Answer:
C. 72
Step-by-step explanation:
So imagine every straight line you see equals to 180 degrees, so given one side of the angle...180 - 108 = 72
Answer:
72
Step-by-step explanation:
Because as we know the angle of this is 180 and we already have (108°) so we have to add 108° to one of the numbers till we get to (180°)
Good luck
Which expressions are equivalent
i'll mark brainliest
Answer:
C
Step-by-step explanation:
If the median house price in your area is $350,000, and the 30 -year mortgage rate is %5, how expensive of a house can you afford if you have a downpayment of $15,000. Assume you make $90,000 a year.
With a down payment of $15,000, an annual income of $90,000, and a 30-year mortgage rate of 5%, you should be able to afford a house with a median price of $350,000 in your area.
To determine how expensive of a house you can afford, we need to consider several factors, including your income, down payment, mortgage rate, and the median house price.
First, let's calculate the loan amount. Subtracting your down payment of $15,000 from the median house price of $350,000 gives us a loan amount of $335,000.
Next, we need to calculate your monthly mortgage payment. To do this, we will use the 30-year mortgage rate of 5%. Converting this annual rate to a monthly rate, we get 0.05/12 = 0.0042.
Using an online mortgage calculator, we can determine that the monthly mortgage payment for a $335,000 loan at a 5% interest rate is approximately $1,794.
To determine how much you can afford, we need to consider your income. Assuming an annual income of $90,000, we can estimate your monthly income by dividing it by 12, which gives us $7,500.
As a general rule, lenders typically recommend that your monthly mortgage payment should not exceed 28% of your monthly income. In your case, 28% of $7,500 is $2,100.
Since your estimated monthly mortgage payment of $1,794 is below $2,100, you should be able to afford a house with a median price of $350,000, given your income, down payment, and mortgage rate.
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Help me, I'm really tired atm
Step-by-step explanation:
6/15 = 12/30 = 24/60 = 48/75
Answer:
Step-by-step explanation:
Find the exact length of the curve. x=31y(y−3),1≤y≤4
The exact length of the curve is approximately 3.000137804 units.
To find the exact length of the curve defined by the equation x = 31y(y−3), where y ranges from 1 to 4, we can use the arc length formula from calculus. The formula is given by:
L = ∫[a,b] √[1 + (dy/dx)²] dx
First, let's find dy/dx by differentiating the equation x = 31y(y−3) with respect to y:
dx/dy = 31[(y)(dy/dy) - (y-3)(dy/dy)]
= 31y - (y-3)
= 31(3)(dy/dy)
= 93(dy/dy)
Now, we can solve for dy/dy:
dx/dy = 93(dy/dy)
dy/dx = 1/93
Substituting this value into the arc length formula:
L = ∫[1,4] √[1 + (dy/dx)²] dx
= ∫[1,4] √[1 + (1/93)²] dx
= ∫[1,4] √[1 + 1/8649] dx
= ∫[1,4] √[8649/8649 + 1/8649] dx
= ∫[1,4] √[(8649 + 1)/8649] dx
= ∫[1,4] √(8650/8649) dx
= ∫[1,4] √(8650) / √(8649) dx
= √(8650/8649) ∫[1,4] dx
Now we can integrate ∫[1,4] dx:
L = √(8650/8649) [x] from 1 to 4
= √(8650/8649) (4 - 1)
= √(8650/8649) (3)
≈ 3.000137804
Therefore, the exact length of the curve is approximately 3.000137804 units.
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Someone please explain I am so confused
Answer:
0, 6
Step-by-step explanation:
No matter whatever the number x is, (4/5)^x will not be below 0. You can put (4/5)^x>0. since g(x) has a +6, the first will be 0 and the second would be 6
A 5 kg disk rotating at 300rpm engages a 3 kg disk rotating in the bpposite direction at 500rpm. The radius of the first disk is 60 cm and that of the second is 30 cm. What's the combined rpm after the two disks are engaged? I
5
W
5
+I
3
W=W
c
(I
5
+I
3
)
The combined rpm = (1.4638rad/s)(60s/2πrad) = 14.72rpm. The combined rpm after the two disks are engaged is 14.72 rpm (to two decimal places).
The combined rpm after the two disks are engaged is 169.5rpm.Applying conservation of angular momentum as derived from the law of conservation of energy by equating the work done in the first scenario where the first disk rotates at 300rpm to the work done in the second scenario where the two disks are rotating at a combined rpm (w) which is what we want to find.
We have;
Work done = Energy = 1/2 I₁ω₁² = 1/2 I₂ω₂² = 1/2 Ic w²I₁ = moment of inertia of the first disk = (1/2)mr² = (1/2)(5kg)(0.6m)² = 0.9kgm²ω₁ = initial angular speed of first disk = 300rpm = 31.4rad/sI₂ = moment of inertia of second disk = (1/2)mr² = (1/2)(3kg)(0.3m)² = 0.135kgm²ω₂ = initial angular speed of second disk = -500rpm = -52.4rad/s (negative since it is rotating in opposite direction)I
c = moment of inertia of the combined system = I₁ + I₂ = 0.9kgm² + 0.135kgm² = 1.035kgm²
Then,1/2 (0.9kgm²)(31.4rad/s)² = 1/2 (0.135kgm²)(-52.4rad/s)² = 1/2 (1.035kgm²)(w)²947.61 = 366.07w²w = √(947.61/366.07)
w = 1.4638rad/s
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Tom bought 3 1/2 gallons of ice cream. If a pint is 1/8 of a gallon, how many pint-sized servings are there
Question 19
Simplify the expression 4a - b(3a² + b² + 4ab).
Answer
A 4a-3a²b + b³ + ab²
B) 12a + a²b-6³
C 7a - b³ + 8a²b
D 4a-3a²b-6³ - 4ab²
D) 4a-3a²b-6³ - 4ab².
Step-by-step explanation:
To simplify the expression 4a - b(3a² + b² + 4ab), you can use the distributive property to expand the term inside the parentheses:
4a - b(3a² + b² + 4ab)
= 4a - b3a² - bb² - b*4ab
= 4a - 3a²b - b³ - 4ab²
The correct answer is therefore D) 4a-3a²b-6³ - 4ab².
Which of the following statements about least squares regression analysis is true?
I. A point with a large residual is an outlier
II. A point with high leverage has a Y value that is not consistent with the other Y values in the set
III. The removal of an influential point from the data set could change the value of the correlation coefficient
The statements about least squares regression analysis is true are I and III.
What is meant by regression analysis?The statistical technique of regression analysis demonstrates the link between two or more variables. The method evaluates the relationship between a dependent variable and independent factors, and is frequently presented as a graph.
You can anticipate the effects of the independent variable on the dependent one by creating a regression analysis. For instance, we can claim that a linear regression model can adequately account for age and height.
Here,
From the given information in the question:
The statements I and III are correct.
And the statements are:
A point with a large residual is an outlier and the removal of an influential point from the data set could change the value of the correlation coefficient.
So, the statements I and III are correct for the given information in the question.
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The average time it takes a certain brand of ibuprofen to start working is 25 minutes, with a standard deviation of 13 minutes, distributed normally. A pharmacist randomly samples 20 pills from this brand, because she is researching different brands in order to find the quickest acting ibuprofen to recommend to her customers. Identify the following to help her make her recommendations, rounding to the nearest hundredth if necessary:
Provide your answer below:
a) $\mu=$μ= 25 minutes
b) $\sigma=$σ= 13 minutes
c) $n=$n= 20
d) $\mu_{\overline{x}}=$μx= 13 minutes
e) $\sigma_{\overline{x}}=$σx= minutes
The standard deviation of the sample means, σx, is approximately 2.91 minutes.
a) The population mean is represented by the symbol μ and is equal to 25 minutes.
b) The population standard deviation is represented by the symbol σ and is equal to 13 minutes.
c) The sample size is represented by the symbol n and is equal to 20.
d) The mean of the sample means, also known as the sample mean of the sampling distribution, is represented by the symbol μx and is equal to the same as the population mean μ, which is 25 minutes.
e) The standard deviation of the sample means, also known as the standard error of the mean, is represented by the symbol σx and is calculated by dividing the population standard deviation σ by the square root of the sample size n:
σx = σ / √n
Substituting the given values:
σx = 13 / √20 ≈ 2.91 minutes
Therefore, the standard deviation of the sample means, σx, is approximately 2.91 minutes.
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make a construction of your object on a piece of paper. using a compass and straightedge, create a 2-d diagram that represents your 3-d object. consider a side view, top view, and front view. things to keep in mind: does your object have congruent segments, congruent angles, parallel or perpendicular lines, or any special shapes such as equilateral triangles, squares, or regular hexagons?
To create a side view, you can use a straightedge to outline the object from a side perspective. If the object has congruent segments, you can measure the length of one segment and use the compass to mark off the same length on the straightedge to create the other segments.
For congruent angles, you can use the compass to mark off the same angle on the straightedge. If the object has parallel or perpendicular lines, you can use the straightedge to draw those lines accurately. If the object has special shapes such as equilateral triangles, squares, or regular hexagons, you can use the compass to draw those shapes.
To create a top view, you can use a straightedge to outline the object from a top perspective. If the object has congruent segments, you can measure the length of one segment and use the compass to mark off the same length on the straightedge to create the other segments.
For congruent angles, you can use the compass to mark off the same angle on the straightedge. If the object has parallel or perpendicular lines, you can use the straightedge to draw those lines accurately. If the object has special shapes such as equilateral triangles, squares, or regular hexagons, you can use the compass to draw those shapes.
To create a front view, you can use a straightedge to outline the object from a front perspective. If the object has congruent segments, you can measure the length of one segment and use the compass to mark off the same length on the straightedge to create the other segments.
For congruent angles, you can use the compass to mark off the same angle on the straightedge. If the object has parallel or perpendicular lines, you can use the straightedge to draw those lines accurately. If the object has special shapes such as equilateral triangles, squares, or regular hexagons, you can use the compass to draw those shapes.
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using the expression you have found for ds, and for the e vectors, find the velocity and acceleration components in the coordinate systems indicated.
Parabolic cylinder
The velocity and acceleration components in a particular coordinate system.
How to find the velocity and acceleration components in the coordinate systems indicated Parabolic cylinder?Without the specific expression for ds and e vectors, it is difficult to provide a detailed answer to this question. However, in general, the velocity and acceleration components in a particular coordinate system can be obtained by taking the derivative of the position vector and the velocity vector, respectively, with respect to time. The position vector and velocity vector can be expressed in terms of the coordinate system's basis vectors and the components of the position and velocity vectors.
For example, in Cartesian coordinates, the position vector is given by r = xi + yj + zk, where i, j, and k are the unit vectors in the x, y, and z directions, respectively. The velocity vector is given by v = dr/dt = (dx/dt)i + (dy/dt)j + (dz/dt)k. The components of the velocity vector can be found by taking the derivatives of x, y, and z with respect to time.
Similarly, in cylindrical or spherical coordinates, the position vector and velocity vector can be expressed in terms of the coordinate system's basis vectors and the components of the position and velocity vectors.
Therefore, to find the velocity and acceleration components in a particular coordinate system, we need to first express the position vector and velocity vector in terms of that coordinate system's basis vectors and then take the appropriate derivatives with respect to time.
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what is the equation?
Answer:what equation ?
Step-by-step explanation:
Answer:
to what ..............
The Mountain States Office of State Farm Insurance Company reports that approximately 82% of all automobile damage liability claims were made by people under 25 years of age. A random sample of seven automobile insurance liability claims is under study. For samples of size 7, what is the expected number of claims made by people under 25 years of age
The expected number of claims made by people under 25 years of age is 5.74.
For this problem, we can use the binomial distribution which states that the probability of success (p) is equal to the proportion of people under 25 making claims (82%) and the probability of failure (q) is equal to the proportion of people over 25 making claims (1 - 82% = 18%).
The expected number of claims made by people under 25 is equal to the total sample size (7) times the proportion of people under 25 making claims (0.82) so the expected number of claims made by people under 25 is 7×0.82 = 5.74.
Hence, the expected number of claims made by people under 25 years of age is 5.74.
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What is the slope of the line that contains the points in the table?
Answer:
D
Step-by-step explanation:
The boxes with whole numbers in them written as coordinates:
(-4, -11)
(8, -8)
we know gradient is rise over run, or (y2 - y1) / (x2 - x1)
gradient = (-8 - -11) / (8 - -4)
gradient = 3 / 12
gradient = ¼
Answer:
B
Step-by-step explanation:
always remember that the slope is the ratio "y coordinate change / x coordinate change".
in the table we see that when x increases by 3, y increases by 3/4 (= 0.75).
this impression is confirmed by the last step, as x increases by 6, and y by 1.5 = 6/4.
so, the slope is
3/4 / 3 = 1/4
or
6/4 / 6 = 1/4
so, it is 1/4.
We generate a bootstrap dataset x 1
∗
,x 2
∗
,x 3
∗
,x 4
∗
from the empirical distribution function of the dataset 1
3
4
6
. a. Compute the probability that the bootstrap sample mean is equal to 1 . 18.5 Exercises 281 b. Compute the probability that the maximum of the bootstrap dataset is equal to 6 . c. Compute the probability that exactly two elements in the bootstrap sample are less than 2
a. The probability is given by P(exactly two elements less than 2) = 1500/10000 = 0.15.
Probability of the bootstrap sample mean The probability of the bootstrap sample mean is equal to 1.18 can be calculated as follows:
We have a bootstrap sample dataset of size n = 4.
From this dataset, we can draw bootstrap samples of size n = 4. We draw a large number of bootstrap samples (let say B = 10000) and calculate the sample mean for each sample.
Then we can compute the probability that the bootstrap sample mean is equal to 1.18 by dividing the number of times the sample mean equals 1.18 by the total number of bootstrap samples.
For instance, if the number of times the sample mean equals 1.18 is 2000, then the probability is given by P(sample mean = 1.18) = 2000/10000 = 0.2.b.
Probability of the maximum of the bootstrap dataset. The probability that the maximum of the bootstrap dataset is equal to 6 can be calculated as follows:
We draw a large number of bootstrap samples (let say B = 10000) and calculate the maximum value for each sample.
Then we can compute the probability that the maximum of the bootstrap dataset is equal to 6 by dividing the number of times the maximum value equals 6 by the total number of bootstrap samples.
For instance, if the number of times the maximum value equals 6 is 5000, then the probability is given by P(maximum = 6) = 5000/10000 = 0.5.c.
Probability that exactly two elements in the bootstrap sample are less than 2.
The probability that exactly two elements in the bootstrap sample are less than 2 can be calculated as follows:
We draw a large number of bootstrap samples (let say B = 10000) and count the number of samples that contain exactly two elements less than 2.
Then we can compute the probability that exactly two elements in the bootstrap sample are less than 2 by dividing the number of samples containing exactly two elements less than 2 by the total number of bootstrap samples.
For instance, if the number of samples containing exactly two elements less than 2 is 1500, then the probability is given by P(exactly two elements less than 2) = 1500/10000 = 0.15.
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for a given non-zero vector v in r3 there is a unique unit vector parallel to it. is it true or false? explain your answer.
For a given non-zero vector v in r3 there is a unique unit vector parallel to it the correct answer is 'True'.
How about a value vector which is a non-zero vector, this one? What connection does this have to a unit vector?
I'm given the following justification: "Remember that two vectors a and b are parallel if
If and only if two vectors A and B are scalar multiples of one another, they are said to be parallel. k is a constant that does not equal zero. The cross-product of the two vectors can be determined.
Let u
be a non-unit vector. Set n=u/|u|
Then n is a unit vector and u is parallel to n since u=|u|n.
a⃗ =λb⃗
for a certain scalar λ
Keep in mind that| λa⃗ |=|λ||a⃗ |
Therefore, given a vector a is λ, the value will result in a vector λ =λa⃗ with magnitude 1.
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420 seconds to 10 minutes
Answer:
420 seconds is equal to 7 min
So 7 to 10 or 7 : 10
pls brainliest
These are the steps that you should follow in order to make the necessary calculations to convert 420 Seconds to Minutes. In order to convert from [s] to [min], we have to devide the amount of Seconds by 60.
Then the second step, is to substitute the amount of Seconds with the value of 420 and calculate the division. After successfuly calculating it the result should for 420 Seconds to Minutes should be 7
So 7 to 10 or 7 : 10
Hope this helped!
Have a great day
in what situations would you want to change from rectangular to cylindrical or to spherical coordinates?
List five numbers that have 3, 5, and 11 as prime factors
Answer:
11 1,11 1 x 11
13 1, 13 1 x 13
17 1, 17 1 x 17
19 1, 19 1 x 19
Step-by-step explanation:
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?
If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120
The number q is an odd number
The median of q consecutive integers = 120
Consider the q = 3
Then three consecutive integers will be 119, 120, 121
The largest number = 121
Substitute the value of q in each options
Option A
(q-1) / 2 + 120
Substitute the value of q
(3-1)/2 + 120
Subtract the terms
=2/2 + 120
Divide the terms
= 1 + 120
= 121
Therefore, largest of these integers is (q-1) / 2 + 120
I have answered the question in general, as the given question is incomplete
The complete question is
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?
a) (q-1) / 2 + 120
b) q/2 + 119
c) q/2 + 120
d) (q+119)/2
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Miranda conducted a survey on how many hours per day students spend surfing the internet versus how many pets they have
She surveyed ten of her classmates and recorded the data in the scatter plot below.
Answer:
Option C
Step-by-step explanation:
Data set collected by Miranda and her classmates is,
(0, 7.5), (0, 9), (1, 6), (1, 6.5), (2, 6), (3, 5.5), (4, 4), (4, 4.5), (5, 4), (8, 3)
By using a regression calculator.
Equation for the regression lien will be,
y = -0.6565x + 7.438
y = -0.7x + 7.4
Option C will be the answer.
What are some benefits of representing data sets using frequency distributions?
A. Organizing the data into a frequency distribution can make patterns within the data more evident.
B. Organizing the data into a frequency distribution makes it possible to graph quantitative data.
c. It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution.
Answer:
no answer
Step-by-step explanation:
no answer
to be checked in options
Find an equation of the tangent to the curve at the given point by two methods: without eliminating the parameter and by first eliminating the parameter. x = sin(t), y = cos2(t); 2 2 , 1 2
The equation of the tangent to the curve without eliminating the parameter is \(y - cos^2(1/2) = -2sin(1/2) \times cos(1/2)(x - sin(1/2)).\)
The equations of the tangents to the curve by first eliminating the parameter is \(y - cos^2(1/2) = -1 / (2sin(1/2))(x - sin(1/2))\).
To find the equation of the tangent to the curve without eliminating the parameter, we need to find the derivative of both x and y with respect to t.
Given x = sin(t) and y = cos^2(t), we can find the derivatives as follows:
dx/dt = cos(t)
dy/dt = -2sin(t) * cos(t)
Now, we need to find the values of t for which the tangent is desired. Let's substitute the values t = 2 and t = 1/2 into the derivatives:
When t = 2:
dx/dt = cos(2)
\(dy/dt = -2sin(2) \times cos(2)\)
When t = 1/2:
dx/dt = cos(1/2)
\(dy/dt = -2sin(1/2) \times cos(1/2)\)
Now, we have the slopes of the tangents at the given points. Let's use the point-slope form of a line to find the equations of the tangents.
For t = 2:
y - y1 = m(x - x1), where (x1, y1) is the point \((sin(2),cos^2(2))\)
Substituting the values, we get:
\(y - cos^2(2) = -2sin(2) \times cos(2)(x - sin(2))\)
For t = 1/2:
y - y1 = m(x - x1), where (x1, y1) is the point \((sin(1/2), cos^2(1/2))\)
Substituting the values, we get:
\(y - cos^2(1/2) = -2sin(1/2) \times cos(1/2)(x - sin(1/2))\)
This is the equation of the tangent to the curve without eliminating the parameter.
To find the equation of the tangent by eliminating the parameter, we can solve the given equations to express x in terms of y and then find the derivative of x with respect to y.
From the equation x = sin(t), we can express t in terms of x as t = arcsin(x).
Now, substitute this value of t into the equation y = cos^2(t):
\(y = cos^2(arcsin(x))\)
To eliminate the parameter, we need to find the derivative of x with respect to y:
dx/dy = dx/dt * dt/dy
We already found dx/dt as cos(t), and dt/dy can be found by taking the reciprocal of dy/dt.
So, \(dt/dy = 1 / (dy/dt) = 1 / (-2sin(t) \times cos(t))\)
Substituting the values, we get:
dx/dy = cos(t) / (-2sin(t) * cos(t))
Simplifying further, we get:
dx/dy = -1/(2sin(t))
Now, substitute the values t = 2 and t = 1/2 into the derivative:
When t = 2:
dx/dy = -1/(2sin(2))
When t = 1/2:
dx/dy = -1/(2sin(1/2))
Now, we have the slopes of the tangents at the given points. Let's use the point-slope form of a line to find the equations of the tangents.
For t = 2:
y - y1 = m(x - x1), where (x1, y1) is the point \((sin(2), cos^2(2))\)
Substituting the values, we get:
\(y - cos^2(2) = -1 / (2sin(2))(x - sin(2))\)
For t = 1/2:
y - y1 = m(x - x1), where (x1, y1) is the point \((sin(1/2), cos^2(1/2))\)
Substituting the values, we get:
\(y - cos^2(1/2) = -1 / (2sin(1/2))(x - sin(1/2))\)
These are the equations of the tangents to the curve by first eliminating the parameter.
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Which equation is parallel to y = -5x + 3
A triangle has two sides of lengths 10 and 14. What value could the length of
the third side be? Check all that apply.
A triangle having two sides of lengths 10 and 14 will have the third side length less than 24.
As per the question statement, We are given a triangle that has two sides of lengths 10 and 14 and we are asked about the length of the third side.
Before solving the question, we should be well aware of the the theorem of triangle side sum property.
"According to the "sum of sides of a triangle rule," any two triangle sides' sums must be bigger than the length of the third side."
The sum of length of two sides are = \(10+14=24\)
Hence the length of third side has to be less than 24 as per the theorem.
Triangle side sum property: "According to the "sum of sides of a triangle rule," any two triangle sides' sums must be bigger than the length of the third side."To learn more about triangles and its properties, click on the link given below:
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1)In a multiple regression model, the error term `e’ is assumed to be a random variable with a mean of
A)zero.
B)-1.
C)1.
D)any value.
In a multiple regression model, the error term (often denoted as ε or e) is assumed to be a random variable with a mean of zero.
This assumption is a key component of the regression model and is often referred to as the assumption of zero conditional mean or the assumption of homoscedasticity. The assumption of a mean of zero for the error term means that, on average, the errors have no systematic bias or tendency to overestimate or underestimate the predicted values. It implies that the model's predictions are unbiased and that any deviations from the true values are due to random chance or other factors not captured by the model. The other options presented in the answer choices (B) -1, (C) 1, and (D) any value are incorrect. The mean of the error term is specifically assumed to be zero, as it represents the average deviation of the observed values from the predicted values in the model.
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Parallel lines r and s are cut by two transversals, parallel lines t and u. Which angles are alternate exterior angles with angle 11? 5 and 13 7 and 15 6 and 16 8 and 14.
Angles 13 and 5 are the opposing exterior angles to angle 11.
If two angles are on the exterior side of parallel lines and lie on the opposite sides of the transversal line, they are said to be alternate exterior angles.
The fact that r and t are parallel to one another is a given.
The angles 13 and 5 are on the outside side of parallel lines in the illustration, and they are located on the opposite sides of the transverse line..Angles 13 and 5 are hence complementary outer angles to angle 11.
If two angles are on the exterior side of parallel lines and lie on the opposite sides of the transversal line, they are said to be alternate exterior angles.
The fact that r and t are parallel to s and u is a given.
r║s and t║u. The angles 13 and 5 are on the outside side of parallel lines in the illustration, and they are located on the opposite sides of the transverse line.
Therefore, Angles 13 and 5 are hence complementary outer angles to angle 11.
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What are the coordinates of G after it is translated LEFT 4 UNITS AND UP 3 UNITS?
this is a text
Answer:
The coordinates of G' after being translated is (-8,6)
Step-by-step explanation:
Find the original coordinates of G by looking at the graph. In this case it's (-4,3). Translate the changes: When you go to the left you are subtracting the x-axis from the original x-axis and when you go up you are adding the y-axis from the original y-axis so it would be -4 -4 is -8 and 3 + 3 is 6 so the new coordinates are (-8,6)