Question 10 of 10
PLEASE PLEASE HELP ME
Which of the following will form the composite function GFX)) shown
below?
GFX)) = 3(x+1)
A. Fx) = x2 and GCX) = 3x + 1
O B. AX) = 3x and GCx) = 1
O C. Fx) = 3x + 1 and G(x) = x2
O D. Fx) = x + 1 and G(X) = 3x2
SUBMIT

Question 10 Of 10PLEASE PLEASE HELP ME Which Of The Following Will Form The Composite Function GFX))

Answers

Answer 1
B cause gfx shows the whole thing

Related Questions

The perimeter of triangle ABC is 26 units. The altitudes of triangle ABC are in the ratio 2: 3: 4. Compute the area of triangle ABC.
please help me w step by step explanation and work tysm !

Answers

Answer:

59

Step-by-step explanation:

Can u help me with this

Answers

Answer:

D)  (6.6, 7.4)

Step-by-step explanation:

Begin by finding the margin of error based on the given information.

[tex]\boxed{\begin{minipage}{7.3cm}\underline{Margin of Error formula}\\\\$\textsf{Margin of Error}= Z \times \dfrac{S}{\sqrt{n}}$\\\\where:\\\phantom{ww} $\bullet$ $Z =$ $Z$ score\\\phantom{ww} $\bullet$ $S =$ Standard Deviation of a population\\\phantom{ww} $\bullet$ $n =$ Sample Size\\\end{minipage}}[/tex]

Given:

S = 1.3n = 50

The z-score for 95% confidence level is 1.96.

Therefore, to find the margin of error, substitute the values into the formula:

[tex]\implies \textsf{Margin of Error}= 1.96 \times \dfrac{1.3}{\sqrt{50}}[/tex]

[tex]\implies \textsf{Margin of Error}=0.360341...[/tex]

To find a reasonable range for the true mean number of hours a teenage spend on their phone, subtract and add the margin of error to the given mean of 7 hours:

[tex]\begin{aligned}\implies \textsf{Lower bound}&=7-0.360341...\\&=6.63965...\\&=6.6\;\; \sf (1\;d.p.)\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Upper bound}&=7+0.360341...\\&=7.360341...\\&=7.4\;\; \sf (1\;d.p.)\end{aligned}[/tex]

Therefore, the reasonable range for the true mean is:

(6.6, 7.4)

The distance between two points A and B on latitude 60°S along their parallel of latitude is 2816km. (I) calculate the angular difference in their longitudes (ii) if A is due west of B and on longitude 20°W, find the longitude of B

Answers

Answer:

i) The angular difference in their longitude is approximately 50.65°

ii) The line of longitude where B is located is approximately 30.65°E

Step-by-step explanation:

The given parameters are;

The angle of latitude where the points A and B are located = 60°S

The distance between points A and B = 2,816 km

(i) The angular difference in their longitude, θ, is given as follows;

θ = 2,816/(2 × π × 6,371 × cos(60°)) × 360 ≈ 50.65°

The angular difference in their longitude, θ ≈ 50.65°

(ii) The location of the point A relative to B = Due west

The line of longitude on which A is located = 20°W

∴ The line of longitude where B is located, P = θ - 20°

∴ P = 50.65° - 20°W = 30.65°E

The line of longitude where B is located ≈ 30.65°E.

A jetski races down the river at a constant speed for t seconds, covering m metres. How long, in
minutes, will it take for the jetski to cover n metres at the same speed?

Answers

It will take a time of n/60m minutes for the jetski to cover n metres at the same speed.

Define the term linear speed?The measurement of a moving object's actual distance travelled is called linear speed. Linear speed is the rate of motion of an object along a straight line.Thus, the angular speed times the r-dimensional distance equals the linear speed of such a point located on the object. The measuring unit is metres per second and metres per second. = the rate of change in radians per second.

Speed = distance/ time

Speed = m/s

For the distance of n meters.

distance = speed * time

n = m/s*time

n = m /s* time

Time = n(m/sec)

Time = n/m * sec

Time = n/60m min

Thus, it will take  n/60m minutes for the jetski to cover n metres at the same speed.

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Evie read an article that said 6\%6%6, percent of teenagers were vegetarians, but she thinks it's higher for students at her large school. To test her theory, Evie took a random sample of 252525 students at her school, and 20\%20%20, percent of them were vegetarians. To see how likely a sample like this was to happen by random chance alone, Evie performed a simulation. She simulated 404040 samples of n=25n=25n, equals, 25 students from a large population where 6\%6%6, percent of the students were vegetarian. She recorded the proportion of vegetarians in each sample. Here are the sample proportions from her 404040 samples: A dot plot for simulated sample proportions has a scale from 0.00 to 0.25 in increments of 0.01. The distribution is right skewed with dots plotted as follows. 0.00, 8. 0.004, 17. 0.08, 5. 0.12, 5. 0.16, 2. 0.20, 2. 0.24, 1. Evie wants to test H_0: p=6\%H 0 ​ :p=6%H, start subscript, 0, end subscript, colon, p, equals, 6, percent vs. H_\text{a}: p>6\%H a ​ :p>6%H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 6, percent where ppp is the true proportion of students who are vegetarian at her school. Based on these simulated results, what is the approximate ppp-value of the test? Note: The sample result was \hat p=20\% p ^ ​ =20%p, with, hat, on top, equals, 20, percent. Choose 1 answer: Choose 1 answer: (Choice A) A p\text{-value}\approx0.01p-value≈0.01p, start text, negative, v, a, l, u, e, end text, approximately equals, 0, point, 01 (Choice B) B p\text{-value}\approx0.025p-value≈0.025p, start text, negative, v, a, l, u, e, end text, approximately equals, 0, point, 025 (Choice C) C p\text{-value}\approx0.03p-value≈0.03p, start text, negative, v, a, l, u, e, end text, approximately equals, 0, point, 03 (Choice D) D p\text{-value}\approx0.075p-value≈0.075

Answers

Answer:

p-value~ 0.075

Step-by-step explanation:

( Choice D on Khan Academy)

The closest answer choice is (Choice A) A p-value ≈ 0.01, is the best approximation among the answer choices given.

What is p-value?

In a statistical hypothesis test, the p-value is a probability value that measures the strength of evidence against the null hypothesis.

It is the likelihood of observing a test statistic that is as extreme as or more extreme than the observed test statistic, assuming the null hypothesis is true.

To find the approximate p-value of the test, we need to calculate the proportion of simulated sample proportions that are greater than or equal to the sample proportion of 20%.

From the dot plot, we can see that only a few simulated sample proportions are greater than or equal to 20%, which suggests that the p-value is small.

Counting the dots from the dot plot, we can see that there are a total of 8 + 17 + 5 + 5 + 2 + 2 + 1 = 40 simulated sample proportions that are greater than or equal to 20%.

Therefore, the proportion of simulated sample proportions that are greater than or equal to 20% is 40/40 = 1.

Since the p-value is the probability of observing a sample proportion as extreme or more extreme than the observed sample proportion, given that the null hypothesis is true, we can approximate the p-value as the proportion of simulated sample proportions that are greater than or equal to the observed sample proportion.

Therefore, the approximate p-value is 1, which is very small and suggests strong evidence against the null hypothesis.

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What Is 8 1/8 - 4 3/8

Answers

Answer:

3 3/4 or 3 6/8

Step-by-step explanation:

hope this helps <3

Given the matrices, calculate AB

Answers

Answer:

C11=-2

C22=8

hope this will help you more

good luck

Plz help will mark brainliest

Answers

Answer:1/3

Y2-y1/x2-x1

3-1/9-6=2/6=1/3
ANSWER: 1/3

to find slope, solve (y2-y1)/(x2-x1)

(3-1)/(9-3) = 2/6 = 1/3

It is a problem about the systems of equations that do not arise.
It is desired to distribute 420 € among three people, so that the first has €40 more than the second, and the third has half of what they have between the first two.
a) It proposes a system of linear equations to calculate what corresponds to each one. b) It solves, using the Gauss method

Answers

The solution to the equations is

The value of first x = € 160

The value of second y = € 120

The value of third z = € 140

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first , second and third be represented as x , y , and z

The total amount to be distributed = € 420

So , x + y + z = € 420   be equation (1)

Now , first has €40 more than the second

So , x = y + 40   be equation (2)

And , third has half of what they have between the first two

So , z = ( 1/2 ) ( x + y )   be equation (3)

Substituting the value of x in the equation (3) , we get

z = ( 1/2 ) ( 2y + 40 )

z = y + 20   be equation (4)

Substituting the value of z and x in equation (1) , we get

( y + 40 ) + y + ( y + 20 ) = 420

On simplifying the equation , we get

3y + 60 = 420

Subtracting 60 on both sides of the equation , we get

3y = 360

Divide by 3 on both sides of the equation , we get

y = € 120

Therefore , the value of x = € 160

The value of z = € 140

Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420

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The point P has coordinates (8, 9). In which quadrant does point P lie?


first quadrant


fourth quadrant


second quadrant


third quadrant

Answers

It is in the first quadrant

Answer:

The coordinates (8,9) lie in quadrant 1

Step-by-step explanation:

The coordinates on quadrant ___ go like this:

Quadrant l : (+,+)

Quadrant ll : (-,+)

Quadrant lll : (-,-)

Quadrant llll : (+,-)

What is the measure or a

Answers

The measures of the angles of the parallelogram are

The measure of ∠A = 72°

The measure of ∠B = 108°

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of ∠A = ( 5y - 3 )°

The measure of ∠C = ( 3y + 27 )°

For a parallelogram , opposite angles are congruent

So , measure of ∠A = measure of ∠C

Substituting the values in the equation , we get

( 5y - 3 )° =  ( 3y + 27 )°

On simplifying the equation , we get

( 5y - 3 ) =  ( 3y + 27 )

Subtracting 3y on both sides of the equation , we get

2y - 3 = 27

Adding 3 on both sides of the equation , we get

2y = 30

Divide by 2 on both sides of the equation , we get

y = 15

So , the measure of ∠A = ( 5y - 3 )°

The measure of ∠A = ( 5 ( 15 ) - 3 ) )°

The measure of ∠A = ( 75 - 3 )°

The measure of ∠A = 72°

Now , for a parallelogram , same-side interior angles (consecutive angles) are supplementary

So , the measure of ∠A + the measure of ∠B = 180°

Substituting the values in the equation , we get

72° + the measure of ∠B = 180°

Subtracting 72° on both sides of the equation , we get

The measure of ∠B = 108°

Hence , the measures of angles of the parallelogram are 72° and 108° respectively

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A new water park was designed to contain two circular pools. Pool A has a diameter of 60 m, and pool B has a diameter of 80 m. a) If the designer wants to outline the pools with rope lights, how many meters will be needed to outline the smaller pool? (Use 3.14 for π.)

Answers

Answer:

140

Step-by-step explanation:

60+80=?......All you need to do is just add 60 and 80 and get the product

I hope that helped.

Why is triangle always 180 degrees?

Answers

Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.

1. A triangle is a three-sided polygon with three angles.

2. The sum of the three angles in any triangle must be 180 degrees.

3. This is known as the Triangle Angle Sum Theorem.

4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.

5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.

6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.

7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.

8. The sum of the three angles will always equal 180 degrees.

9. Therefore, triangle is always 180 degrees.

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IS THERE A SOLUTION ?? IF SO , WHAT IS IT ?? PLEASE HELP !! I WILL MARK BRAINLIEST !!!!

Answers

Answer:

y=4x+2

Step-by-step explanation:

-8x+2y=4

y=4x+2

−8x+2(4x+2)=4-8x+2(4x+2)=4

y=4x+2

−8x+8x+4=4-8x+8x+4=4

y=4x+2

0+4=40+4=4

y=4x+2

4=4

y=4x+2

How do you write no solution?

Answers

No solution is when a system of equations has no solution. This means that the equations are inconsistent, and there is no set of values that can make the equations true.

For example, if the system of equations is 2x + 3y = 4 and 2x + 3y = 5, then there is no solution. This is because no matter what values are chosen for x and y, the equations cannot both be true. This means that the system of equations is inconsistent, and there is no solution.

To symbolically represent no solution, you can use the following notation:

2x + 3y = 4, 2x + 3y = 5   No solution

This notation is used to indicate that the equations are inconsistent and that there is no solution.

Complete question: What is the solution to the equation 2x + 3y = 4 and 2x + 3y = 5?

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You have four sweaters, five pairs of pants, and three pairs of shoes. How many different combinations can you make, wearing one of each

Answers

Therefore, 60 different combinations can be made wearing one of each type

What is Fundamental Counting Principle? If an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m × n.This video uses manipulatives to review the five counting principles including stable order, correspondence, cardinality, abstraction, and order irrelevance. When students master the verbal counting sequence they display an understanding of the stable order of numbers.Fundamental Principle of Counting helps to determine how selection is done on the basis of available choices. Fundamental Principle of Counting simplifies the approach of selection considering all the possible choices and their combinations for calculating the ProbabilityThe fundamental counting principle states that if there are p ways to do one thing, and q ways to do another thing, then there are p×q ways to do both things. Example 1: Suppose you have 3 shirts (call them A , B , and C ), and 4 pairs of pants (call them w , x , y , and z ). Then you have. 3×4=12.

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Quadrilateral STUV is rotated 270° counterclockwise about the origin. If the coordinates of V were (3, -4), what are the coordinates of V’?

Answers

Given:

Quadrilateral STUV is rotated 270° counterclockwise about the origin.

The coordinates of V were (3, -4).

To find:

The coordinates of V’.

Solution:

If a figure rotated 270° counterclockwise about the origin, then the rule of rotation is:

[tex](x,y)\to (y,-x)[/tex]

The coordinates of V were (3, -4). Using the above rotation rule, we get

[tex]V(3,-4)\to V'(-4,-3)[/tex]

Therefore, the coordinates of V’ are (-4,-3).

Time vs. Position of Battery Operated Car
5
4
Position (m)
2
0
5
10
Time (s)
15
20
What type of relationship is shown in the graph?
a non-linear, negative relationship
a linear, negative relationship
a linear, positive relationship
O a non-linear, positive relationship

Answers

A linear, negative relationship is the type of relationship which is shown in graph of Time vs. Position of Battery Operated Car .

what is linear equation ?

A linear equation is an algebraic expression such as y=mx+b. The slope is m, and the y-intercept is B. A "linear equation in two variables" is the term used to describe the previous sentence, which has variables named y and x. Two different variables can be found in bivariate linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

The area's 46-16 opposed to 14 is different from the area's 18 and T in a different way. The place is there. It isn't linearly getting farther apart. The lee is actually growing as a result.

Option B, the slanting upwards, is what we're going to go with. Since it will be linear, it isn't option C. It is untrue that the speaking has not been constant over the distance. Because it is a D-option, this increase-decrease is untrue. Option B is the best choice. Absolutely.

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Someone pls solve this math puzzle.

Answers

Answer:

x (blue circle thing) = 46

y (dna) = -63

z (molecules) = 52

Step-by-step explanation:

Graph the image of square CDEF after a dilation with a scale factor of 2, centered at the
origin.

pls help lol

Answers

Answer:

Image attached

Step-by-step explanation:

Origin looks to be (0, -1), so move each point out by 2


9. The following illustration represents the height beam on the adult scale. Each small line represents 1/4 inch.
Each long line represents 1 inch. From the bottom to the break, readings are taken in an upward direction.
If a patient is taller than 50 inches, readings are taken in a downward direction and recorded directly at the
break in the scale.

Answers

Answer:

Helloooooooooo theree

Answer:

don't

Step-by-step explanation: it hard

someone help me plsss

Answers

x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.

what is discriminant ?

The "discriminant" is the value that aids in identifying the many types of solutions when using the quadratic formula to solve a problem. It is a unique function of a co-efficient in a mathematical equation (a quadratic equation), and the value it yields provides details about the roots of the equation. Calculating the discriminant involves square rooting the "b" term and subtracting four times the "a" term from the "c" term. Alongside "D," there is a (delta) that represents discrimination. A quadratic equation with two distinct real number solutions is said to have a positive discriminant. A quadratic equation with a discriminant of zero has repeated real number solutions. Both of the solutions are not real numbers, as indicated by a negative discriminant.

given

x2 - 3x - 5 = 0

D=b2−4ac

D= −32−4×1×5

D=92−20

D= −11

x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.

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I need some help with the problem from my math class (-4w - 7)5

Answers

-20w-35

I used the distributive property to distribute terms, and then simplified

One computer in a lab is programmed to back up data at the turn of the minute every five minutes. Another computer is programmed to back up data at the turn of the minute every two minutes. Find the number of times in twenty-four hours that the two computers back up data at the same time.

(Assume that the computers do not back up at the start of the 24-hour period.)

Answers

The number of times which the two computers back up at the same time in twenty four hours as required is; 144.

How many times does the computers back up at the same time in 24 hours?

It follows from the task content that the first computer backs up after every five minutes and the second computer backs up every two minutes.

On this note, the least common multiple of both backup times represents when the two computers back up at the same time.

Hence, since the LCM of 5 and 2 is; 10.

It follows that the two computers back up at the same time after every ten minutes.

Ultimately, the number of times for which they backup at the same time in 24 hours; since 60 minutes = 1 hour is;

= ( 24 × 60 ) / 10

= 24 × 6

= 144 times.

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helpppppppppppppppppppppppppp

Answers

Step-by-step explanation:

[tex]2\pi {r}^{2} + 2\pi rh[/tex]

[tex]2(3.14) {(20)}^{2} + 2(3.14)(20)(11)[/tex]

[tex]6.28(400) + 6.28(220) \\ 2512 + 1381.6 = 3893.6 {mi}^{2} [/tex]

Find the distance between the pair of points.

(−6, 4) and (−9, 4)

Answers

Answer:

6

Step-by-step explanation:

6

PLEASE SOMEONE HELP MEEEE I AM LITERALLY FRYING NY BRAIN. NO LINKS OR I WILL REPORT YOU... PLEASE AND THANKS

Answers

Shahaha ahahaha sjejebd d

Answer:

1. True

2. False

3. True

4. False

Step-by-step explanation:

Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith’s assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities he should delegate to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn’t have time to teach the assistant to be an accountant

Answers

The tasks that Keith can delegate to the assistant are List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet, Add the Debit and Credit columns of the trial balance and Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet.

List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet: Keith should delegate this task to his assistant. This is a relatively straightforward task that does not require a deep understanding of accounting principles. The assistant can be provided with clear instructions on how to pull the account balances from the general ledger and list them in the trial balance columns of the spreadsheet.

Add the Debit and Credit columns of the trial balance: Keith should delegate this task to his assistant. This is a simple arithmetic task that the assistant can perform with clear instructions.

Make the adjusting entries on the spreadsheet: Keith should retain this task. Adjusting entries involve more complex accounting knowledge and require a deeper understanding of accounting principles. It would be difficult for the assistant to complete this task without proper training.

Complete the spreadsheet: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet: Keith should delegate this task to his assistant. The assistant can be provided with clear instructions on how to organize the data from the spreadsheet into formal financial statements. It does not require a deep understanding of accounting principles.

Journalize and post the adjusting entries: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

--The question is incomplete, answering to the question below--

"Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith's assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities could be delegated to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn't have the time to teach the assistant to be an accountant.

For each task listed, state whether Keith should continue to do the work or delegate the task to his assistant. Explain each answer.

1. List the account balances from the general ledger in the Trial Balance columns of the work sheet.

2. Add the Debit and Credit columns of the trial balance.

3. Make the adjusting entries on the work sheet.

4. Complete the work sheet.

5. Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the work sheet.

6. Journalize and post the adjusting entries."

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Find a basis for the eigenspace corresponding to each listed eigenvalue of A below.
A = 4 0 -1 14 5 -10 2 0 1 λ=5,2,3
A basis for the eigenspace corresponding to λ = 5 is { }. (Use a comma to separate answers as needed.) A basis for the eigenspace corresponding to λ = 2 is { }. (Use a comma to separate answers as needed.) A basis for the eigenspace corresponding to λ = 3 is . { }. (Use a comma to separate answers as needed.)

Answers

The basis for the eigenspace corresponding to lambda=5,1,4 are None,[tex]\left[\begin{array}{c}-1 \\\frac{1}{2} \\0\end{array}\right][/tex] and [tex]$\left[\begin{array}{l}2 \\ 1 \\ 1\end{array}\right]$[/tex]

[tex]$$A=\left[\begin{array}{ccc}5 & -12 & 10 \\0 & 7 & -3 \\0 & 6 & -2\end{array}\right]$$[/tex]

Eigenspace corresponding to lambda=5,1,4

The eigenspace E_lambda corresponding to the eigenvalue lambda is the null space of the matrix a [tex]\mathrm{A}-(\lambda) \mathrm{I}"[/tex]

for lambda=5

[tex]$$\mathrm{E}_5=\mathrm{N}(\mathrm{A}-5 \mathrm{I})$$[/tex]

Reducing the matrix A-5I by elementary row operations

[tex]$$\begin{aligned}A-5 I & =\left[\begin{array}{ccc}5-5 & -12 & 10 \\0 & 7-5 & -3 \\0 & 6 & -2-5\end{array}\right] \\& =\left[\begin{array}{ccc}0 & -12 & 10 \\0 & 2 & -3 \\0 & 6 & -7\end{array}\right] \\& \sim\left[\begin{array}{ccc}0 & -12 & 10 \\0 & 1 & -\frac{3}{2} \\0 & 6 & -7\end{array}\right] R_2 \rightarrow \frac{R_2}{2} \\& \sim\left[\begin{array}{ccc}1 & 0 & -8 \\0 & 1 & -\frac{3}{2} \\0 & 6 & -7\end{array}\right] R_1 \rightarrow R_1+2 R_2\end{aligned}$$[/tex]

[tex]\sim\left[\begin{array}{ccc}1 & 0 & -8 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 2\end{array}\right] R_3 \rightarrow R_3-6 R_2$$\\\sim\left[\begin{array}{ccc}1 & 0 & -8 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 1\end{array}\right] R_3 \rightarrow \frac{\mathrm{R}_3}{2}$$\\\sim\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 1\end{array}\right] \mathrm{R}_1 \rightarrow \mathrm{R}_1+8 \mathrm{R}_3$[/tex]

[tex]$\sim\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] R_2 \rightarrow R_2+\frac{2 R_3}{2}$[/tex]

The solutions x of A-5I=0 satisfy x_1=x_2=x_3=0 that is, the null space solves the matrix

[tex]$$\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]$$[/tex]

Hence The null space is [tex]\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] E_5[/tex] has no basis

[tex]$$\begin{aligned}& \text { case: } 2 \\& \text { for } \lambda=1 \\& \mathrm{E}_5=\mathrm{N}(\mathrm{A}-(1) \mathrm{I})\end{aligned}$$[/tex]

we reduce the matrix A-I by elementary row operations as follows.

[tex]$$\begin{aligned}A-1 & =\left[\begin{array}{ccc}5-1 & -12 & 10 \\0 & 7-1 & -3 \\0 & 6 & -2-1\end{array}\right] \\& =\left[\begin{array}{ccc}1 & -3 & \frac{5}{2} \\0 & 6 & -3 \\0 & 6 & -3\end{array}\right] R_1 \rightarrow \frac{R_1}{4} \\& \sim\left[\begin{array}{ccc}1 & -3 & \frac{5}{2} \\0 & 1 & -\frac{1}{2} \\0 & 6 & -3\end{array}\right] R_2 \rightarrow \frac{R_2}{6}\end{aligned}[/tex]

[tex]$$$\sim\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 6 & -3\end{array}\right] R_1 \rightarrow R_1+3 R_2$\\$\sim\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 0 & 0\end{array}\right] R_3 \rightarrow R_3-6 R_2$[/tex]

Thus, the solutions x of (A-I) X=0 satisfy

[tex]$\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 0 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$[/tex]

x_3=t

[tex]$\Rightarrow \mathrm{x}_1=-\mathrm{t}, \mathrm{x}_2=\frac{\mathrm{t}}{2}$[/tex]

[tex]$\vec{x}=\left[\begin{array}{c}-t \\ \frac{t}{2} \\ t\end{array}\right]=\left[\begin{array}{c}-1 \\ \frac{1}{2} \\ 1\end{array}\right] t$[/tex]

The Basis for the nullspace A-I will be: [tex]$\left.\left(\begin{array}{c}-1 \\ \frac{1}{2} \\ 1\end{array}\right]\right)$[/tex]

case:3

lambda=4

[tex]$$\mathrm{E}_5=\mathrm{N}(\mathrm{A}-(4) \mathrm{I})$$[/tex]

we reduce the matrix A-4I by elementary row operations as follows.

[tex]$\begin{aligned} A-4 \mid & =\left[\begin{array}{ccc}5-4 & -12 & 10 \\ 0 & 7-4 & -3 \\ 0 & 6 & -2-4\end{array}\right] \\ & =\left[\begin{array}{ccc}1 & -12 & 10 \\ 0 & 3 & -3 \\ 0 & 6 & -6\end{array}\right] \\ & \sim\left[\begin{array}{ccc}1 & -12 & 10 \\ 0 & 1 & -1 \\ 0 & 6 & -6\end{array}\right] R_2 \rightarrow \frac{R_2}{3}\end{aligned}$[/tex]

[tex]$\begin{aligned} & \sim\left[\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 6 & -6\end{array}\right] \mathrm{R}_1 \rightarrow \mathrm{R}_1+12 \mathrm{R}_2 \\ & \sim\left[\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 0 & 0\end{array}\right] \mathrm{R}_3 \rightarrow \mathrm{R}_3-6 \mathrm{R}_2\end{aligned}$[/tex]

Thus, the solutions x of (A-4IX)=0 satisfy

[tex]$$\left[\begin{array}{ccc}1 & 0 & -2 \\0 & 1 & -1 \\0 & 0 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]$$[/tex]

x_3=t

[tex]$\Rightarrow \mathrm{x}_1=2 \mathrm{t}, \mathrm{x}_2=\mathrm{t}$[/tex]

[tex]$$\vec{x}=\left[\begin{array}{c}2 t \\t \\t\end{array}\right]=\left[\begin{array}{l}2 \\1 \\1\end{array}\right] t$$[/tex]

The Basis for the nullspace A-4 I will be [tex]\left(\left[\begin{array}{l}2 \\ 1 \\ 1\end{array}\right]\right)[/tex]

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Composite Figures Question 9.
A. 57 ft
B. 288 ft
C. 208 ft
D. 264 ft

Answers

Answer:

D

Step-by-step explanation:

find area of first rectangle

18 x 6 = 108

find area of second rectangle

20 x 5 = 100

find area of two triangles

7 x 8 =56

56/2 = 28

each triangle has an area of 28

28+28+100+108 = 264ft

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