Given that line segments are taken to line segments of the same length during rigid transformations, which transformation maps the line segment AB onto itself?
The line is -2,1 and 4,3
A) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → x-axis reflection
B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection
C) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
D) rotation counterclockwise of 180° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
Answers
Answer:
Correct choice is C
Step-by-step explanation:
Consider segment AB with endpoints A(-2,1) and B(4,3).
1. Rotation counterclockwise of 90° has a rule
(x,y)→(-y,x),
then
A(-2,1)→C(-1,-2);B(4,3)→D(-3,4).2. x-axis reflection has a rule
(x,y)→(x,-y),
then
C(-1,-2)→E(-1,2);D(-3,4)→F(-3,-4).3. Rotation counterclockwise of 270° has a rule
(x,y)→(y,-x),
then
E(-1,2)→G(2,1);F(-3,-4)→H(-4,3).4. y-axis reflection has a rule
(x,y)→(-x,y),
then
G(2,1)→A(-2,1);H(-4,3)→B(4,3).
Answer:
C) Rotation counter-clockwise of 90 degree → x-axis reflection → rotation counter-clockwise of 270 degree → y-axis reflection
Step-by-step explanation:
We are given the line segment AB with end points (-2,1) and (4,3).
It is provided that after applying rigid transformations the line segment AB maps onto itself.
So, according to the options,
1. Rotation counter-clockwise by 90 degree changes (x, y) into (-y, x)
i.e. (-2,1) → (-1,-2) and (4,3) → (-3,4)
2. X-axis reflection changes (x, y) into (x, -y)
i.e. (-1,-2) → (-1,2) and (-3,4) → (-3,-4)
3. Rotation counter-clockwise by 270 degree changes (x,y) into (y, -x)
i.e. (-1,2) → (2,1) and (-3,-4) → (-4,3)
4. Y-axis reflection changes (x,y) into (-x,y)
i.e. (2,1) → (-2,1) and (-4,3) → (4,3)
Hence, we see that after applying transformations to AB we are again obtaining the line AB as seen below in the figure.
So, option C is correct.
Related Questions
Mark cycled 25 miles at a rate of 10 mph how long did it take Mark two cycle 25 miles?
Answers
Answer:
2.5 hours
Step-by-step explanation:
25 miles/10 mph= 2.5 hours
Answer:
The awnser is 2.5 because,
Step-by-step explanation:
.25 divided by 10 = 2.5
The decimal moves one time to the left because there is ONE zero (0) in 10.
You purchase a $220 airline ticket. You have a discount code to receive 10% off. There is a 10.5% service charge added to the total. How much do you pay for your ticket?
The only three options for answers are $231, $218.79, and $198
Answers
Mrs. Nelson is buying folding chairs that are on sale for $10. if she has $50, which inequality can be solved to show the number of chairs c she can buy?
A.) 10c≤50
B.) 10c≥50
C.) 10c>50
D.) 10c<50
Answers
Answer:
A.) 10c≤50
Step-by-step explanation:
This inequality shows less than or equal to 10 chairs can be bought with $50
Answer: A.) 10c≤50
Step-by-step explanation:
Hi, to answer this question we have to write an inequality using the information given:
Mrs. Nelson is buying folding chairs that are on sale for $10.So, if the number of chairs is "c", we can multiply "c" by $10 to obtain the cost of buying "c" number of chairs.
She only has $50, so, the cost of the chairs must be less or equal to 50.
Mathematically speaking:
10c≤50 (option A)
Feel free to ask for more if needed or if you did not understand something.
what is a number that is less that -2 4/5 and greater that -3 1/5?
Answers
Answer:
-3
Step-by-step explanation:
hm this is a little tricky!
so on a number line, -3 will be behind -2 because it is less than the two since it is negative. If we have 4/5 and 1/5 we will need to think what comes between them.
5/5 and 0/5
which means that -3 comes between them both
First and foremost, notice that because the two integers are negative, [tex]- 2\frac{4}{5}[/tex] is greater than the other number [tex]-3 \frac{1}{5}[/tex] . As just a result, a number less than [tex]- 2\frac{4}{5}= -\frac{14}{5}[/tex] and greater than [tex]- 3 \frac{1}{5}= -\frac{16}{5}[/tex] means a value between such two integers.
There could be an infinite amount of integers between any two such values. If we have two numbers a and b, then an integer [tex]\frac{ma+nb}{m + n}[/tex] where m and n are any two positive numbers exists between a and b, then we'll have a unlimited number of such number by picking a variety of m and n.Let us choose, [tex]m = 1 \ \ and\ \ n = 1[/tex] this number is [tex]\frac{a+b}{2}.[/tex] That's what we [tex]a= -\frac{14}{5}\ \ and\ \ b = -\frac{16}{5}[/tex] currently possess[tex]= \frac{-\frac{14}{5} -\frac{16}{5}}{2} =-\frac{30}{5} \times \frac{1}{2} = -\frac{15}{5}=-3[/tex] . Since [tex]\frac{ma+nb}{m + n}[/tex] all numbers m, n, a, and b are rational numbers, [tex]\frac{ma+nb}{m + n}[/tex] would only return rational numbers between a and b. In reality, there might be infinite irrational numbers between a and b which is [tex](a^m. b^n)^{\frac{1}{m+n}}[/tex].Learn more:
brainly.com/question/6782293
What is the apparent solution to the system of equations? y=−x+2y=4x+7 Graph the system of equations using the Line tool. Plot a point at the apparent solution to the system using the Point tool
Answers
Answer:
Given the system of equation:
[tex]y = -x + 2[/tex] and
[tex]y =4x+7[/tex]
Table for the equation [tex]y = -x + 2[/tex] ;
x y
-1 -3
0 2
1 1
2 0
Then, the points for this equations are: (-1, -3), (0, 2) , (1, 1 ) and (2, 0)
Also, table for the equation: [tex]y =4x+7[/tex]
x y
-1.75 0
-1 3
0 7
1 11
Then, the points for this equations are: (-1.75, 0) , (-1, 3) , (0, 7) and ( 1, 11)
Using Point tool , we plot these points of the given system of equation on the Cartesian plane.
You can see the graph as shown below in the attachment.
Also, the two lines intersects at (-1, 3)
Therefore, the apparent solution for the given system of equation is; (-1, 3)
Final answer:
To find the apparent solution to the system of equations, you need to solve the equations simultaneously. The apparent solution to the given system of equations is (-1, 3).
Explanation:
To find the apparent solution to the system of equations, we need to solve the equations simultaneously. The given equations are:
y = -x + 2
y = 4x + 7
We can solve these equations by setting them equal to each other:
-x + 2 = 4x + 7
Now, we can solve for x:
-x - 4x = 7 - 2
-5x = 5
x = -1
Substituting this value of x back into either of the original equations, we can find the corresponding value of y:
y = -(-1) + 2
y = 3
Therefore, the apparent solution to the system of equations is (-1, 3).
The formula for the volume of a pyramid is V=1/3Bh. Which of the following equations is equivalent to the given formula?
A) B=3V/h
B) B=3h/V
C) B=V-1/3/h
D) B=V+1/3/h
Answers
A) B=3V/h
Multiply both sides by 3 to get 3V=Bh. Divide both sides by h, and you get 3V/h=B
Answer:
A) B = 3V/h
Step-by-step explanation:
Given: The formula for the volume of a pyramid is V=1/3Bh.
From the above equation, we have to solve for B.
We use inverse operation to find B.
Multiply by reciprocal of 1/3 on both sides. the reciprocal of 1/3 is 3.
So, multiply by 3 on both sides, we get
3V = 3*1/3*B*h
3V = B*h
Now divide both sides by h, we get
3V/h = Bh/h
3V/h = B
Therefore, the answer is A) B = 3V/h
please help | A department store buys 400 shirts at a cost of $6,400 and sells them at a selling price of $20 each. Find the percent markup.
Answers
The department store's percent markup on the shirts is 25%. This was determined by dividing the markup price by the cost price and then multiplying by 100.
Explanation:The question asks to find the percent markup of shirts by a department store. First, we need to determine the cost per shirt, which we do by dividing the total cost by the number of shirts. In this case, $6,400 divided by 400 gives us a cost of $16 per shirt.
Next, we subtract the cost from the selling price to find out the markup per shirt. So, $20 (selling price) minus $16 (cost price) gives us a markup of $4 per shirt.
To find the percent markup, we divide the markup by the cost price and multiply by 100. Hence, $4 (markup price) divided by $16 (cost price), and then multiplied by 100, results in a 25% markup.
Learn more about Percent Markup here:https://brainly.com/question/31776242
#SPJ12
Convert 2 3/8 into a decimal
Answers
Answer:
The Answer is 2.25
Answer:
2.375 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
2 3/8 = 2.375
divide 3 by 8 and you will get the .375
The whole number of 2 will be to the left of the decimal to represent a whole number.
5. Grayson a green number cube and a white number cube. the faces of the cubes are number 1 through 6. Graysen roll each cube one time. What is the probability that the green cube will land with an even number face up and the white cube will land with a number greater than 2 face up?
A.1/9
B.1/36
C.1/3
D.1/6
Answers
Answer: P(G even and W>2) = 1/3 or 0.333 or 33.3%
Step-by-step explanation:
Independent events multiply probabilities,
P(G even)=1/2, P(W>2)=2/3, P(G even and W>2)= 1/2 × 2/3 = 1/3.
Without using definition of "independent events", or rules referring to them, I use sample space S of 36 points, and P(event) = #(event)/#(sample space).
Points are labeled with two digits, left is green die, right is white die. S = {11,12,13,14,15,16,21,...26,...,61,...,66}, and #(S)=36.
An event E is a subset of S, and
0 <= #(E) <= #(S) = 36.
Event G even is GE={21,22,23...,41,42,...,61,...,66},
#(G even)=18
Event "W>2" = W2 ={13,14,15,16,23,24...,63,64,65,66},
#(W>2)=24.
Event G even and W>2 GEW2={23,24,25,26,43,44,45,46,63,64,65,66),
#(GEW2)=12
P(GEW2)=#(GEW2)/#(S)=12/36=1/3=33.3%
To find the probability of the green cube landing with an even number face up and the white cube landing with a number greater than 2 face up, multiply the probabilities of each event happening. The probability is 1/3.
Explanation:To find the probability that the green cube will land with an even number face up and the white cube will land with a number greater than 2 face up, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The green cube has 3 even numbers (2, 4, and 6) out of 6 faces, so the probability of the green cube landing with an even number face up is 3/6 or 1/2.
The white cube has 4 numbers greater than 2 (3, 4, 5, and 6) out of 6 faces, so the probability of the white cube landing with a number greater than 2 face up is 4/6 or 2/3.
To find the probability of both events happening, we multiply the probabilities: (1/2) * (2/3) = 1/3.
Therefore, the probability that the green cube will land with an even number face up and the white cube will land with a number greater than 2 face up is 1/3. Option C, 1/3, is the correct answer.
help me please i keep getting stuck on this question
Answers
Answer:
-3 <= x <=8
Step-by-step explanation:
-16 -3|2x-5| >= -49
The first step is to get the absolute value alone. We need to add 16 to each side.
-16+16 -3|2x-5| >= -49+16
-3|2x-5| >= -33
Now divide each side by -3. This will flip the inequality.
(-3/-3)|2x-5| =< -33/-3
|2x-5| =< 11
This is where we can separate the absolute value inequality into 2 pieces, one positive and one negative. Remember to flip the inequality symbol when we take the negative inequality.
2x-5 <=11 and 2x-5>=-11
Add 5 to each side.
2x-5+5 <=11+5 and 2x-5+5>=-11+5
2x<=16 and 2x>=-6
Divide by 2 on each side.
2x/2<=16/2 and 2x/2>=-6/2
x <=8 and x >=-3
Rewrite as a compound inequality
-3 <= x <=8
What is 1.67 × 104 in standard form?
A) 1,670,000
B) 16,700
C) 0.1670
D) 0.0167
Answers
Answer:
B is the answer
Step-by-step explanation: B is the answer because 10^4 is 10*10*10*10 which is 10000 so 10000 times 1.67 is 16700
Jin spent 32 hours on math and language arts homework last month. She spent about 30% of this total time on math. About how many hours were spent on math?
Answers
Answer: 9.6
Step-by-step explanation: A percent is like a decimal so 15% would be 0.15 so if you use that for this you must multiply 32 hours by the 30%/0.30 to find the answer
Twenty-five subtracted from one-half a number is 10.What is the number?
Answers
Answer:
70
Step-by-step explanation:
The simplest way to find the number is work backwards. If you know the final answer is 10, start with 10 and make the number x. Then set up the original equation.
0.5x-25=10
Then start working backwards(isolate).
0.5x-25=10
+25 +25
in other words, 10+25=0.5x. (the 25 cancels out because -25+25=0)
10+25=35, so 35=0.5x.
Now, instead of dividing by 2, multiply by 2(opposite again).
35=0.5x
/0.5(aka *2) /0.5(cancels out)
now you are left with 70=x, so the number is 70.
Azul orders 5 veggie pizzas for his birthday party.he orders enoghe for every one to eat 5/6 of the pizza hpw many people can he feed
Answers
Answer:
He can feed 5 people
Step-by-step explanation:
divide pizzas in the number of people to how much people will eat.
divide 5 by invisible number, x. getting the answer of 5/6
x=6
Answer:6
Step-by-step explanation:
You can walk 1 3/4 miles in 1/2 hour. What’s your average speed?
Answers
Answer:
avg speed is 3.5 miles per hour
Step-by-step explanation:
1.75 x 2 = 3.5 miles per hour
Answer:
3 and 1/2
Step-by-step explanation:
hope this helps
HELP! solving systems of equations by substituting (find x and y)
Answers
Answer:
First solve for x or y in the first equation. Then substitute that number in the second equation for its same variable. Solve the second equation for that variable. Now you have your first number. Now you want to take that number and substitute it back into the first equation to find your second value. Put your two values in an ordered pair (x, y)
Step-by-step explanation:
A community center is going on a trip to Philadelphia via several buses. The ratio of men to women to children is 1:2:3. If there are 150 people going on the trip, how many men are going? How many women are going? How many children are going? Show the steps you use to solve the problem
Answers
1x+2x+3x=150.
6x=150
6x/6=150/6
x=30
1x=1×30=30 | 30 men
2x=2×30=60 | 60 women
3x=3×30=90 | 90 children
6=to the total ratio of people going for the trip.
men=1/6
women=2/6
children=3/6
6/6=150 people
1/6=?
1/6*150*6/6=25men.
6/6=150
2/6=?
2/6*150*6/6=50women.
6/6=150
3/6=?
3/6*150*6/6=75children
Which models can be used to solve the problem
Answers
Answer:
The answer is C. 0.60b + 0.30w = 150; 60 + 0.30w = 150
Step-by-step explanation:
find the x and y-intercept of the line -6x+12y=24
Answers
[tex]-6x+12y=24\\\\x-intercept\ for\ y=0:\\\\-6x+12(0)=24\\-6x=24\qquad\text{divide both sides by (-6)}\\\boxed{x=-4}\to(-4,\ 0)\\\\y-intercept\ for\ x=0:\\\\-6(0)+12y=24\\12y=24\qquad\text{divide both sides by 12}\\\boxed{y=2}\to(0;\ 2)[/tex]
really confused and am on final attempt!
Answers
Answer:
C
Step-by-step explanation:
the legs of a 30-60-90 triangle are 1 and [tex]\sqrt{3}[/tex], while the hypotenuse is 2.
the ratio of the legs is therefore 1 : [tex]\sqrt{3}[/tex] → C
12. A pack of cinnamon-scented pencils sells for $4.00. What is the sales tax rate if the total cost of the pencils is $4.32?
13. How can you solve problems involving percents?
Answers
Answer:
12) tax rate is 8%
13) convert percent to decimal format
Step-by-step explanation:
12) 4.32/4.00 = 1.08
1.08 - 1 = 0.08
0.08 * 100 = 8%
13) Convert all % to decimal format.
Do this by dividing the percent by 100
e.g. 10% = 10/100 = 0.10
Factor the expression using the GCF.
21a squared b to the 5th power + 49a to the 4th power b cubed
Answers
[tex]21a^2b^5+49a^4b^3=(7a^2b^3)(3b^2)+(7a^2b^3)(7a^2)=7a^2b^3(3b^2+7a^2)[/tex]
Area of a rectangle is 540 sq m. If the length was reduced by 5m and the width was increased by 5m, the are of the rectangle will be increased 35 sq m. Calculate the length and the width of the first rectangle
Answers
[tex]l-length\\w-width\\\\\text{The formula of an area of a rectangle:}\ V=lw\\\\\text{We have the area}\ 540\ m^2\to lw=540\\\\\text{New rectangle}\\\\l-5-length\\w+5-width\\\\\text{We have the area}\ 540\ m^2+35\ m^2=575\ m^2\to (l-5)(w+5)=575\\\\\text{Therefore we have the system of equation:}\\\\\left\{\begin{array}{ccc}lw=540&\to w=\dfrac{540}{l}&(*)\\(l-5)(w+5)=575&&(**)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**)[/tex]
[tex](l-5)\left(\dfrac{540}{l}+5\right)=575\qquad\text{use distributive property}\\\\(l)\left(\dfrac{540}{l}\right)+(5)(l)-(5)\left(\dfrac{540}{l}\right)-(5)(5)=575\\\\540+5l-\dfrac{2700}{l}-25=575\\\\515+5l-\dfrac{2700}{l}=575\qquad\text{subtract 575 from both sides}\\\\-60+5l-\dfrac{2700}{l}=0\qquad\text{multiply both sides by }\ l\neq0\\\\-60l+5l^2-2700=0\\\\5l^2-60l-2700=0\qquad\text{divide both sides by 5}\\\\l^2-12l-540=0\\\\l^2+30l-18l-540=0\\\\l(l+30)-18(l+30)=0\\\\(l+30)(l-18)=0\iff l+30=0\ \vee\ l-18=0\\\\l=-30<0\ \vee\ \boxed{l=18\ cm}[/tex]
[tex]\text{Substitute the value of}\ l\ \text{to}\ (*):\\\\w=\dfrac{540}{18}\\\\\boxed{w=30\ cm}[/tex]
[tex]Answer:\ \boxed{length=18\ cm,\ width=30\ cm}[/tex]
The original dimensions of the rectangle are 30 meters in length and 18 meters in width.
We need to find the dimensions of the original rectangle given an area of 540 sq m and the changes in area after altering the dimensions. Let's represent the length of the rectangle as L meters and the width as W meters.
From the information provided:
Original Area: L * W = 540
New Area: (L - 5) * (W + 5) = 540 + 35
By solving these equations step-by-step:
L * W = 540
(L - 5)(W + 5) = 575
LW + 5L - 5W - 25 = 575
LW - 5(W - L) - 25 = 575
Substitute the original area (LW = 540):
540 - 5(W - L) - 25 = 575
-5(W - L) = 60
W - L = -12
Now we have two simultaneous equations:
L * W = 540
W - L = -12
We can solve these equations for L and W.
Solving the system of equations, we get:
L = 30 meters
W = 18 meters
Therefore, the original dimensions of the rectangle are 30 meters in length and 18 meters in width.
Stuck at this question I need in 5 mins! Need it ASAP
Answers
Answer:
64 plants/32 seed packets =
2 plants/seed packet
90 plants ÷ 2 plants/seed packet =
45 seed packets
Eduardo piensa en un número entre 1 y 20 que tiene exactamente 5 factores. ¿En qué número está pensando?
Answers
Answer:
Hola,
1, 2, 4, 5, 10, 20
Step-by-step explanation:
How do you simplify that?
Answers
Hey there!
You could solve those equations many ways but, here's a more "Easier way" to solve that
[tex]3^3[/tex]= [tex]3(3)(3)[/tex][tex]3(3) = 9,right?[/tex][tex]9(3) = 27,right?[/tex]Therefore: [tex]\boxed{Answer: 27}[/tex]Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
An item has a listed price of $45.If the sales tax rate is 5%,how much is the sales tax (in dollars)?
Answers
Answer:
sales tax = 2.25
Step-by-step explanation:
To find the sales tax, we multiply the list price by the tax rate
We need to convert the tax rate of 5% to decimal form 5% = .05
sales tax = 45 * .05
sales tax = 2.25
a factory makes parts for toys in different quantities,as shown in the table. how much would 11 parts costs
Answers
Based on the given table, the cost for 11 parts would be approximately $4.95.
How to determine the cost for 11 parts
To determine the cost for 11 parts, find the corresponding cost per part from the given table.
Let's analyze the given data:
Number of parts: 2, 7, 12, 15
Cost ($): 0.90, 3.15, 5.40, 6.75
We can observe that the cost per part increases as the number of parts increases.
To calculate the cost for 11 parts, interpolate between the quantities given in the table.
Using linear interpolation, find the cost for 11 parts as follows:
First, determine the cost per part for 7 parts and 12 parts:
Cost for 7 parts = $3.15
Cost for 12 parts = $5.40
To find the cost for 11 parts, interpolate between these two values:
Cost for 11 parts ≈ Cost for 7 parts + [11 - 7] / [12 - 7] * (Cost for 12 parts - Cost for 7 parts)
Cost for 11 parts ≈ $3.15 + [11 - 7] / [12 - 7] * ($5.40 - $3.15)
Calculating this expression:
Cost for 11 parts ≈ $3.15 + 4/5 * ($5.40 - $3.15)
Cost for 11 parts ≈ $3.15 + 4/5 * $2.25
Cost for 11 parts ≈ $3.15 + $1.80
Cost for 11 parts ≈ $4.95
Therefore, the cost for 11 parts would be approximately $4.95.
A factory makes parts for toys in different quantities, as shown in the table. how much would 11 parts costs
number of parts: 2, 7, 12, 15
cost($): 0.90, 3.15, 5.40, 6.75
Connor has $9.00 in dimes and quarters. If he has twice as many quaters as dimes, how many of each coin does he have?
Answers
Hi There!
Answer:
30 quaters.
15 dimes.
Step-by-step explanation:
Quarter = $0.25
Dime = $0.10
Quarters: 0.25 * 30 = $7.50
Dimes: 0.10 * 15 = $1.50
Check: 7.50 + 1.50 = $9
Hope This Helps :)
[tex]0.1d+(0.25)2d=9[/tex]
This says that dimes(0.1 dollars) and twice as many dimes(quarters so 0.25) is 9 dollars. So it is
[tex]0.1d+0.5d=9[/tex]
Combining we get
[tex]0.6d = 9[/tex]
Dividing by 0.6 we get
[tex]d=15[/tex]
Since there are twice as many quarters as dimes, the answer is 15 dimes and 30 quarters.
list the integers that satisfy both these inequalities.
2x + 9 < 0
x > -12
put the answers on one line.
Answers
Answer: -12 < x < [tex]-\frac{9}{2}[/tex]
Step-by-step explanation:
2x + 9 < 0 and x > -12
2x < -9
x < [tex]-\frac{9}{2}[/tex]
Since it is an "and" statement, x is between -12 and [tex]-\frac{9}{2}[/tex], so -12 < x < [tex]-\frac{9}{2}[/tex]
Graph: -12 o-----------------o [tex]-\frac{9}{2}[/tex]
Interval Notation: (-12, [tex]-\frac{9}{2}[/tex])
The integers that satisfy the inequalities 2x + 9 < 0 and x > -12 are -11, -10, -9, -8, -7, -6, and -5.
To find integers that satisfy both inequalities 2x + 9 < 0 and x > -12, we first solve each inequality separately.
For the inequality 2x + 9 < 0, we subtract 9 from each side to get 2x < -9. Then we divide each side by 2 to find x < -4.5. Since we are looking for integers, x must be less than or equal to -5.
For the inequality x > -12, since x must be greater than -12 and is an integer, the least integer x can be is -11.
Putting these together, the integers that satisfy both inequalities are the set of all integers from -11 through -5. Therefore, we list the integers on one line as: -11, -10, -9, -8, -7, -6, -5.