, a denotes the initial value
1-b denotes the rate of decay.
So, On comparing both the equations, we get that
[tex]1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933\times 100=93.3\%[/tex]
Hence, the rate of decay is 93.3%.
which relation defined by mapping diagram is a function
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The diagonals BF and CE divide the hexagon ABCDEF into two equilateral triangles and a square. Find the perimeter of the hexagon if BF = 3 cm. Answer: P = cm
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Because all the sides are the same size
Answer: The perimeter of the hexagon is 18 cm.
Step-by-step explanation: As given in the question, hexagon is shown in the attached figure.
The diagonals g and h divides the hexagon into two two equilateral triangles and one square .
Also, length of diagonal g = 3 cm.
We are to find the perimeter of hexagon.
We know that all the sides of a square are equal, so we have
length of b = length of h = length of e = length of g = 3 cm.
Since the two triangles are equilateral, so all their sides will be equal.
That is, length of a = length of f = length of g =length of c =length of d = length of h = 3 cm.
We know that the perimeter of a polygon is equal to the sum of the lengths of its sides.
Therefore, the perimeter of hexagon is given by
P = a + b + c + d + e + f = 3 + 3 + 3 + 3 + 3 + 3 = 18 cm.
Thus, the perimeter of the hexagon is 18 cm.
9ax+9b-6=21
based on the equation above what is the value of ax+b
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We add 6 to both sides. [tex]9ax+9b=27[/tex].
Now, to solve for [tex]ax+b[/tex], we factor out and divide by a 9 to get
[tex]9(ax+b)=27 \\ ax+b=3[/tex].
The value of equation ax + b is 3.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To find the value of ax + b, we need to isolate that expression on one side of the equation.
Starting with:
9ax + 9b - 6 = 21
We can add 6 to both sides:
9ax + 9b = 27
Then, we can factor out 9 from the left-hand side:
9(ax + b) = 27
Dividing both sides by 9, we get:
ax + b = 3
Therefore,
The value of equation ax + b is 3.
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Suppose that the polynomial function A(x) = - 0.0082x2 + 0.06x approximates a person's blood-alcohol level x hours after drinking 5 ounces of 80-proof whiskey. What is the person's blood-alcohol level after 3 hours?
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A(3)=-0.0082(3)²+0.06(3)
A(3)=-0.0738+0.18
A(3)=0.1062
the amount of blood-alcohol after 3 hours will be 0.1062
Five hummingbirds drink 7.5 ounces of sugar water a day. How much sugar water is needed for 14 hummingbirds?
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Each bird needs 1.5 ounces per day.
Then just multiply that by 14 to get 15.5 ounces of sugar water.
Hope this helps!
You should divide 7.5 by 5, and that equals 1.5
Then you're going to multiply 1.5 by 14 because there are 14 hummingbirds
1.5 * 14 = 21
21 ounces of sugar water is needed for 14 hummingbirds.