Which of the following sequences of transformations maps
Figure 1 to Figure 2?
90° clockwise rotation around
the origin, then a reflection
across the x-axis
90° counterclockwise rotation
around the origin, then a
reflection across the x-axis
-4
reflection across the y-axis, then
a reflection across the x-axis
reflection across the x-axis, then
a reflection across the y-axis
Answers
Answer:
First choice: 90° clockwise rotation around the origin, then a reflection across the x-axis.Explanation:
The vertices of the figure 1 are:
(-3, 2)(-4, 5)(-3, 8)(-7,5)The vertices of figure 2 are:
(2, -3)(5, -4)(8, -3)(5, -7)By simple inspection, you can tell that if you rotate the figure 1 90º clockwise and then reflect the image across the x-axys you obtain the figure 2.
You can prove that analitically.
1. Rotation 90º clockwise
A 90º clockwise reotation is the same that a 270º counterclockwise rotation and the mathematical rule for this is:
(x,y) → (y, x)Applying that rule to the vertices of figure 1, you obtain:
(-3, 2) → (2, 3)(-4, 5) → (5, 4)(-3, 8) → (8, 3)(-7,5) → (5, 7)2. Reflection across the x-axis.
A reflection across the x-axis keeps the same x-coordinate and changes the sign of the y-coordinate. The rule is:
(x,y) → (x, -y)Applying that rule to the previous points yields to:
(2, 3) → (2, -3)(5, 4) → (5, -4)(8, 3) → (8, -3)(5, 7) → (5, -7)Which are the coordinates of the figure 2. Thus, you have proved that the sequence of transformations 90° clockwise rotation around the origin, then a reflection across the x-axis (first choice) maps the figure 1 to figure 2.
Answer:
First choice: 90° clockwise rotation around the origin, then a reflection across the x-axis.
Step-by-step explanation:
Related Questions
The radius of a basketball hoop is 9 inches. Which expression can be used to find the hoop's circumference in inches?
(A)π ⋅ 9^2
(B)9/π
(C)9 ⋅ π
(D)2 ⋅ 9 ⋅ π
Answers
The right answer is Option D.
Step-by-step explanation:
Given,
Radius of basketball hoop = 9 inches
As the basketball hoop is in circular shape.
Circumference of basketball hoop = 2πr
We will put given radius = 9
Circumference of basketball hoop = 2*π*9
Circumference of basketball hoop = 2 . 9 . π
Therefore,
Circumference of basketball hoop is 2*9*π.
The right answer is Option D.
Keywords: circle, circumference
Learn more about circumference at:
brainly.com/question/10364988brainly.com/question/10435816#LearnwithBrainly
Answer:
2*9*π
Step-by-step explanation:
How do we express one-half of the
difference of a number cubed and one?
Answers
Answer:
Step-by-step explanation:
1/2 (n^3 - 1)
the difference means subtract
Step-by-step explanation:
1/2 (n^3 - 1)
I need help please and thank you
Answers
Answer:
∠3 = 114°
Step-by-step explanation:
Angle 3 is a corresponding angle to angle 7, since they are both in the southwest corner of the intersection of the transversal and the parallel lines. Corresponding angles have the same measure, so ...
∠3 = ∠7 = 114°
What is the answer for 2x3/5+1/5
Answers
Answer:
Step-by-step explanation:
2x3/5+1/5
Going by BoDMAS
Multiplication comes before addition
2x3/5+1/5 = 6/5 + 1/5 = (6+1)/5
= 7/5 = 1 2/5
Final answer:
The expression 2x3/5+1/5 is solved by first multiplying 2 by 3/5 to get 6/5 or 1.2, and then adding this to 1/5 to get the final answer of 7/5 or 1.4.
Explanation:
To solve the expression 2x3/5+1/5, you first need to perform the multiplication before the addition, according to the order of operations (PEMDAS/BODMAS). So, you need to multiply 2 by 3/5:
2 x 3/5 = 6/5 or 1.2
Now add this result to 1/5:
6/5 + 1/5 = 7/5 or 1.4
Therefore, the answer is 7/5 or 1.4.
A painter can paint 350 square feet in 1.25 hours what is the painting rate per square feet per hour
Answers
Answer:280 square feet per hour.
Step-by-step explanation:
What two fractions are equivalent to 12/27
Answers
Step-by-step explanation:
I have no answer to choose...
[tex]\dfrac{12}{27}=\dfrac{12:3}{27:3}=\dfrac{4}{9}\\\\\dfrac{12}{27}=\dfrac{12\cdot2}{27\cdot2}=\dfrac{24}{54}\\\\\dfrac{12}{27}=\dfrac{4}{9}=\dfrac{4\cdot2}{9\cdot2}=\dfrac{8}{18}\\\vdots[/tex]
You can multiply (divide) the numerator and the denominator by the same number different from 0 then the value of the fraction will not change
(you will get a fraction equal to given)
What type of function is shown above?
A. Exponential
B. absolute value
C. Polynomial
D. Step
Answers
Answer:
that would be an exponential function
Step-by-step explanation:
A triangle has a base of 4 units and a height of 3 units. Mark draws the triangle again but doubles the height. How does the area of the triangle change?
A. The area increases by 3 square units.
B. The area increases by 6 square units.
C. The area increases by 12 square units.
D. The area does not change.
Answers
Answer:the correct answer is b
Step-by-step explanation:
How do you get 3/5 of 18
Answers
Answer:
54/5
Step-by-step explanation:
(3/5)(18)=54/5
A rectangle has width that is 6 meters less than the length. The area of the rectangle is 280 square meters. Find the dimensions.
Answers
Dimensions are length 20 meter and width 14 meter
Solution:
Let "a" be the length of rectangle
Let "b" be the width of rectangle
Given that,
A rectangle has width that is 6 meters less than the length
Width = length - 6
b = a - 6
The area of the rectangle is 280 square meters
The area of the rectangle is given by formula:
[tex]Area = length \times width[/tex]
Substituting the values we get,
[tex]Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0[/tex]
Solve the above equation by quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}[/tex]
[tex]a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14[/tex]
Since, length cannot be negative, ignore a = -14
Thus solution of length is a = 20
Therefore,
width = length - 6
width = 20 - 6 = 14
Thus dimensions are length 20 meter and width 14 meter
a recipe for lemonade calls for 2 cups of sugar for every 1/2 cup of lemon juice. How many cups of sugar would be needed if you had 3 cups of lemon juice?
Answers
Answer: 12cups of sugar
Step-by-step explanation:
2cups of sugar = 1/2cup of memo
Xcups of sugar =3cups of lemon
X = 6÷ 1/2
= 12
Answer:
12 cups sugar
Step-by-step explanation:
there are a couple ways to do this...by unit rate or a proportion...
2 cups of sugar for every 1/2 cup of lemon juice
2 / (1/2) = 2 * 2 = 4.....the unit rate is 4/1....or 4 cups of sugar for every 1 cup of lemon.
so if u have 3 cups of lemon, and 1 cup of lemon = 4 cups of sugar, then 3 cups of lemon would equal (4 * 3) = 12 cups of sugar
or set it up as a proportion...
2 cups sugar to 1/2 cup lemon = x cups sugar to 3 cups lemon
2 / (1/2) = x / 3....cross multiply
(1/2)(x) = (3)(2)
1/2x = 6
x = 6 * 2
x = 12 cups sugar
either way u choose to do it will result in the same answer.
What is the common difference of 80,60,45,33.75
Answers
Answer:
they are all less than 100
What is the slope of a line passing through (3, 4) and (5, 8)?
Answers
Answer:
The slope of the two points is 2.
Answer:
2 is teh answer
Step-by-step explanation:
Y = -X + 1
Y = 3
Substitution method
Answers
Answer:
x=-2, y=3. (-2, 3).
Step-by-step explanation:
y=-x+1
y=3
----------
-x+1=3
-x=3-1
-x=2
x=-2
y=-(-2)+1
y=2+1=3
A, B, C? No explanation needed.
Answers
Answer: the answer is b
Step-by-step explanation: you said you needed none.
leah would like to earn at least $160 per month. She works at a restaurant for $5 an hour and works at an ice cream shop for $8 an hour. Leah wants to work at least 7 hours at the restaurant, and at least 10 hours at the ice cream shop.
Answers
Answer:
Leah can make more than $160 in a month if he works 7 hours for $35 and 10 hours for $80 daily or weekly.
Step-by-step explanation:
Classify each figure as a polyhedron or not a polyhedron.
Then name the figure.
person to get it right will get brainlliest
Answers
Answer:
Not a polyhedron and it's a sphere
Step-by-step explanation:
It's not a polyhedron because a polyhedron has to have faces more than 6
What is y = 4 * (0.8) ^ t
Answers
The function y = 4 * (0.8)^t is an exponential decay function, representing the decrease of a quantity over time, with y being the value at time t. To find y at any given t, substitute t into the equation and calculate the result.
Explanation:The given function y = 4 * (0.8)^t is an exponential decay function, where y represents the value of the function at time t, the number 4 is the initial value of the function when t = 0, and 0.8 is the decay factor relevant for each time unit. This type of function is often used in contexts such as radioactive decay, depreciation of value over time, or population decrease in a closed environment, where some quantity decreases by a consistent percentage over equal time intervals.
To solve for y at a given time t, simply substitute the value of t into the function and evaluate the exponential expression. It is important to use a calculator or software tool to evaluate the exponential term accurately when t is not a round number.
Ali has painting class every 20 days ria has a pottery class every 5 days they both met at the art building today. How many days will it be until they meet each other again
Answers
Answer:
4
Step-by-step explanation:
20 divided by 5 = 4
Answer:
20 days
Step-by-step explanation:
Since 20 is a multiple of 5 then the least common multiple of 5 and 20 is 20
therefore they will meet after 20 days
a coffee shop used 30% more sugar this month than last month. if the coffee shop used 728 kilograms of the sugar this month, how much did it use last month
Answers
It used 560 kilograms of sugar last month
Step-by-step explanation:
The given is:
A coffee shop used 30% more sugar this month than last monthThe coffee shop used 728 kilograms of the sugar this monthWe need to find how much it used last month
Assume that the coffee shop used x kg sugar the last month
∵ The coffee shop used x kilogram of sugar last month
∵ It used 30% more sugar this month than last month
- Find the value of 30% of x and add it to x to find how many
kilograms it used for this month
∵ 30% of x = [tex]\frac{30}{100}[/tex] × x = 0.3 x
∴ It used this month = x + 0.3 x
∴ It used this month = 1.3 x kg
∴ The coffee shop used 1.3 x kilograms of sugar this month
∵ The coffee shop used 728 kilograms of the sugar this month
- Equate 1.3 x by 728 to find x
∴ 1.3 x = 728
- Divide both sides by 1.3
∴ x = 560
It used 560 kilograms of sugar last month
Learn more:
You can learn more about the word problems in brainly.com/question/10557938
#LearnwithBrainly
Given f(x)= x-7 and g(x)=x^2 Find f(g(4)).
fo(4)) =
Answers
Good morning,
Answer:
f(g(4)) = 9
Step-by-step explanation:
f(x)= x-7
g(x)=x²
fog(x) = f(g(x)) = x² - 7
then
f(g(4)) = 4² - 7 = 16 - 7 = 9
:)
Andrew and Karleigh each run for 1 hour. Which statement explains who ran a greater distance?
Answers
Answer: The one who ran at the greater Average Speed in 1 hour ran the greater Distance.
Step-by-step explanation:
Speed (S) is the ratio of the distance (D) covered to the time (t) taken.
That is, S = D/t
Suppose Andrew ran a distance D1 in 1 hour (3600 seconds) at a Speed, say S1, we have
S1 = D1/t
We can then say he ran a distance
D1 = t × S1
= 3600S1
Similarly, let's say Karleigh ran a distance
D2 = t × S2
= 3600S2
Let us compare these two, you will notice that the bigger number between S1 and S2 is going to determine the bigger number between D1 and D2.
Let's choose random numbers for S1 and S2 for clarity, say S1 = 5, S2 = 10
D1 = 3600 × 5
= 18000
D2 = 3600 × 10
= 36000
This makes D2 bigger than D1.
I hope this is clear.
Answer:
Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of 1/10 mile per minute compared to Andrew’s 1/12 mile per minute.
Step-by-step explanation:
$37.50 decreased by 4% =
Answers
Answer:
$36
Step-by-step explanation:
The original value is $37.50 so that is 100%.
A decrease of 4% from original value means that you are finding 96% of the value, since 100% -4%= 96%
So the new value is 37.50/100 ×96= $36
This is because:
100% ----- $37.50
1% --------- $0.375
96% ------- $36
or taking 96% of original value would be
96/100 × $37.50= $36
Which would give you the same answer
Which ordered pair is a solution to the system of linear equations Negative 4 x + y = 8 and x minus 5 y = 17?
Answers
Answer:
(-3, -4).
Step-by-step explanation:
-4x + y = 8
x - 5y = 17 Multiply this by 4:
4x - 20y = 68 Add this to the first equation:
-19y = 76
y = 76/-19
y = -4.
Plug this into the second equation:
x - 5(-4) = 17
x = 17 - 20
x = -3.
CHECK this result in equation 1:
-4(-3) + -4 = 8
12 - 4 = 8
8 = 8 <------ OK.
The solution of the given system of equations is [tex]y=-4[/tex].
Important information:
[tex]-4x+y=8[/tex] ...(i)[tex]x-5y=17[/tex] ...(ii)System of equations:Multiply both sides by 5 in equation (i).
[tex]-20x+5y=40[/tex] ...(iii)
Add equation (ii) and (iii).
[tex]-19x=57[/tex]
[tex]x=\dfrac{57}{-19}[/tex]
[tex]x=-3[/tex]
Substitute [tex]x=-3[/tex] in (i).
[tex]-4(-3)+y=8[/tex]
[tex]12+y=8[/tex]
[tex]y=8-12[/tex]
[tex]y=-4[/tex]
Thus, the solution of the given system of equations is [tex]y=-4[/tex].
Find out more about 'System of equations' here:
https://brainly.com/question/13722693
x-1=2
Work out the value of 2x squared
Answers
Step-by-step explanation:
x-1=2 therefore x is 3 so 2x squared is 36
Answer:
1.22474487139
Step-by-step explanation:
x = 3
so if 2x^2 - 1 = 2
add 1 to both equations
2x^2 = 3
next, divide 2 from both sides
x^2 = 3/2
x^2 = 1.5
now find the square root of 1.5
the answer is:
1.22474487139
I got both #5 wrong can someone please help me? :(
Answers
Answer:
insted of choosing a it should have been b the < symbol is the aligator thing you learn in like 1st grade
Will give brainliest
Answers
Answer:
D
Step-by-step explanation:
95/100 is equal valent to 95℅.
What is the formula for margin of error? ME = ME = ME = ME =
Answers
Answer:
the answer is C on edgen.
Step-by-step explanation:
What is 7.5 divided by 8
Answers
Answer:
0.9375
Step-by-step explanation:
Answer:
I believe the answer to this question is: 0.94375.
What is a 1 killometers= ?
Answers
Answer:
0.62 miles
Step-by-step explanation:
ask google or siri