For triangle ABC, a = 79, b = 68, c = 61, then M∠A= ___ °Round answer to one decimal place.

For Triangle ABC, A = 79, B = 68, C = 61, Then MA= ___ Round Answer To One Decimal Place.

Answers

Answer 1

Given a triangle ABC below

To find the value of m∠A, we use the cosine formula which is

\(\cos A=\frac{b^2+c^2-a^2}{2bc}\)

Where

\(\begin{gathered} a=79 \\ b=68 \\ c=61 \end{gathered}\)

Substitute the values into the cosine formula above

\(\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc} \\ \cos A=\frac{68^2+61^2-79^2}{2(68)(61)} \\ \cos A=\frac{2104}{8296} \\ \cos A=0.2536 \\ A=\cos ^{-1}(0.2536) \\ A=75.3\degree\text{ (one decimal place)} \end{gathered}\)

Hence, m∠A is 75.3° (one decimal place)

For Triangle ABC, A = 79, B = 68, C = 61, Then MA= ___ Round Answer To One Decimal Place.

Related Questions

Gabriella has a smart phone data plan that costs $25 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Gabriella have to pay in a month where she used 5 GB over the limit? How much would Gabriella have to pay in a month where she used went over by x x GB?

Answers

I believe the answer would be 75+25= so $100

SOMEONE HELP !!
A shop teacher has four sockets in a drawer. They are labeled 5/16 - inches 3/8 - inches 13/32 - inches and 15/32 - inches . Which of these sockets has the smallest measurement?
A. 15/32 -inches
B. 13/32 - inches
C. 5/16 - inches
D. 3/8 - inches

Answers

Answer:

C. 5/16 - inches

Step-by-step explanation:

15/32= 0.467

13/32=0.406

5/16=0.313

3/8=0.375

fg to the power of negative 1 over g to the power of 2​

Answers

Answer:

= f / g^3.

Step-by-step explanation:

fg^-1 / g^2

= fg^(-1-2)

= fg^-3

= f / g^3.

is the sum of interior angles the same if the polygon if irregular or not
say a hexagon and a irregular hexagon might have the same interior angle sum

Answers

Answer:

Yes, it would still be considered a hexagon. The reason why we require "6 angles" is probably just because you don't want the 6 lines to cross and create "more than 6 angles". The hexagons you are probably thinking of (the one with all the angles and sides equal) would be regular hexagons.

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I NEED HELPPPP COME HELPPP THIS THE LAST ONE

I NEED HELPPPP COME HELPPP THIS THE LAST ONE

Answers

Yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes

Which statement compares the numbers correctly 23.811 > twenty-three and eight hundred eleven thousandths Twenty-three and eight hundred eleven thousandths > 23.811 Twenty-three and eight hundred eleven thousandths < 23.811 Twenty-three and eight hundred eleven thousandths = 23.811

Answers

Answer:

The correct answer is A.

Step-by-step explanation:

The areas of two similar triangles are 144 cm² and 81 cm. If one side of the first triangle is 6 cm, what is the length of the corresponding side of the second?​

Answers

Answer:

4.5 centimeters

Step-by-step explanation:

For the triangle with area 144 square cm:

144 = (1/2)(6)x

144 = 3x, so x = 48 cm

So for the triangle with area 81 square cm:

(1/2)(x)(8x) = 81

4x^2 = 81

x^2 = 81/4 so x = 9/2 = 4.5 cm and

8x = 36 cm

Answer:

4.5

Step-by-step explanation:

use ratio method to form the equation (X/6)^2=81/144solve

(-2,0) lies on the graph of the equation y = |x-1| + 3.

Answers

Answer:

Yes true i tried it out

What is the area of the regular pentagon with 5 inch sides and apothem that measures 4.2 inches?
52.5 in2
21 in2
105in2
10.5 in2

Answers

Answer:

The area of the pentagon is 52.5 in²

Step-by-step explanation:

The area of a regular pentagon is given by:

area = (5*l*a)/2

Where l is the length of each side and a is the length of the apothem. Applying the data from the problem we have:

area = (5*5*4.2)/2

area = (105)/2

area = 52.5 in²

The area of the pentagon is 52.5 in²

Select the correct answer from each drop-down menu. Graph of proportional relationships. X-axis labeled Number of Plants. Y-axis labeled Number of Roses. Line begins from origin and goes through plotted closed points at (1, 5), (2, 10), (3, 15), (4, 20). According to the graph, the relationship between the number of rose plants and the number of roses is . Reset Next

Answers

The relationship between the number of plants and the number of roses is a linear relationship.

What are the characteristics of a linear relationship?

The given points on the graph are;

(1, 5), (2, 10), (3, 15), (4, 20)

The difference between consecutive x-values is 1, which is constant;

2 - 1 = 3 - 2 = 4 - 3 = 1

Similarly, the difference between consecutive y-values is also a constant, 5;

10 - 5 = 15 - 10 = 20 - 15 = 1

The x-values are the x-coordinates of the points found by using the numbers along the X-axis, while the y-values are the y-coordinates of the points, corresponding to the numbers located along the y-axis

Given that the differences between consecutive terms of the x and y-values are constant, therefore;

The relationship between the Number of plants and the Number of Roses is a linear relationship.

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Answer:

See image

Step-by-step explanation:

Plato

Select the correct answer from each drop-down menu. Graph of proportional relationships. X-axis labeled

Show your work. The height of players in inches for a basketball team is: 85. 83. 76. 78. 89. 80. 79 81. 74. 82, 82, 84, 80, 84 The height of players in inches for a soccer team 7 70, 65, 79, 80, 69, 66, 71, 70, 74, 62, 65, 74, 74. 79, 70, 71, 72, 69, 77, 74, 70, G7, 67, 72 What is the approximate mean height difierenco between the two sports? 1. Find the mean of the basketball team. 2.5 points 2. Find the mean of the soccer team. 2.5 points 3. What is the approximate mean height difference between the two sports? 5 points​

Answers

"Basketball players are generally taller.

Basketball player heights vary slightly more.

Step-by-step explanation:

I hope this helps!

Basketball players are taller because the average (mean) of basketball players is greater than soccer players.

Basketball player heights vary more because the MAD is greater or more than the soccer players."

Ariana is going to invest in an account paying an interest rate of 1.9% compounded monthly. How much would Ariana need to invest, to the nearest ten dollars, for the value of the account to reach $110,000 in 14 years?

Answers

Answer:

110000=p(1+0.019)^168

23.62p=110000

p=4660

credit: sqdancefan

Answer:

84330

Step-by-step explanation:

The compound interest formula gives the value of an investment.

 A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. Using your given values, we can solve for P.

 110,000 = P(1 +0.019/12)^(12·14)

 P = 110,000/(1 +0.019/12)^(12·14) ≈ 110,000/1.00158333...^168

 P ≈ 110,000/1.30446

 P ≈ 84326.04 ≈ 84,330 . . . . dollars

Ariana is going to invest in an account paying an interest rate of 1.9% compounded monthly. How much

How much interest would $1,600 earn in 1 year at an annual rate of 3% compounded
annually? What would be the new balance?

Answers

48$ dollars would be the correct anwser

What is the domain? I need help on this problem

What is the domain? I need help on this problem

Answers

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

How to determine the domain of the function

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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a)
Multiply:
2y x 6y2 x (-4y)​

Answers

Answer:

-48y⁴

Step-by-step explanation:

2y × 6y² × (-4y)​

-48y⁴

Answer=-48y*4
2y x 6y*2 x(-4y) =
-48y*4

a dealership is allowing residents to test drive the following vehicles: 2 sports cars, 3 vans, and 3 trucks. if you select a random car to test drive, what are the odds it is not a sports car? write your answer as 1:2 which is reduced as much as possible.

Answers

Step-by-step explanation:

To find probability ratio wise

Sports Cars: Total Cars

3 + 3 + 2 = 8 total cars

2 sports cars

Ratio is 2:8

Reduces to 1:4

Which is equivalent to the following expression?
4(9m + 3) + 9 - 2(3m)
a. 16m + 9
b. 30m + 21
c. 30m + 9
d. 42m +21

Answers

30m +21

4(9m + 3) + 9 - 2(3m), distribute the numbers into the parenthesis 36m+12+9-6m, combine like terms 30m + 21

Answer:

\( \huge{ \bold{ \boxed{ \text{30m + 21}}}}\)

Step-by-step explanation:

\( \text{4(9m + 3) + 9 - 2(3m) }\)

\( \text{Step \: 1} : \text{Distribute \: 4 \: through \: the \: parentheses}\)

➵ \( \text{36m + 12 + 9 - 2(3m)}\)

\( \text{Step \: 2} : \text{Multiply \: 2 \: by \: 3m}\)

➵ \( \text{36m + 12 + 9 - 6m}\)

\( \text{Step \: 3 : \: Combine \: like \: terms}\)

\( \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}\)

➵ \( \text{36m - 6m + 12 + 9}\)

➵ \( \text{30m \: + 12 + 9}\)

\( \text{Step \: 4 : Add \: the \: numbers}\)

➵ \( \text{30m \: + \: 21}\)

\( \sf{Hope \: I \: helped}\)!

\( \sf{Best \: regards}\) !

~TheAnimeGirl

The eigenvalues of a matrix A are the same as the eigenvalues of the reduced row echelon form of A.TRUE/FALSE

Answers

False, The eigenvalues of a matrix A are not same as the eigenvalues of the reduced row echelon form of A.

A matrix's eigenvalues are not the same as those of the matrix's reduced row echelon form, contrary to what is claimed.

This is due to the fact that when a matrix is reduced to its echelon form via row operations, its eigenvalues may not always stay the same. The eigenvalues of a matrix may be different in the reduced row echelon form than they are in the original matrix as a result.

Think about these matrices as an illustration:

Likewise, B's reduced row echelon form is B, and B's eigenvalues are both 1.

A = [1 2; 2 1]

and

B = [1 0; 0 1].

The eigenvalues of a matrix and its reduced row echelon form are thus typically not the same.

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FALSE. The eigenvalues of a matrix A are NOT the same as the eigenvalues of the reduced row echelon form of A.

Explanation:

Eigenvalues are scalar values that, when multiplied by an eigenvector, produce the same effect as the original matrix A on that eigenvector. Mathematically, for a matrix A and its eigenvector v, Av = λv, where λ is the eigenvalue.

Row echelon form is a matrix transformation using elementary row operations to obtain a triangular form. The reduced row echelon form (RREF) is a further simplified version of the row echelon form.

However, transforming a matrix A to its RREF changes the properties of the matrix, and therefore the eigenvalues of matrix A and its RREF are generally not the same. The eigenvalues are preserved only under specific matrix transformations, such as similarity transformations, which row echelon form is not one of them.

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Look for a pattern in the first three diamonds below. For the fourth diamond, explain how you could find the missing numbers (?) if you know the two numbers

Copy the Diamond Problems below onto your paper. Then use the pattern you discovered to complete each one.

HELPPP PLEASE

Look for a pattern in the first three diamonds below. For the fourth diamond, explain how you could find

Answers

Answer:

See below.

Step-by-step explanation:

The top number is the product (multiplication) of the two side numbers. The bottom number is the sum (addition) of the two side numbers.

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Look for a pattern in the first three diamonds below. For the fourth diamond, explain how you could find

10÷2=5

5+2=7

6÷3=2

2+3=5

4÷-4=-1

-1-4=-5

this is the pattern

What is a response variable in stats?

Answers

A response variable in statistics is a variable that is being measured or observed in a study. It is thought to be affected by the explanatory variable.

Response variable in statistics is a variable that is being measured or observed in a study. It is also known as the dependent variable or the outcome variable.

This variable is thought to be affected by the explanatory variable, also known as the independent variable.

This allows us to understand if the changes involved are significantly related or not or whether it is due to certain factors.

For example, if a study is examining the effect of exercise on weight loss, the response variable would be weight loss and the explanatory variable would be exercise. The response variable is typically plotted on the y-axis of a graph, while the explanatory variable is plotted on the x-axis.

In summary, a response variable in statistics is a variable that is being measured or observed in a study.

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does anyone know how to do this​

does anyone know how to do this

Answers

Step-by-step explanation:

So you're going to try to always make the equation be in a y= mx +b point slope form. It just makes creating a graph easier.

First, we're going to put x to the opposite side so it's in the y= mx + b form. Remember that every time you cross the equal sign you do the opposite -\(x^{2}\) turns into + \(x^{2}\).  

y- \(x^{2}\) = -1 becomes y = \(x^{2}\) -1.

Now all you have to do is plug in values. I recommend you start off small, so they can fit in your graph.

An example would be x = 2 now you plug in to find y which is \(2^{2}\) = 4 -1 = 3. So you graph the point (2, 3).

To find the x- intercept and y- intercept you need to plug in 0. For the y-intercept, plug in 0 for x, since you're trying to find the y.

y = \(0^{2}\) - 1. The y-intercept is -1 or the point (0, -1)

For the x-intercept, plug in 0 for y, since you're trying to find the x.

0 = \(x^{2}\) -1 . Because you're trying to find x, you need to isolate x. Move -1 to the other side. Again, remember since you're moving across the = sign it changes to be positive. 1 = \(x^{2}\). To get rid of squared, you're going to have to square root it. \(\sqrt{x^2}\) = x and \(\sqrt{1}\) = 1. So the x- intercept is 1 or the point (1, 0).

To make the graph, know that the y axis is vertical (up and down) and the x axis is horizontal (left right). So, the point (0,0) would be on the bottom left corner.

Un auto A se desplaza por una carretera recta a una velocidad constante de 80 km/h otro auto B se localiza 30 km delante del auto a y se desplaza por la misma carretera a una velocidad constante de 60 km/h  ¿cuál es la regla de correspondencia de ambos autos? Y sutabla de valores?

Answers

Question in English:

Car A travels along a straight road at a constant speed of 80 km / h another car B is located 30 km in front of the car and it travels along the same road at a constant speed of 60 km / h cuál what is the rule of correspondence of both cars? And your table of values?

Plzzzzz give me Brainliest!!!!!  

Question 3 Type numbers in the boxes. 10 points Let A and B be two independent events such that P(A) = 0.34 and P(B) = 0.56. What is P(A or B)? Your answer should be given to 4 decimal places.
Question 4 Type numbers in the boxes. 10 points Let A and B be two independent events such that P(A) = 0.3 and P(B) = 0.5. What is P(A and B)? Your answer should be given to 2 decimal places.
Question 5 Type numbers in the boxes. 10 points Let A and B be two disjoint events such that P(A) = 0.41 and P(B) = 0.1. What is P(A and B)?
Question 6 Type numbers in the boxes. 10 points Let A and B be two disjoint events such that P(A) = 0.05 and P(B) = 0.4. What is P(A or B)?

Answers

Question 3: The probability that two separate event A and B will occur together (P(A or B)) is 0.7424

Question 4: The probability of the intersection of event A and B P(A and B) is 0.15.

Question 5: The probability of the intersection of event A and B P(A and B) is 0.

Question 6: The probability that two separate event A and B will occur together (P(A or B)) is 0.45

Question 3:

You may calculate the probability that two separate event A and B will occur together as follows:

P(A or B) = P(A) + P(B) - P(A and B)

As, A and B are independent events,

P(A and B) = P(A) x P(B)

P(A or B) = P(A) + P(B) - P(A) x P(B)

P(A or B) = 0.34 + 0.56 - 0.34 x 0.56

P(A or B) = 0.7424

Rounding to four decimal places, the chance of choosing A or B is therefore 0.7424.

Question 4:

As per the given information,

A and B are independent events,

The probability of their intersection can be calculated as:

P(A and B) = P(A) x P(B)

P(A and B) = 0.3 x 0.5

P(A and B) = 0.15

With two decimal places added, the probability of A and B is thus 0.15.

Question 5:

As per the given information,

A and B are nonoverlapping events, so they have no outcomes in common,

so their intersection has probability zero:

P(A and B) = 0

Question 6:

As per the given information,

A and B are nonoverlapping events, so they have no outcomes in common,

so their intersection has probability zero:

P(A and B) = 0

To find the probability of the union of A or B, we can use the following formula:

P(A or B) = P(A) + P(B) - P(A and B)

As A and B are nonoverlapping event, P(A and B) = 0:

P(A or B) = P(A) + P(B)

P(A or B) = 0.05 + 0.4

P(A or B) = 0.45

So, the probability of A or B is 0.45.

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the total of three consecutive numbers is 210. what are the numbers. show all work

Answers


Let n = the first of three consecutive numbers.

Let n + 1 = the second consecutive number, and ...

Let n + 2 = the third consecutive number.

Since we're given that: "the sum of three consecutive numbers is 210," then we can now translate this statement mathematically into the following equation to be solved for the unknown number n:
n + (n + 1) + (n + 2) = 210

n + n + 1 + n + 2 = 210

Collecting like-terms on the left, we get:
3n + 3 = 210

3n + 3 - 3 = 210 - 3

3n + 0 = 207

3n = 207

(3n)/3 = 207/3

(3/3)n = 207/3

(1)n = 69

n = 69

Therefore, ,...
n + 1 = 69 + 1 = 70 and

n + 2 = 69 + 2 = 71

CHECK:
n + (n + 1) + (n + 2) = 210
69 + (70) + (71) = 210
69 + 70 + 71 = 210
210 = 210

Therefore, the three consecutive numbers whose sum is 210 are indeed 69, 70, and 71, and 71 is obviously the largest of these three numbers

The shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, determine what percentage of the circle is shaded

Answers

If the shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, the percentage of the circle is shaded is: 31.83% .

What percentage of the circle is shaded?

We can start by finding the area of the entire circle. The formula for the area of a circle is:

A = πr^2

where A is the area and r is the radius. Since the diameter of the circle is 10 cm, the radius is half of that, or 5 cm. Therefore, the area of the entire circle is:

A = π(5 cm)^2 = 25π cm^2

Next, we can find what percentage of the circle is shaded by dividing the shaded area by the total area of the circle and multiplying by 100:

Percentage shaded = (shaded area / total area) x 100

Percentage shaded = (25 cm^2 / 25π cm^2) x 100

Percentage shaded = 100 / π ≈ 31.83%

Therefore, approximately 31.83% of the circle is shaded.

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Look at the shape below.

How many angles inside the shape are less than a right angle.

Answers

Answer:

i need to see shape

Step-by-step explanation:

Which ratio is the odd one out?
6:24
4:16
1:4
3:12
8:31

Answers

Answer:

8:31

Step-by-step explanation:

all of them are equal with 1:4 except 8:31

what is Hola, soy el chico nuevo de la clase y me gustan los coches. in english and what is 20+20+x56?

Answers

1. Hi, Im the new kid in class and I like cars.

2. 2240.

( 20 + 20 = 40)

40 x 56 = 2240.

Answer:

it means ''Hi I'm the new kid from class and I like cars.

and 2240 is the answer for the equation

Step-by-step explanation:

hope this helped you!

Describe your reaction upon beginning this course. What are you hoping to gain from taking this course? Are you already familiar with epidemiological concepts and methods? If so, how? Which topics are most interesting to you, and why? How do you think epidemiology impacts positive social change? How do you think that you will or can use information from this course in your career as a public health professional to effect positive social change?

Answers

Epidemiology is the study of the patterns, causes, and effects of health and disease conditions in populations. While I don't have personal experiences or hopes, individuals taking an epidemiology course may have various expectations and goals.

Some common reasons for taking an epidemiology course may include gaining a comprehensive understanding of epidemiological concepts and methods, acquiring practical skills for conducting research and analyzing data, and applying epidemiological knowledge to improve public health outcomes.

Epidemiology is a multidisciplinary field that encompasses a wide range of topics, such as study design, data analysis, disease surveillance, outbreak investigation, and risk assessment. Each topic offers unique insights into understanding and addressing public health challenges. For example, studying disease transmission patterns can help identify preventive measures and develop effective interventions to control infectious diseases. Analyzing risk factors for chronic diseases can inform targeted prevention strategies and health promotion initiatives.

Epidemiology plays a crucial role in driving positive social change by providing evidence-based insights for decision-making and policy development. By understanding the distribution and determinants of health and disease, epidemiologists can identify health disparities, assess the effectiveness of interventions, and contribute to health equity initiatives. Epidemiology also informs public health responses during outbreaks and emergencies, helping to protect populations and minimize the impact of disease outbreaks.

Professionals in public health can utilize the knowledge and skills gained from an epidemiology course to conduct research, collect and analyze data, evaluate interventions, and contribute to evidence-based public health practices. They can use this information to advocate for policy changes, implement preventive measures, and address health disparities, ultimately working towards positive social change in their communities and beyond.

In summary, an epidemiology course equips individuals with the necessary tools and understanding to contribute to public health and effect positive social change. By applying epidemiological concepts and methods, public health professionals can make informed decisions, develop effective interventions, and advocate for policies that improve population health outcomes.

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Evaluate. 6! (6-3)! 61 (6-3)!

Answers

Six factorial (6!) is equal to six multiplied by five multiplied by four multiplied by three multiplied by two multiplied by one, divided by three multiplied by two multiplied by one expression  (3 × 2 × 1).

6! (6-3)!

= 6 × 5 × 4 × 3 × 2 × 1 / 3 × 2 × 1

= 6 × 5 × 4 / 3 × 2 × 1

= 120 / 6

= 20

6! (6-3)! is a mathematical expression that can be simplified by breaking it down into two parts. The first part is 6! which stands for 6 factorial and is equal to 6 multiplied by 5 multiplied by 4 multiplied by 3 multiplied by 2 multiplied by 1. The second part is (6-3)! which stands for (6 minus 3) factorial and is equal to 3 multiplied by 2 multiplied by 1. When these two parts are combined, the expression can be simplified to 6 × 5 × 4 divided by 3 × 2 × 1, which equals 120 divided by 6, which is equal to 20.

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we can use analysis to reach a _____ Simplify the expression x - 2/3 - 1/2x . (A) 1/2x - 2/3(B) -1/3x - 3/4(C) 1/4x - 1/2 what are 5 resources valued by human society? please solve a and b thank you2. Consider the points F(-4, -1), G(-2,-5), H(4, -2) and J(2,2). a. Graph the points. b. What type of quadrilateral is FGHJ? Justify your reasoning. Your goal is to create a college fund for you child. Suppose you find a fund that offers an apt of 6% . How much should you deposit monthly to accumulate $80,00 in 14 years Use Calculus of polar curves to SET UP an integral that would compute the area of the region that is outside the circle r = 2 and inside the circle r = 4 cos . DO NOT evaluate the integral after it is set up. A sketch of the curves is found below. (5 points) Complete each sentence or statement.The city of___________ became the city of New York. SAS Text Miner is one of the commercial software tools utilizedto analyze unstructured data and extract relevant insights.Identify and briefly explain (not more than 500 words)five useful features what is the Solution for 3x-8y=29 3x+y=-2 Which property is used in the following expression?7(9 + 8) = 63 + 56A.Distributive PropertyC. Commutative Property ofAdditionB.Associative Property of AdditionD. AssociativeProperty of Multiplication Cu 16. Hm s y=4 -x t gi tr nh nht ti x. Gi tr ca x l:A. x=3.B.x=0 hoc x=2. C.x=0.D.x=-2 hoc x=2. Year 0 1 2 3 4 Cash Flow -12,000 5000 5000 5000 5000 Assume the appropriate discount rate for this project is 13%. The payback period for this project is closest to OA) 2.40 years OB) 1.92 years OC) 2.88 years D) 3.60 years if y=3x - 5, find the value of y when x = -1yn Please help!12. Re-write the following sentence in the negativeJe prends le bus pour aller lcole. A car moving at 60 mph slams on its brakes to stop before hitting a deer. Another identical car traveling at 60 mph slows to a stop at a stop sign. Who experiences the greatest impulse during the stop What is the missing word in this sentence? Millimetres of _____ are the units used to measure blood pressure. Explain how cell division is linked to cell theory. how does mariam change as she sees rasheed becoming more upset with laila? What is the speed 0.36km/h in cm/s Select all of the equations below that are equivalent to:8 = k 3Use properties of equality.