The direction angle of the vector with initial point (1, -1) and terminal point (7, 2) is approximately 26.57 degrees, found by calculating the arctangent of the ratio of the y and x components of the vector.
The direction angle of the vector v is the angle it makes with the positive x-axis, measured counterclockwise.
To find this angle, we need to calculate the difference between the y-coordinates and x-coordinates of the terminal and initial points of the vector, respectively. Then, we can use the arctangent function to find the angle.
Let's first find the components of the vector v
v = <7 - 1, 2 - (-1)> = <6, 3>
Now, we can find the direction angle as follows
θ = arctan(3/6)
θ = 0.4636 radians (in decimal form)
To convert this to degrees, we can multiply by 180/π
θ ≈ 26.57°
Therefore, the direction angle of the vector v is approximately 26.57 degrees.
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The question is on the image when u get the answer get back to me asap
Answer:
Step-by-step explanation:
y=-2x+2
Solve for x, y and z
2x – y + 3z = 10
x + 3y – 2z = 5
3x – 2y + 4z = 12
Answer:
Given system of linear equations are
2x+3y+3z=5
x−2y+z=−4
3x−y−2z=3.
Represent it in matrix form
⎣
⎢
⎢
⎡
2
1
3
3
−2
−1
3
1
−2
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
−4
3
⎦
⎥
⎥
⎤
which is in the form of AX=B
A=
⎣
⎢
⎢
⎡
2
1
3
3
−2
−1
3
1
−2
⎦
⎥
⎥
⎤
∣A∣=10+15+15=40
=0
∴ A
−1
exists
To find adjoint of A
A
11
=5,A
12
=5,A
13
=5
A
21
=3,A
22
=−13,A
23
=11
A
31
=9,A
32
=1,A
33
=−7
Adj(A)=co-factor
⎣
⎢
⎢
⎡
5
3
9
5
−13
1
5
11
−7
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
A
−1
=
∣A∣
1
Adj(A)
=
40
1
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
X=A
−1
B
=
40
1
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
5
−4
3
⎦
⎥
⎥
⎤
X=
40
1
⎣
⎢
⎢
⎡
25−12+27
25+52+3
25−44−21
⎦
⎥
⎥
⎤
X=
40
1
⎣
⎢
⎢
⎡
40
80
−40
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1
2
−1
⎦
⎥
⎥
⎤
Hence, x=1,y=2 and z=−1
The solution to the system of equations is
x = 3
y = 2
z = 2
How to solve the simultaneous linear equation?To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.
First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:
(3) (2x – y + 3z = 10)
6x – 3y + 9z = 30
(1) (x + 3y – 2z = 5)
x + 3y – 2z = 5
Adding the two equations gives:
7x + 7z = 35
Simplifying, we get
x + z = 5 (Equation 1)
Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:
(2) (x + 3y – 2z = 5)
2x + 6y – 4z = 10
(3) (3x – 2y + 4z = 12)
9x – 6y + 12z = 36
Adding the two equations gives:
11x + 8z = 46
Substituting x + z = 5 from Equation 1 into the above equation, we get:
11(x + z) + 8z = 46
11x + 19z = 46
Solving for z, we get:
z = 2
Substituting z = 2 into x + z = 5 from Equation 1, we get:
x + 2 = 5
x = 3
Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:
2x – y + 3z = 10
2(3) – y + 3(2) = 10
6 – y + 6 = 10
y = 2
Therefore, the solution to the system of equations is:
x = 3
y = 2
z = 2
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can you please help me with the answer?
The dimension is gioven as 69.26 feet
How to solve for the dimensionxy = 1836
This is the area
The cost of fence = 2x + 2y
cost of interior fencing
2x + 4y
C = 20.40(C1) + 12.00(C2)
We have to put the vakues in the formula above
C = 20.40(2x + 2y) + 12.00(2x + 4y)
= 40.80x + 40.80y + 24.00x + 48.00y
= 64.80x + 88.80y
from xy = 1836
y = 1836 / x
We have to put the value in C
C = 64.80x + 88.80(1836/x)
= 64.80x + 164236.80/x
Take the deriveative with respect to x
64.80 - 164236.80/x^2 = 0
x = √(164236.80/64.80)
= 69.26 feet
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How knows how do this help me please
Answer:
Step-by-step explanation:
Which set of ordered pairs gives the polygon shown?
(-4.2), (-4, -5), (1.5, -5), (1.5, 2)
(1.5, 2), (1.5, -4.5), (-4.5, -4), (2, -4)
(-4, -4.5), (-4.5, 1.5), (1.5, 2), (-4, 2)
(1.5, -4.5), (-4, -4.5), (-4, 2), (1.5, 2)
The points of the polygon are:
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
Option D is the correct answer.
We have,
From the coordinate plane,
There are 4 points that form the polygon,
The points are all in ordered pairs.
So,
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
Thus,
The points of the polygon are:
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
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The answer…………………..:
Answer:
what?
Step-by-step explanation:
Abby is collecting data for her science fair project about nutrition. She gathers data about the number of grams of fat and the number of calories in a serving of fruit.
Describe patterns in the data
There is no association between the number of fat grams and the number of calories because there are no outliers or clusters.
What does no association mean ?To make this clear, when we claim that there is no correlation between two variables, it indicates a lack of comprehensible patterns or connections. Put another way, adjustments in one factor do not seem to impact the other.
In relation to the inquiry at hand, if fat grams and calorie figures have no notable outliers or groupings, there might be an inference that these two variables are not related.
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Solve the equation and check your solution. 5 t = 7 and one-half Multiply 5t by 5; the answer is 7 and one-half. Divide 5t by 5; the answer is 7 and one-half. Divide both sides by 5; the answer is 1 and one-half. Multiply both sides by 5; the answer is 37 and one-half.
Answer: the answer is 13 and one-half
Step-by-step explanation:
C
Step-by-step explanation:
The table shows the distribution, by age and gender, of the million people in a certain region who live alone. Use the data in the table to find the probability that a randomly selected person in the region is a woman in the 1824 age range living alone.
The probability that a randomly selected person in the region is a woman in the 18-24 age range living alone is approximately 0.14 or 14%.
To find the probability that a randomly selected person in the region is a woman in the 18-24 age range living alone, we need to look at the intersection of the "Female" row and the "0-24" age column in the table.
The probability of selecting a woman in the 18-24 age range living alone is:
P(woman, 18-24, living alone) = (Number of women in the 18-24 age range living alone) / (Total number of people living alone)
From the table, we can see that the number of women in the 18-24 age range living alone is 20.9. The total number of people living alone is 153.6.
P(woman, 18-24, living alone) = 20.9 / 153.6
P(woman, 18-24, living alone) = 0.1362 or approximately 0.14
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The complete question:
The table shows the distribution, by age and gender, of the million people in a certain region who live alone. Use the data in the table to find the probability that a randomly selected person in the region is a woman in the 1824 age range living alone. Age |0-24|25-49|50+ |Total
Male|21.9|25.3 |28.6|75.8
Fem |20.9|26.1 |30.8|77.8
Tot |42.8|51.4 |59.4|153.6
A plane is heading due east with a ground speed of 398 mph. A 50-mph wind is blowing at a bearing 48 degrees. Find the planes resulting speed.
if u were to flip a coin 15 times how many times will the coin land on tails
help me please fr i just need these questions
a) The base area of the cylinder is given as follows: 78.54 ft².
b) The height of the cylinder is given as follows: 2 ft.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The base area is given as follows:
Ab = πr².
Considering the radius of 5 ft, the base area is of:
Ab = 3.1416 x 5²
Ab = 78.54 ft².
Considering the volume of 157.08 ft³, the height of the cylinder is obtained as follows:
78.54h = 157.08
h = 157.08/78.54
h = 2 ft.
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Jake just learned to identify the difference between an oak tree and a
maple tree. He was curious about the concentration of these trees in his
neighborhood, so he went out and identified several trees that were either
by the pond or in the field.
Unfortunately, he smudged his data tables and can't read some of the
values. The absolute and relative frequency tables below show Jake's
salvaged data. Can you help him figure out the rest?
Fill in the missing values from each table.
The value of row total of the column total's is 165.
The value of row total of field is 91
How to calculate the valueColumn total of maple can be found by:
(46.32 /100) * y =44
Or y = (44 *100)/46.32
Or y = 94.991 =95 (approx)
Now we get value of field under maple by
Value of field under maple = (column total - value of pond under maple) = (95 - 44) = 51
Value of row total of the column total's = (column total of oak + column total of maple = (70 + 95) = 165 (total data)
Value of row total of field = ( value of field under oak + value of field under maple) = (40 + 51) = 91
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Graph with x axis labeled Quantity Demanded and numbered in hundreds, 100 to 500. Y axis is Price, with prices 0 to 6. A line representing the Demand Curve starts at 100, 5 and drops at an angle down to 500, 1. Solid lines extend upward from the x axis to the green line at points 100, 5, 200, 4, 300, 3, 400, 2, and 500, 1. Public Domain Based on the graph, how is quantity demanded related to price? (5 points) Quantity demanded decreases as price decreases. Quantity demanded is equal to the product's price. Quantity demanded decreases as price increases. Quantity demanded increases as price increases.
Based on the information, the correct information regarding the graph is that C. Quantity demanded decreases as price increase.
How to explain the graphThe graph shows that for every increase of 100 units of the goods demanded, price reduces by 1 unit.
When 500 units was demanded, the price was at 1. Therefore, if 550 units are demanded, the price will reduce by half, which means the price would drop to 0.5.
The price would drop to 0.5. In this case, the the correct information regarding the graph is that Quantity demanded decreases as price increase.
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Find the magnitude and direction angle for each vector. Give the measure of the direction angle as an angle in [0,360]
Answer:
(b) 10; 150°
Step-by-step explanation:
You want the polar coordinate equivalent of (-5√3, -5).
ConversionThe polar form of (a, b) is ...
(a, b) = (r; θ)
where ...
r = √(a² +b²)
θ = arctan(b/a) . . . . . with attention paid to quadrant
ApplicationFor the given values, the polar form is ...
r = √((-5√3)² +5²) = √(75 +25) = 10
θ = arctan(5/(-5√3)) = arctan(-1/√3) = 150°
The angle is a quadrant II angle with a reference angle of 30°.
The polar form is (10; 150°).
__
Additional comment
Some calculators will do the coordinate conversion based on a vector or ordered pair. Others require the coordinates of the point to be expressed as a complex number, as in the attachment. (Note the calculator mode is set to DEGrees.)
Please answer asap!! what is the equation that best models the data from the table after the data has been linearized?
The equation that best models the data from the table after the data has been linearized is y=294755 * 1.21728^x. This equation follows an exponental model.
When is the exponential model best used for an equation?Looking at the data, it is very evident that it is not increasing linearly but rather exponentially.
An exponential equation has the general pattern of formula which y = ab^x, where a is the main value and b is the growth factr.
The question below is as seen in the picture, and the above answer is dependent on it.
What is the equation that best models the data from the table after the data has been linearized?
X y
2 4.4
7 18.2
13 120.0
19 715.4
22 1,768.3
26 5,775.9
30 10.508.5
(1 point)
logy=0.12502x+0.427231
y=1,350 76x+1,350.76
y=294755 * 1.21728^x
y=5,927 281og x-3,880 59
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Assume that the speed of automobiles on an expressway during rush hour is normally distributed with mean of 62 mph and a standard deviation of 5 mph.
What percent of cars are traveling slower than 62 mph?
Write your percentage as a decimal (so 12% = 0.12)!
The percentage of cars traveling slower than 62 mph during rush hour is 0.5 or 50%.
Since the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 62 mph and a standard deviation of 5 mph, we can use the cumulative distribution function (CDF) of the normal distribution to find the percentage of cars traveling slower than 62 mph.
Let X be the speed of an automobile on the expressway during rush hour. Then, X follows a normal distribution with mean (µ) = 62 mph and standard deviation (σ) = 5 mph.
We want to find P(X < 62), which represents the probability that a car is traveling slower than 62 mph.
Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find the z-score corresponding to the value X = 62, using the formula;
z = (X - µ) / σ
Plugging in the given values;
z = (62 - 62) / 5 = 0
Now, we can find the cumulative distribution function (CDF) of the standard normal distribution at z = 0, denoted as Φ(0), which represents the probability that a standard normal random variable is less than or equal to 0.
Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find Φ(0) to be approximately 0.5.
So, P(X < 62) = Φ(0)
= 0.5
Therefore, the percentage of car is 0.5 or 50%
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Find s(t), where s(t) represents the position function, v(t) represents the velocity function, and a(t) represents the acceleration function.a(t)= -30t+6, with v(0)=8 and s(0)=2
The position function is s(t) = -5t³ + 3t² + 8t + 2.
We have,
To find s(t), we need to integrate the velocity function v(t) since velocity is the rate of change of position with respect to time.
To do this, we need to first find the velocity function v(t) by integrating the acceleration function a(t):
a(t) = -30t + 6
Integrating with respect to t, we get:
v(t) = -15t² + 6t + C1
We are given that v(0) = 8, so we can use this to solve for the constant C1:
v(0) = -15(0)² + 6(0) + C1 = C1
C1 = 8
Now we have the velocity function:
v(t) = -15t² + 6t + 8
To find s(t), we need to integrate v(t) with respect to t:
s(t) = -5t³ + 3t² + 8t + C2
We are given that s(0) = 2, so we can use this to solve for the constant C2:
s(0) = -5(0)³ + 3(0)² + 8(0) + C2 = C2
C2 = 2
Now we have the position function:
s(t) = -5t³ + 3t² + 8t + 2
Therefore,
The position function is s(t) = -5t³ + 3t² + 8t + 2.
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Please help!!!!! I am in need of it, this is for math nation unit 1 and im failing!!!!!!!
Answer:
5
Step-by-step explanation:
use the table, when it asks f(2) that says what is the output *y) when the input is 2. Find when x=2 your answer is the y value, f(2)=5
dude what is this i dont understand
Answer:
g(1) = 1
Step-by-step explanation:
the absolute value function always gives a positive result, that is
| - a | = | a | = a
to evaluate g(1) substitute x = 1 into g(x)
g(1) = - 3| 1 - 2| + 4
= - 3| - 1| + 4
= - 3(1) + 4
= - 3 + 4
= 1
opic: Choosing ping-pong balls without replacement.
There are 6 white and 3 orange ping-pong balls in a brown paper bag. Two balls are randomly chosen.
Enter your answers as fractions. They do not need to be reduced.
(The "Preview" simply displays your answer in nice mathematical text.
It does not mean that your answer is either right or wrong.)
a) How many total balls are in the bag at the start?
b) What is the probability that the 1st ball is orange?
P(1st = orange) =
c) What is the probability that the 2nd ball is also orange, given that the 1st ball was orange?
P(2nd = orange | 1st = orange) =
d) What is the probability that both the 1st and the 2nd balls are orange
a) The total number of balls in a bag is 9.
b) The probability that the first ball chosen is orange is 1/3.
c) The probability that the 2nd ball is also orange is 1/4.
d) The probability that both balls are orange is 1/12.
Given that:
Balls, White = 6 and Orange = 3
a) The total of ping-pong balls in the bag at the start is calculated as,
Total ball = 6 + 3
Total ball = 9
b) The probability that the first ball chosen is orange is calculated as,
P(Orange) = 3/9
P(Orange) = 1/3
c) There will be 8 balls in the bag, of which 2 are orange if the first ball selected was an orange ball. Then the probability is calculated as,
P(Orange) = 2/8
P(Orange) = 1/4
d) The product rule of probability may be used to determine the likelihood that the first and second balls are both orange:
P(Orange and Orange) = 1/3 x 1/4
P(Orange and Orange) = 1/12
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Find the equation of a line that passes through the point ( 4 , 2 ) that is perpendicular to the line y = 4 3 x . Show your work.
The equation of the line that passes through the point (4, 2) and is perpendicular to the line y = 43x is y = (-1/43)x + (90/43).
What is the equation of a line that passes through the point ( 4 , 2 ) that is perpendicular to the line y = 43x?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given that the line has a slope of 43.
To find the slope of the line perpendicular to it, we use the fact that the product of the slopes of two perpendicular lines is -1.
So, the slope of the perpendicular line is -1/43.
Using the point-slope form of a line, we can write the equation of the line as:
y - y1 = m(x - x1),
where (x1, y1) = (4, 2) and m = -1/43
Plugging in the values, we get:
y - 2 = (-1/43)(x - 4)
y - 2 = (-1/43)x + (4/43)
y = (-1/43)x + (4/43) + 2
y = (-1/43)x + (90/43)
Therefore, the equation of the line is y = (-1/43)x + (90/43).
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Find the average of 327 and 827
Answer:
577
Step-by-Step Explanation:
577 is right between 327 and 827.
327+827=1,154
1,154/2=577
the function h is defined by the following rule. h(x)=4x+5 complete the function table
For the function h(x) the values of h(x) when x=0,1,2,3,4,5 are 5, 9, 13,17,21,25 respectively
The given function is h(x) 4x+5
h of x equal to four times of x plus five
We have to find the values of h(x) for different values of x
x=0, h(x) = 5
x=1, h(x)=9
x=2, h(x)=13
x=3, h(x)=17
x=4, h(x)=21
x=5, h(x)=25
Hence, for the function h(x) the values of h(x) when x=0,1,2,3,4,5 are 5, 9, 13,17,21,25 respectively
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1) Consider the quadratic function: f (x) = (x + 3)2 – 2 and a function, g(x), which is created by translating
f (x) three units to the right, two units up, and reflected vertically over the x-axis. Complete the following tasks:
a) 15 points: Graph f (x) on the axes below and label it. Graph g(x) on the axes below and label it.
10 points: Write the vertex form equation for g(x) below.
A graph of f(x) is shown in the image below.
A graph of f(x) is shown in the image below.
The vertex form equation for g(x) is g(x) = -x²
What is a translation?In Mathematics and Geometry, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
Since the parent function is f(x)= (x + 3)² - 2, g(x) would be created by translating f(x) three units to the right, two units up, and reflected vertically over the x-axis as follows;
f(x) = (x + 3)² - 2
g(x) = -[(x + 3 - 3)² - 2 + 2]
g(x) = -x²
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A marble is selected at random from a jar containing 10 red marbles, 50 yellow marbles, and 40 green marbles. Find the theoretical probability that it is
either red or green.
P(red or green) = (Type an integer or a simplified fraction.)
Answer:0.5.
Step-by-step explanation:
Answer:
0.5
Step-by-step explanation:
hope this helps
Factor each polynomial function. Based on these factors, which polynomial’s graph crosses the x-axis at only one point? A. f ( x ) = x 3 − 7 x 2 + 3 x − 21 B. f ( x ) = x 3 − 3 x 2 − 4 x + 12 C. f ( x ) = x 3 + 2 x 2 − 9 x − 18 D. f ( x ) = x 3 − 2 x 2 − 16 x + 32
Based on these factors, the polynomial that graph crosses the x-axis at only one point is A. f ( x ) = x ³ − 7 x² + 3 x − 21
What is a polynomial?A polynomial in mathematics is a mathematical statement made up of variables (also known as indeterminates) and coefficients that only include the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
Polynomials are a fundamental algebra topic that is used in many areas of mathematics. A polynomial's degree is the largest exponent of the variable x in the expression. The correct option is A.
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The Downtown Community Barbecue served 404 dinners. A child's plate cost $2.80 and an adult's plate cost $6.90. A total of $1,963.50 was collected. How many of each type of plate was served? Round answers to the nearest whole person.
The number of childs plate are 201 and adult's plate are 203.
Let's use C to represent the number of child plates and A to represent the number of adult plates.
We know that a child's plate costs $2.80 and an adult's plate costs $6.90.
Therefore, we can write two equations based on the information given:
The total number of plates served is 404
C + A = 404 ...(1)
C=404-A
The total amount collected is $1,963.50
2.8C + 6.9A = 1963.5 ..(2)
2.8(404-A)+6.9A= 1963.5
1131.2 - 2.8A +6.9A=1963.5
4.1 A =1963.5 -1131.2
4.1A=832.3
Divide both sides by 4.1
A=832.3/4.1
A=203
Now put A in equation (1)
C+203=404
C=404-203
C=201
Hence, the number of childs plate are 201 and adult's plate are 203.
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Use the graph to answer the question.
graph of triangle ABC with vertices at negative 2 comma negative 7, 3 comma negative 2, 2 comma negative 10 and a second triangle A prime, B prime C prime with vertices at 2 comma 7, negative 3 comma 2, negative 2 comma 10
Determine the direction and degree of rotation used to create the image.
90° counterclockwise rotation
270° counterclockwise rotation
90° clockwise rotation
180° clockwise rotation
Answer:
(d) 180° clockwise rotation
Step-by-step explanation:
Given points A(-2, -7), B(3, -2), C(2, -10) and A'(2, 7), B'(-3, 2), C'(-2, 10), you want to know the angle and direction that rotates ∆ABC to ∆A'B'C'.
SignsWe notice the signs of each of the coordinates of ABC have been reversed for the coordinates A'B'C'. For example, A(-2, -7) became A'(2, 7).
A line joining these points is a straight line through the origin. The measure of its angle at the origin is 180°. This is the angle of rotation of A'B'C' with respect to ABC.
The image is created by 180° clockwise rotation, choice D.
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Additional comment
When rotation is 180°, the direction is immaterial. A clockwise rotation gets you to the same place as a counterclockwise rotation.
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mary read 1/7 pages on monday.there are 490 pages. how many pages did she read?
Answer: 70 pages
Step-by-step explanation: If she read 1/7 pages on monday and the book is 490 pages, divide. 490 ÷ 1/7 = 70. 70 × 7 is 490. So use these operations in future problems. Just make sure to read carefully!