SOMEONE HELP ME PLEASE, I AM STUCK....................

Ray knows that the m∠3 = m∠6. Which of the following conclusions can Ray make based on the given information? 1. Lines l and m are parallel because alternate interior angles are equal. 2. Lines l and m are parallel because alternate exterior angles are equal. 3. Lines l and m are parallel because corresponding angles are equal. 4. No conclusion can be made about the lines.​

SOMEONE HELP ME PLEASE, I AM STUCK....................Ray Knows That The M3 = M6. Which Of The Following

Answers

Answer 1

Answer:

A) Lines I and M are parallel because alternate (interior) angles are equal.

Step-by-step explanation:

Hello, as I just did this lesson, to confirm my answer - look at the graph.

If you know the difference between alternate interior and alternate exterior, answering this should be fairly easy. Hope this helps! (:


Related Questions

Which of the following has four, eight and one nine??
A.88889
B.4819
C.888819
D.489

Answers

Answer:

D. 489

Step-by-step explanation:

489 has the number,

four - 4

eight - 8

and ONE nine - 9

Hope this helps :)

D) 489, if you mean that there is ONE nine.

consider a pair of integers (a b) the following operations can be performed on (a,b) in any order, zero or more times

Answers

If we consider  a pair of integers (a b) and the given operations, then the java program that depicts it is as written below.

How to carry out programming in Java?

The program that carries out the required operations on the pair of integers is;

static LinkedList<Pair<Integer,Integer>> pairs = new LinkedList<Pair<Integer, Integer>>();

   public static String isItPossible(Integer a, Integer b, Integer c, Integer d){

       pairs.addLast(new Pair<Integer, Integer>(a,b));

       while (!pairs.isEmpty()){

           Pair<Integer,Integer> pair = pairs.poll();

           Integer key = pair.getKey();

           Integer value = pair.getValue();

           if(key.equals(a) &&

                   value.equals(b)){

               return "YES";

           }

           int sum=key+value;

           if (sum<=c){

               pairs.addLast(new Pair<Integer, Integer>(sum,value));

           }

           if (sum<=d){

               pairs.addLast(new Pair<Integer, Integer>(key,sum));

           }

 

       }

 

       return "NO";

   }

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Complete question is;

Consider a pair of integers, (a, b). The following operations can be performed on (a, b) in any order, zero or more times:

• (a, b)(a + b, b)

• (a, b) → (a, a + b)

Return a string that denotes whether or not (a, b) can be converted to to (c,d) by by performing zero or more of the operations specified above. Example

(a, b) = (1, 1)

(c,d) = (5,2)

Perform the operation (1,1 + 1) to get (1, 2), perform the operation (1 + 2, 2) to get (3, 2), and perform the operation (3+2, 2) to get (5,2). Alternatively, the first operation could be (1+1, 1) to get (2, 1) and so on.

Complete the function is possible in the editor below. isPossible has the following parameter(s): int a: first value in (a, b) int b: second value in (a, b) int c: first value in (c,d) int d: second value in (c,d) Returns: str: Return 'Yes' if (a, b) can be converted to (c,d) by performing zero or more of the operations specified above, or 'No' if not Constraints • 1 sa,b,c,ds 1000

if f(x)=x+2/x^2-9 and g(x)=11/x^2+3x

A. find f(x)+g(x)

B. list all of the excluded values

C. classify each type of discontinuty


To receive​ credit, this must be done by Algebraic method​s, not graphing

Answers

The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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(BRAINIEST AND 7 POINTS !) One year ago Derek joined a health club. He paid a yearly membership fee of $28 that covered all the club's services except the raquetball
court. Derek paid an additional $7 each time he used the raquetball court. For the entire year at the health club, Derek paid a total of $119.

PART 1: Write an equation to represent the number of times (x) that Derek used the raquetball court.
Equation:

PART 2: Solve the Equation your wrote for part 1.
X=
—————————————
This is worth 60% of my grade ! Please help.


(BRAINIEST AND 7 POINTS !) One year ago Derek joined a health club. He paid a yearly membership fee of

Answers

Answer: 7x+28=119

x=13

Step-by-step explanation:

Answer:

119= 7x + 28

x=13

Step-by-step explanation:

This problem requires an equation. y= mx+ b, where y is your total, mx is your slope, and b is your y intercept. Your total is 119, your yearly fee is 28 ( which is b since it only happens ones), and 7 is x (since x represents each time) So 119=7x+28. Now to solve this we would subtract 28 from both sides and then divide that number by 7. So 119-28 is 91. 91/7 is 13. He used the racketball court 13 times. You can plug 13 to make sure.

119= 7(13) + 28.

Write a sentence of the form “–––––––––––––– is a function of –––––––.”
Type your response in the space below.

Answers

"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.

It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.

In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.

Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.

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Can you help meeeeeee this is math and there have to be not one answer many like 3,2 and some time 1 ok Thankyou

Can you help meeeeeee this is math and there have to be not one answer many like 3,2 and some time 1

Answers

i’m not sure but i think it’s b

Can someone help me find the area

Can someone help me find the area

Answers

Answer:

Area of the composite figure = 84 in²

Step-by-step explanation:

Area of the composite figure = Area of rectangle DEFG + Area of rectangle BCGH + Area of triangle ABH

Area of rectangle DEFG = DE × EF

                                        = 5 × 10

                                        = 50 in²

From ΔBHA,

AB = ED = 5 in [Given]

AH = FA - (GH + FG)

     = 15 - (7 + 5)

     = 15 - 12

     = 3 in.

By applying Pythagoras theorem in ΔABH,

AB² = HB² + AH²

5² = HB² + 3²

25 - 9 = HB²

HB = √16

HB = 4 in

Area of rectangle BCGH = BC × HB

                                         = 7 × 4

                                         = 28 square in.

Area of triangle ABH = \(\frac{1}{2}(\text{Height})(\text{Base})\)

                                   = \(\frac{1}{2}(BH)(AH)\)

                                   = \(\frac{1}{2}(4)(3)\)

                                   = 6 in²

Therefore, area of the composite figure = 50 + 28 + 6

                                                                  = 84 in²

Can someone help me find the area

Which statement is true regarding the graphed
functions?
A)f(0) = 2 and 9(-2) = 0
B)f(0) = 4 and g(-2) = 4
C)f2) = 0 and 9(-2) = 0
D)f(-2) = 0 and g(-2) = 0

Which statement is true regarding the graphedfunctions?A)f(0) = 2 and 9(-2) = 0B)f(0) = 4 and g(-2) =

Answers

Answer:

C

Step-by-step explanation:

at x=2 for f(x) , y=0

at x=-2 for g(x) , y=0

A bag of tokens contains 6 red, 6 green, and blue tokens. What is the probability that a randomly selected token is purple? Answer in a fraction

Answers

Answer:

The probability that a randomly selected token is red and green is 27/200 in fraction form and 0.135 in decimal form.

Step-by-step explanation:

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Given that a bag of tokens contains 9 red, 6 green, and 5​ blue tokens.

Total = 9 red + 6 green + 5 blue = 9 + 6 + 5 = 20

Total token = 20

P(E₁) is 9 out of 20 are red.

P(E₂) is 6 out of 20 are green.

⇒ P(E₁) = 9/20

⇒ P(E₂) = 6/20

Required probability P(E) = P(E₁)×P(E₂)

Required probability P(E) = 9/20 × 6/20

Required probability P(E) = 54/400

Required probability P(E) = 27/200 = 0.135

Therefore, the probability that a randomly selected token is red and green is 27/200.

Whats the correct answer answer asap for brainlist?

Whats the correct answer answer asap for brainlist?

Answers

Answer:

b elephants and zebras

Step-by-step explanation:

Answer:

Step-by-step explanation:

Comment

I'll give you the answer, but my guess is the question will be deleted because it is in the wrong place.

The answer is B. You might think it is D but those creatures are mostly in North America.

NEED HELP NOW DUE TODAY

Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.


Part A: Write an equation that could be used to determine the length of each of the five pieces of wood he cut. (1 point)


Part B: Explain how you know the equation from Part A is correct. (1 point)


Part C: Solve the equation from Part A. Show every step of your work. (2 points)

NEED HELP NOW DUE TODAYWarren is building shelves for his 3-D printed model collection. He has a piece

Answers

Part A: The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5

Part B: The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

Part C: the length of each of the five pieces of wood cut by Warren is 3.8 feet.

What is equation?

It is made up of two mathematical objects, with an equals sign (=) between them. Equations are used to represent relationships between unknown variables and can be solved to find their values.

Part A:

The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5, where x is the length of each piece of wood.

Part B:

The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

This equation can be used to calculate how much wood Warren has cut off from the original 4.5 feet of wood, which is the length of each of the five pieces of wood.

Part C:

Solving the equation from Part A:

x + 0.7 = 4.5

Subtract 0.7 from both sides:

x + 0.7 - 0.7 = 4.5 - 0.7

x = 3.8

Therefore, the length of each of the five pieces of wood cut by Warren is 3.8 feet.

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Please can someone who knows the right answer help me? From a group of 5 boys and 3 girls, a boy and a girl will be selected to attend a conference. In how many ways can the select be made?

Answers

The selection can be made in 15 different ways, taking into account the distinct combinations of a boy and a girl from the given group of 5 boys and 3 girls.

To determine the number of ways a boy and a girl can be selected from a group of 5 boys and 3 girls to attend a conference, we can use the concept of combinations.

The number of ways to choose one boy from 5 boys is 5C1, which is equal to 5. Similarly, the number of ways to choose one girl from 3 girls is 3C1, which is equal to 3.

To select one boy and one girl, we need to multiply the number of ways to choose a boy and a girl together. Using the multiplication principle, we multiply the number of choices for each category: 5C1 * 3C1 = 5 * 3 = 15.

Therefore, there are 15 ways to select a boy and a girl from the given group to attend the conference.

Each combination represents a unique pair consisting of one boy and one girl. For example, if the boys are labeled as B1, B2, B3, B4, and B5, and the girls are labeled as G1, G2, and G3, the possible pairs could be (B1, G1), (B1, G2), (B1, G3), (B2, G1), (B2, G2), and so on, up to (B5, G3).

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. A recipe calls for 32 ounces of pasta to be used. How many pounds of pasta is that if 1 ounce equals about 0.06 pounds?

Answers

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If 1 ounce is equal to 0.06 pounds then 32 ounces of pasta is equivalent to 1.92 pounds of pasta.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A recipe calls for 32 ounces of pasta to be used.

Also given that 1 ounce is equal to 0.06 pounds.

Therefore, To convert the amount of pasta to pounds from ounces we have multiply the unit rate which is (32×0.06).

= 1.92 pounds.

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what are composite numbers out of 49, 35, 32, 41, and 47​

Answers

41 and 47 because there is no multiplication fact for those numbers

Step-by-step explanation:

Composite numbers are 32,35,and 49 .

I hope it's helpful!

Simplify:

4(5y+9)


56y

9y + 13

20y + 36

I don't know.

Answers

Answer:

20y + 36

Step-by-step explanation:

Distribute the 4 to everything in the parenthesis (multiply).

4 x 5y = 20y

4 x 9 = 36

The solution of the expression 4(5y + 9 ) will be 20y + 36. The correct option is C.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The expression 4(5y+9) will be solved as below:-

E = 4 ( 5y+9 )

E = 20 y + 36

Therefore, the solution of the expression 4(5y + 9 ) will be 20y + 36. The correct option is C.

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find the point p that partitions the line segment AB given the ratio. A(3,5)B(4,3) with the ratio. 3:1

Answers

The coordinates of p which divides the line AB in ratio 3:1 is (3.75, 3.5).

What is section Formula?

The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.

P ( x , y ) = ( c ⋅ m + a ⋅ n m + n , d ⋅ m + b ⋅ n m + n ) .

Ratio of line = 3:2

m and n represents the ratios 3:2

let the coordinates of p(x, y).

using Section formula

= [ (3(4) + 1(3) / (3+1), 3(3) + 1(5) / 3+ 1]

= (15/ 4, 14/4)

= (3.75, 3.5)

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what does k equal in the proportion k/4=33/20

Answers

Answer:

\(x = \frac{33}{5} \)

or

\(x = 6 \frac{3}{5} \)

or

\(x = 6.6\)

Step by Step:

Step 1: Rewrite the equation (I used x instead of k.)

\( \frac{x}{4} = \frac{33}{20} \)

Step 2: Make x a loner by moving the 4 to the right side.

\(4 \times \frac{x}{4} = \frac{33}{20} \times 4 \)

Step 3: Cancel multiplied terms on the left, multiply numbers on the right.

\(x = \frac{165}{100} \)

Step 4: Simplify.

\( x = \frac{33}{5} \)

Mofor has homework assignments in five subjects. He only has time to do two of
them.

Answers

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Petra is making donuts by stamping circles in dough using a pastry stamp with a radius of 4.25 inches. For the donut hole, she stamps out a circle of dough using a pastry stamp with a radius of 0.4 inches

Answers

Answer:

If the radius of the pastry stamp Petra uses to stamp circles in the dough for the donuts is 4.25 inches, then the diameter is 2 * 4.25 = 8.5 inches. The area of each donut can be calculated using the formula for the area of a circle:

Area of a circle = π * radius^2

So, the area of each donut is:

π * (4.25)^2 = 56.75π square inches (rounded to two decimal places)

If the radius of the pastry stamp Petra uses to stamp out circles for the donut holes is 0.4 inches, then the diameter is 2 * 0.4 = 0.8 inches. The area of each donut hole can be calculated using the same formula:

Area of a circle = π * radius^2

So, the area of each donut hole is:

π * (0.4)^2 = 0.16π square inches (rounded to two decimal places)

Hope This Helps!

What is the slope of the line that passes through the points (0, -6) and (0, -5)?

Answers

The slope of the line that passes through the points (0, -6) and (0, -5)is undefined.

What is the slope of the line that passes through the points (0, -6) and (0, -5)?

Slope is line's inclination with regard to the horizontal is quantified numerically. In analytical geometry, a line, ray, or line segment's slope is the ratio of the vertical to horizontal distance between any two points on the line, ray, or line segment ("slope equals rise over run").

In differential calculus, the derivative of a function yields the slope of a line tangent to its graph, which represents the function's instantaneous rate of change with respect to changes in the independent variable.

Ok so slope is the change in y over change in x.

Your why changed from 6 to -5 so you can write this as -5 - 6

Your x didn’t change it went from 0 to 0

You can write this as 0-0

Now -11/0 is what you end up with as a slope.

Any number divided by 0 is undefined so your slope is undefined.

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Your teacher pulls you aside after class and tells you that during the year, you spent 65 minutes total out of class going to the restroom. You
know that every time you would walk out of class, you would come back in 5 minutes. How many times total did you use the restroom pass this
year?
What equation answers this question?

Answers

Answer:

a. You used the restroom 13 times this year.

b. The equation is 65 minutes divided by 5 minutes = 13 times you left class.

Step-by-step explanation:

If you used the bathroom for 65 minutes, and each visit was 5 minutes, you divide 65 / 5 to get 13.

Cómo dividir los números 24/-8

Answers

Answer:

-3

Step-by-step explanation:

Cómo dividir los números 24/-8:

24/-8 = -3

8 cabe en 24, 3 veces. Como el 8 es negativo, la respuesta es -3.

This data is from a sample. Calculate the mean, standard deviation, and variance. Suggestion: use technology. Round answers to two decimal places.

x
22.8
49.8
17.5
44.1
33.2
20.6
43.2
37.7


Mean =


Standard Deviation =


Variance =


Ooops - now you discover that the data was actually from a population! So now you must give the population standard deviation.

Population Standard Deviation =

Answers

1. Mean = 33.61

2. Standard Deviation = 11.3284

3. Variance = 128.33

What are the mean, standard deviation, and variance?

The given data are: \(22.8, 49.8, 17.5, 44.1, 33.2, 20.6, 43.2, 37.7\)

To get mean, we will sum up all the numbers and divide by the total count. The mean is:

= (22.8 + 49.8 + 17.5 + 44.1 + 33.2 + 20.6 + 43.2 + 37.7) / 8

= 268.9 / 8

= 33.62

Standard Deviation: \(\sqrt((22.8 - 33.61)^2 + (49.8 - 33.61)^2 + (17.5 - 33.61)^2 + (44.1 - 33.61)^2 + (33.2 - 33.61)^2 + (20.6 - 33.61)^2 + (43.2 - 33.61)^2 + (37.7 - 33.61)^2) / 8\)

= \(\sqrt{128.3336}\)

= 11.3284420818

= 11.3284

Variance = (Standard Deviation)^2

Variance = \(11.3284 ^2\)

Variance = 128.33264656

Variance = 128.33.

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Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A ∪ B' ? Your Answer:

Answers

Consequently, there are 5 elements in A B'.

Given the following definitions:

U = {1, 2, 3, 4, 5, 6, 7}A = {1, 2, 4, 5}B = {1, 3, 5, 7}

The complement of a set B is the set of all elements that belong to the universal set U but not to B.

A’ = {x | x ∈ U and x ∉ A} = {3, 6, 7}B’ = {x | x ∈ U and x ∉ B} = {2, 4, 6}

The union of sets A and B is the set of all elements that belong to set A or set B, or both.

A ∪ B = {x | x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 7}A ∪ B'

= {x | x ∈ A or x ∈ B’}

= {1, 2, 4, 5, 6}

Therefore, the number of elements in A ∪ B' is 5.

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Find the area of the polygon

Find the area of the polygon

Answers

Answer:

40

put some efforts dude...they are so easy

Answer:

40

Step-by-step explanation:

area of a triangle= ½×base× height½×4×6=10since the polygon ha four equal triangles with the same measurement,multiply by four10×4=40ans=40

hope that helps

Given: If x, then not y, if not y, then z.
Y is true. So:

Answers

If x, then not y, if not y, then z. Y is true. So: X is true, Z is True

How to Interpret Conditional Statements?

A conditional statement is a type of structure to express the relationship between two dependent variables. Its structure is as follows:

If P, then Q...

Now, from the question we are told that;

If x, then not y, if not y, then z.

Y is true. So:

Now, when looking at conditional statements in depth, and comparing to this question we can easily see that since Y is true, then it means that if X is true, then Z is also true.

Thus,

If x, then not y, if not y, then z.

Y is true. So: X is true, Z is True

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Can someone help me with this? lolz


Can someone help me with this? lolz

Answers

Answer:

Right angled triangle

Scalene

What is the distance from Mto N?
4
N(2,3)
3
2
1
5 4 3 2
1
1 2
3 4 5
2
-3
4
M-4.-5)
A. 14 units
B. 100 units
C. 10 units
D. 2 units

Answers

9514 1404 393

Answer:

  C.  10 units

Step-by-step explanation:

The distance MN can be found using the distance formula.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((2 -(-4))² +(3 -(-5))²) = √(6² +8²) = √100 = 10

The distance from M to N is 10 units.

Construction each spatial figures


Blue pyramid
Black cown
Yellow cube
Green rectangular prism
Red silendar
Violet sphere

Answers

A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a common point. The height of a pyramid is the perpendicular distance from the base to the apex.

How to explain the shapes

A cube is a three-dimensional shape that has six square faces of equal size. All angles of a cube are right angles, and all edges have the same length. The volume of a cube is given by the formula V = s³ where s is the length of one edge.

A rectangular prism is a three-dimensional shape that has six rectangular faces. The opposite faces are congruent and parallel, and all angles are right angles. The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the lengths of the three perpendicular edges.

A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

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Construction each spatial figures Blue pyramidBlack cownYellow cubeGreen rectangular prismRed silendarViolet
Construction each spatial figures Blue pyramidBlack cownYellow cubeGreen rectangular prismRed silendarViolet
Construction each spatial figures Blue pyramidBlack cownYellow cubeGreen rectangular prismRed silendarViolet
Construction each spatial figures Blue pyramidBlack cownYellow cubeGreen rectangular prismRed silendarViolet
Construction each spatial figures Blue pyramidBlack cownYellow cubeGreen rectangular prismRed silendarViolet

A data set has three data points {(2, 3), (3, -8), (4, 12)}. Find the quadratic interpolant,
Show all the following steps on a separate sheet of paper and submit to Gradescope.
a. Write the system of equations.
b. Indicate the Vandermonde matrix (V), the Y matrix, and the C matrix.
c. Write the MatLab command used to find the c values and the matrix solution that is found using MatLab
d. Write the final answer as a quadratic interpolant.

Answers

The quadratic interpolant for the given data set is y = -1.75\(x^{2}\)+ \(11.75x - 6.\)

a. To find the quadratic interpolant, we need to solve for the coefficients of the quadratic equation y = a\(x^{2}\) \(+ bx + c\), using the given data points. Plugging in the coordinates of each data point, we get the following system of equations:

\(4a + 2b + c = 3\\9a + 3b + c = -8\\16a + 4b + c = 12\)

b. The Vandermonde matrix (V), the Y matrix, and the C matrix are as follows:

V = [ \(2^{2}\)2 1;  \(3^{2}\)3 1;  \(4^{2}\)4 1] = [4 2 1; 9 3 1; 16 4 1]

Y = [3; -8; 12]

C = [a; b; c]

c. We can use MatLab to find the c values and the matrix solution. The MatLab command to solve this system of equations is:

C = V\Y

The solution we get is:

\(C = [-1.7500; 11.7500; -6.0000]\)

d. The final answer as a quadratic interpolant is:

\(y = -1.75x^2 + 11.75x - 6\)

Therefore, the quadratic interpolant for the given data set is y = -1.75\(x^{2}\)+ \(11.75x - 6.\)

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