a cube+a square b+ ab square


Please help

Answers

Answer 1

Step-by-step explanation:

\( {a}^{3} + {a}^{2} b + a {b}^{2} \)

[Taking a common from each term]

\( = a( {a}^{2} + ab + {b}^{2} )\)

\(as \: {a}^{2} + ab + {b}^{2} = {(a + b)}^{2} \)

Hence,

\( = a {(a + b)}^{2} (ans)\)


Related Questions

3√+5√? i need help asap!!

Answers

It is true that the expression √3 + 5  cannot be simplified

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to determine if the expression can be simplified?

The expression is given as

√3 + 5

The above expression is a combination of a radical expression and an integer

The radical expression √3 cannot be simplified

This means that the expression √3 + 5 cannot be simplified

Hence, the expression √3 + 5  cannot be simplified

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Complete question

Can √3 + 5 be simplified?

Yes or no

How many places will the decimal point move when solving the division problem 119.25 ÷ 100. How do you know you are correct?

Answers

Answer:

Remember a key rule in dividing numbers with decimals—you need to do the same thing to both numbers in the expression. To make 15.75 a whole number, we need to multiply it by 10 twice, or, you could say, we need to multiply it by 100. That in effect moves the decimal place over two places to the right, giving us 1,575.

Step-by-step explanation:

The table below shows the transportation method of all of the employees who work at the mall. What percent of employees walk to work?


Car: 758

Bus: 530

Walk: 7

Other: 105

Answers

Answer:

0.005 or 0.5% walk

Step-by-step explanation:

Total:

758 + 530 + 7 + 105 = 1400

To find how many employees walk:

7/1400 = 0.005

true or false? The sum of the difference is not always zero for any distribution consisting of n observations

Answers

Answer:

i believe the answer is false !

Step-by-step explanation:

given the set -2<_x<_2 where x is an integer what is the solution of -2(x-5)<10

Answers

For the given set -2≤ x ≤ 2 , x is given as integer, the solution for the given expression -2(x-5)< 10 is equal to x = 1 and x =2.

As given in the question,

Given set is equal to :

-2≤ x ≤ 2

where x belongs to integer

For the given expression -2(x-5) < 10 the solution set is equal to :

-2(x-5) < 10

Divide by -2 both the side we have,

( x -5 ) > 10 /-2

⇒ (x-5) >-5

Add 5 both the side we get,

x-5 +5 > -5 +5

⇒ x > 0

Value of x is less than or equal to 2.

x = 1 and x =2

Therefore, for the given set  -2≤ x ≤ 2 , x is given as integer, the solution for the given expression -2(x-5)< 10 is equal to x = 1 and x =2.

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explain how to determine weather two known pairs of points are on the same line

Answers

Answer: To determine if two known pairs of points are on the same line, you must calculate the slope of the line connecting the two points. If the slope of both pairs of points are equal, then the two points are on the same line. The formula for calculating the slope of a line connecting two points is (y2-y1)/(x2-x1).

Step-by-step explanation:

3x - y = 5
2x + 3y = 7
I need solving systems of equations!!!! HURRY

Answers

X = 2
Y = 1
6 - 1 = 5
4 + 3 = 7



Verify each identity.Express cosθ / secθ+tanθ in terms of sinθ .

Answers

In summary:

cosθ / (secθ + tanθ) = 1 - sinθ

To verify the given identity and express cosθ / (secθ + tanθ) in terms of sinθ, we'll start by manipulating the expression using trigonometric identities.

Recall the definitions of secθ and tanθ:

secθ = 1/cosθ

tanθ = sinθ/cosθ

Substituting these values into the expression cosθ / (secθ + tanθ), we get:

cosθ / (1/cosθ + sinθ/cosθ)

Simplifying the denominator by finding a common denominator, we have:

cosθ / (1 + sinθ) / cosθ)

To divide by a fraction, we can multiply by its reciprocal:

cosθ  (cosθ / (1 + sinθ)

Multiplying the numerators, we get:

cos²θ / (1 + sinθ)

Now, using the identity cos²θ = 1 - sin²θ (the Pythagorean identity), we can substitute it into the expression:

(1 - sin²θ) / (1 + sinθ)

To simplify further, we can factor out a common factor in the numerator:

[(1 - sinθ)(1 + sinθ)] / (1 + sinθ)

Canceling out the (1 + sinθ) term, we're left with:

(1 - sinθ)

Therefore, cosθ / (secθ + tanθ) simplifies to (1 - sinθ) in terms of sinθ.

In summary:

cosθ / (secθ + tanθ) = 1 - sinθ

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If x is a normal N(4,64) distribution, find P(X ≤ –5.2)

Answers

X is a normal distribution with mean 4 and standard deviation 8 (since the variance is 64), therefore P(X ≤ –5.2) is approximately 0.1251.

If X follows a normal distribution N(4,64), then it has a mean (μ) of 4 and a variance (σ²) of 64, with a standard deviation (σ) of 8. To find the probability P(X ≤ -5.2), we need to calculate the z-score for -5.2 and use the standard normal distribution table.
Substituting in the values, we get:
z = (-5.2 - 4) / 8
z = -1.15
Now, we can look up the probability of a standard normal distribution with a z-score of -1.15 using a table or calculator, which gives us:
P(Z ≤ -1.15) = 0.1251
Therefore, P(X ≤ –5.2) is approximately 0.1251.

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Is 3x-5y=20 and y=3/5x-1 perpendicular parallel or neither

Answers

They have the same slope, the lines are parallel to one another.

If two non-vertical lines that are in the same plane has the same slope, then they are said to be parallel. Two parallel lines won't ever intersect.

The slopes of two perpendicular lines are negative reciprocals. The product of the slopes of two perpendicular lines is -1

We need to put these equations into y=mx+b format.

3x-5y=20

-5y=-3x+20. (take 5x from both sides)

y=3/5 x -4 ( divide both sides by -3)

The slope is 3/5

y=3/5x-1

The slope is 3/5

Therefore, we can conclude that the lines are parallel to each other as they have same slope.

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Becky buys a shirt for $25, a pair of pants for $32, and a new pair of shoes for $48. She has a 20% coupon off her total. How much is the discount?

Answers

your answer should be $84

What is the volume of a cylinder in cubic ft with a height of 14ft and a base diameter of 12ft round to the nearest tenth

Answers

Answer: volume of the cylinder = 1583.36 ft3

Step-by-step explanation: where volume of a cylinder = π h

where h = 14 ft

diameter 12 ft, so radius = 12 / 2 = 6 ft

therefore volume = π * * 14 = 1583.362697 to the nearest tenths place will be 1583.36

You have two sets of data. One has an R^2 value of 0.95. the other has an R^2 value of 0.81. Which one is more linear (that is, the data more nearly fits onto a single line)? a. The one with R^2 = 0.95 is more linear b. The one with R^2 = 0.81 is more linear c. They are equally lineard. It is impossible to determine this from the information given.

Answers

As there is a greater linear relationship between the variables in the data set with an  R² value of 0.95, it is more linear. The solution given in option a, "The one with  R² = 0.95 is more linear," is correct.

In a linear regression model, the coefficient of determination, or  R², quantifies the percentage of the dependent variable's variation that is explained by the independent variable(s).

Strong linear relationships between the variables are indicated by an R² value that is close to 1, whereas weak linear relationships are indicated by a value that is close to 0.

Therefore, Because there is a stronger linear relationship between the variables in the data set with an R² value of 0.95 than in the data set with an R² value of 0.81, it is more linear.

The more closely the data points are grouped around a single line, the stronger the linear relationship, and the closer the R² number is to 1.

Therefore, We can deduce that the proper response is an option a, "The one with R²= 0.95 is more linear." Write your response in two lines.

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%50 POINTZ Which set of statements explains how to plot a point at the location (Negative 2.5, 3.75)?
Start at the origin. Move 2.5 units left because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units up because they-coordinate is 3.75. 3.75 is between 3 and 4.
Start at the origin. Move 2.5 units left because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units down because they-coordinate is 3.75. 3.75 is between 3 and 4.
Start at the origin. Move 2.5 units up because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units left because the y-coordinate is 3.75. 3.75 is between 3 and 4.
Start at the origin. Move 2.5 units right because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units up because they-coordinate is 3.75. 3.75 is between 3 and 4.

Answers

Answer:

Move 2.5 units left because the x-coordinate is -2.5. -2.5 is between -2 and -3. Move 3.75 units up because they-coordinate is 3.75. 3.75 is between 3 and 4.

Step-by-step explanation:

Look at the picture.

(x ; y)

x < 0 - move x units left

x > 0 - move x units right

y < 0 - move y units down

y > 0 - move y units up

%50 POINTZ Which set of statements explains how to plot a point at the location (Negative 2.5, 3.75)?Start

Answer:

answer is A

Step-by-step explanation:

your welcome :)

Declaring variables - Declare two integer variables x and y, - Assign them any values. - Print addition/subtraction/multiplication and division of these two variables on to the screen
Submission Task (- Grade 1%) Follow the same steps asin Exercise 2, but change the step 2 to ask the user for input forthese values by using Scanner class.

Answers

Two integer variables x and y, prompts the user to enter values for them using the Scanner class, and performs addition, subtraction, multiplication, and division operations on those variables:

import java.util.Scanner;

public class VariableOperations {

   public static void main(String[] args) {

       Scanner scanner = new Scanner(System.in);

       System.out.print("Enter the value for x: ");

       int x = scanner.nextInt();

      System.out.print("Enter the value for y: ");

       int y = scanner.nextInt();

       // Addition

       int addition = x + y;

       System.out.println("Addition: " + addition);

       // Subtraction

       int subtraction = x - y;

       System.out.println("Subtraction: " + subtraction);

       // Multiplication

       int multiplication = x * y;

       System.out.println("Multiplication: " + multiplication);

       // Division

       if (y != 0) {

           double division = (double) x / y;

           System.out.println("Division: " + division);

       } else {

           System.out.println("Cannot divide by zero.");

       }

   }

}

This code prompts the user to enter values for x and y, performs the four basic arithmetic operations, and displays the results on the screen.

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What is an
equation of the line that passes through the points (-4, 2) and
(-8, -3)?

Answers

Answer:

\(y = 1\frac{1}{4}x+7\)

Step-by-step explanation:

The equation of a straight line can be written as \(y=mx+b\).

With the pair of coordinates (coordinates are written in the form \((x,y)\) ) , the following can be written:

\(2=-4m+b\)

\(-3=-8m+b\)

To solve for a variable, we can use elimination:

\(-4m+b-(-8m+b)=2-(-3)\)  (subtract the second equation from the first)

\(-4m+b+8m-b=2+3\)

\(4m=5\) (\(b\) is eliminated)

\(m=\frac{5}{4}\)

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

To solve for the other variable, we can use substitution:

\(2=-4m+b\)

\(2=-4(1\frac{1}{4})+b\)

\(2 = -5 + b\)

\(b = 7\)

\(\therefore y=1\frac{1}{4}x+7\) is the linear equation for the line that passes through the points \((-4, 2)\) and \((-8,-3)\)

A student was asked to simplify the expression 2(x+3)+(4x−8)−7x .

Answers

Answer:

-x -2

Step-by-step explanation:

1- Apply the Distributive Property

2- Calculate the product or quotient

3- Determine the sign

4- Reorder and gather like terms

   Collect coefficients of like terms

   Calculate the sum or difference

PROBLEM 24
Can you write the equations for this word problem? Having trouble figuring out how to write the problem from a word problem.

PROBLEM 24Can you write the equations for this word problem? Having trouble figuring out how to write

Answers

Answer:

23. 22x + 15y = 228

     x + y = 11

Step-by-step explanation:

I can't really figure out the other two, I'll let you know if I get it though D: Really sorry, I wish I could help you more. Good luck man.

please help with question below

please help with question below

Answers

Answer:

0

Step-by-step explanation:

to evaluate the composite function work from the inside out

first evaluate h(2) , then substitute the value obtained into g(x) then substitute the value obtained here into f(x)

h(2) = \(\frac{1}{2}\) , then

g( \(\frac{1}{2}\) ) = \(\sqrt{2(\frac{1}{2}) }\) = \(\sqrt{1}\) = 1 , then

f(1) = 1² - 1 = 1 - 1 = 0

simplify the expresssion 2x^2+8+3x^2+4x-10

Answers

Answer:

x= 0.348 OR X= -1.148

Step-by-step explanation:

Given that:

2x^2+8+3x^2+4x-10

The first step is to rearrange the parameters given, by doing so, we have:

= 2x^2 +3x^2 +4x -10+8

= 5x^2 +4x - 2

The above equation forms the basis of a quadratic equation;

So using quadratic formula

= (-b +/- (√b^2-4ac))/2a

= (-4 +/- (√4^2 -4*5*(-2))/2*5

= -4 +/- (√ 16 - (-40))/10

=( -4 +/- √ 56 ) / 10

=( -4 +√ 56 ) / 10 OR =( -4 - √ 56 ) / 10

= (-4 + 7.48)/10 OR (-4 -7.48)/10

= 3.48/10 OR -11.48/10

= 0.348 OR. -1.148

SO, x= 0.348 OR X= -1.148

the expected value for a binomial probability distribution is group of answer choices e(x) = pn(1 - n) e(x) = p(1 - p) e(x) = np e(x) = np(1 - p)

Answers

The correct answer is e(x) = np. The expected value for a binomial probability distribution is given by the formula e(x) = np, where n represents the number of trials and p represents the probability of success in each trial.

The expected value is a measure of the average or mean outcome of a binomial experiment. It represents the number of successful outcomes one would expect on average over a large number of trials.

The formula e(x) = np arises from the fact that the expected value of a binomial distribution is the product of the number of trials (n) and the probability of success (p) in each trial. This is because in a binomial experiment, the probability of success remains constant for each trial.

Therefore, to calculate the expected value of a binomial probability distribution, we multiply the number of trials by the probability of success in each trial, resulting in e(x) = np.

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Round to the nearest thousand.64,47364,473 rounded to the nearest thousand is ?

Answers

Given the number 64,473

From the right:

• Unit digit = 3

,

• Tens digit = 7

,

• Hundred digit = 4

,

• Thousand digit =4

,

• Ten thousand digit =6

To round 64,473 to the nearest thousand, we first identify the thousand digit.

Thousand digit = 4

Next, identify the number after the thousand digit.

The number after the thousand digit = 4

When rounding numbers:

• If the number after the required number place is (0,1,2,3,4), we simply write the number.

,

• If the number after the required number place is (5,6,7,8,9), we round up.

Since the number after the thousand digit is 4. we therefore have that:

64,473 rounded to the nearest thousand = 64,000

Aj needs to buy a new car.
His dream car costs 68,700
He gets paid 625 per minute
He has got 53,350
How long does he have to wait to get his car

Answers

Answer:

24.56 minutes

Step-by-step explanation:

68,700 - (625 * x) = 53,350

We subtract 53,350 from both sides

15,350 - (625 * x) = 0

625x = 15350

x = 15350/625

x = 24.56

He needs to wait 24.56 minutes to get his car.

Just question 10 please

Just question 10 please

Answers

a. The minimum point is located at x = 2 and y = -4. The coordinates is (2,-4).

b. The equation of the line of symmetry of the graph is x = 2.

c. The solutions are approximately x = 1.3 and x = 2.7.

d. 2x²-4x+3=0 has no solutions because when 2x²-4x is graphed, the graph never intersects the x-axis at the y-value of 3. Therefore, the equation 2x²-4x+3=0 has no solutions.

What is equation of the line of symmetry?The equation of the line of symmetry is the equation of a line that passes through the center of a geometric figure such that it divides the figure into two equal parts. The equation of the line of symmetry is usually expressed in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line of symmetry is always equal to the opposite reciprocal of the slope of the original line, and the y-intercept is equal to the midpoint of the two end points of the original line. For example, if the equation for a line is y = 4x + 2 then the equation for the line of symmetry that would pass through the midpoint of the line would be y = -1/4x + 3, where 3 is the midpoint of the two end points of the original line. The line of symmetry is an important concept in geometry, as it divides a figure into two equal halves, allowing us to easily identify the center of the figure. It is also useful in calculus, as the line of symmetry helps us to calculate the area under the graph of a function. It is also used in other branches of mathematics, such as trigonometry and statistics.

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steps to describe an inscribed regular hexagon.

Answers

Answer:

many sides

unique shape

Which of the following steps is included in the construction of a perpendicular line
through a point off the line?

Answers

The  step that  is included in the construction of a perpendicular line through a point off the line is  B: Connect arcs that are either above or below the original line and a point off the line with a straightedge.

What is a perpendicular line?

Perpendicular lines can be regarded as the lines that intersect at a 90-degree angle.

for  instance,  line AB is perpendicular to line CD, hence, The  step that  is included in the construction of a perpendicular line through a point off the line is  B: Connect arcs that are either above or below the original line and a point off the line with a straightedge.

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CHECK THE COMPLETE QUESTIOPN BELOW:

Question 1 Multiple Choice Worth 1 points)

(01.03 LC)

Which of the following steps is included in the construction of a perpendicular line through a point off the line?

A: Connect arc above the line with arcs below the given line

B: Connect arcs that are either above or below the original line and a point off the line with a straightedge

C: Create arcs on either side of a point that is off the given line

D: Create a copied angle by using the first two lines as the original angle

Answer: b

Step-by-step explanation:

Select all the correct answers. the square of a number is 3 less than four times the number. which values could be the number?

Answers

The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645

In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:

When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -

x² = 3 -

When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x

x² = 3 - 4x

Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0

Where:

a=  1b= 4c= -3

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)

x= {- 4 ± √ (16 + 12)} / 2

x= {- 4± √ 28} / 2

x= (- 4 ± 5.29 ) / 2

x1= (- 4 + 5.29 ) / 2

x1= (1,29) / 2

x1= 0.645

x2= (- 4 - 5.29 ) / 2

x2= (9.29) / 2

x2= -4.645

We can check the values, replacing them into the equation:

(x1)² = 3 - 4(x1)

(0.645)² = 3 - 4*(0.645)

0.42 = 0.42

(x2)² = 3 - 4(x2)

(-4.645)² = 3 - 4*(-4.645)

21.58 = 21.58

What is a quadratic equation?

It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:

ax²+ bx + c = 0

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An 8 metre long ramp reaches a vertical height of 3 feet. What angle does it make with the ground. Convert 8 metres to feet and solve for the angle using trignometric ratios. The answer gets Brainliest:)​

Answers

Answer:

The Answer is 22.024

Step-by-step explanation:

Pretty sure its 22.024, sorry if i'm wrong

Have a nice day

What is the value of x? ​

What is the value of x?

Answers

Answer:

45 degrees, considering the angle as either equilateral or right would also work.

I think it’s 30, as the very bottom angle is 60 (equilateral from the smaller triangle) and the tangent-to-radius forms a right angle.
And 60+90=150,
180-150=30

5.

Find the coordinates of B, C, and D given that AB = 5 and BC

= 10.

Answers

The coordinates of B, C, and D are (3,-5), (3,5), and (-7,5) respectively.

Given point A (-2,-5) and the lengths of the sides AB = 5 and BC = 10, we can use this information to determine the coordinates of B, C, and D.

Using the information provided, we know that B is 5 units away from A in the positive x-direction. Therefore, the x-coordinate of B is (-2) + 5 = 3 and the y-coordinate of B is the same as that of A, which is -5. So point B is (3,-5).

Next, we know that C is 10 units away from B in the positive y-direction. Therefore, the x-coordinate of C is the same as that of B, which is 3, and the y-coordinate of C is (-5) + 10 = 5. So point C is (3,5).

Finally, we know that D is 10 units away from C in the negative x-direction. Therefore, the x-coordinate of D is 3 - 10 = -7 and the y-coordinate of D is the same as that of C, which is 5. So point D is (-7,5).

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The question is -

Find the coordinates of B, C, and D given that AB = 5 and BC = 10 where A = (-2,-5).

Other Questions
2) State True or False. 1. Abacus is an electronic device. 2. ROM is read and writes memory of computer. 3. Header and footer appear at the top and bottom of 4. The first microprocessor is INTEL 4004. 5. CTRL + A is used to print data in M.S. word. Answer the following questions: At a restaurant, Lana gets a bill that is $40 for the food plus a 5% sales tax. Lana decides to tip 20% on the total bill. How much will Lana pay in total? the alpha helix and beta pleated sheet are examples of:______. What's the factors of 2, 4,6,8? Select the correct answer from the drop-down menu. Katie is watching a helicopter flying at an altitude of 5 miles. If the angle of elevation is , the distance between katie and the helicopter is approximately miles. Chuse the correct ERGY s temperature B. M Molecules the 1 and bland 19. What is at 25C for the followers COCO.(a) a. 21 b. 45.9 217 B_20. Choose the incorrea statement Gases have less entropy than their solids Solutions have more entropy than the solids dissolved. c. Gases have more entropy than the liquids d. Liquids have more entropy than there solids. Entropy of a substance increases as its temperature increases. 21. Which of the following statements is true? Spontaneous processes proceed without outside intervention b. A spontaneous reaction is a fast reaction. c. Only exothermic processes are spontaneous. d. All the statements are true. B 22. Which of the following processes is non-spontaneous? a. Salt dissolves in water b. Photosynthesis occurs C. Ice cream melts on a hot summer day d. Hot soup gets cold before it's served 23. The change in free energy for a reaction: a. predicts speed c. equals heat b. equals AH-TAS d. depends on the standard state chosen 24. In a sealed container, the rate of dissolving is equal to the rate of crystallization would expect: d. N a. AS=0 b. AGO C. AG = 0 25. A reaction is spontaneous if 1) AG is a negative value. 11) Both enthalpy and entropy increase. III) AH is negative and AS is positive. IV) Both enthalpy and entropy decrease. V) AH is positive AS is negative. a. III and IV b. I and 111 c.land 11 the distribution of conquered towns, the right to rule the indians and the land around them, and the right to exact tribute and labor from the indians was called group of answer choices Help!!!please!!!!!!! Winter coat are marked 70% off on February 1t if a coat cot 57. 75 on January 31t how much will it cot on February 1t He is palying football into question tag me Digo qual e a resposta what is the independent variable? what is the dependent variable? what is an appropriate title? Question 3 of 25Which of the following statements best explains why some people get lifeinsurance and others don't?A. Life insurance is a cost that has no direct benefit.B. Some people have more than one life-insurance policy.C. Different people are willing to face different kinds of risks.D. Some life insurance companies go out of business before you die. What is the area of the rectangle?0 10 units20 20 units20 24 units20 48 units2 Billy exterminators inc has sales of $817,000, costs of$343,000, depreciation expense of $51,000, interest of $38,000, anda tax rate of 21%. what is the net income? Help please and also u dont just write it down it has to be like the first one but different words please help if u can Mike Klein lives in a state with an income tax rate of3.5%. What is the state withholding on a weekly grossincome of $456.85? : Write one large paragraph: If the Federal Job Act was implemented now how would that affect the next election and political tensions in the USA? Read the excerpt from Part 2 of "The Most Dangerous Game, by Richard Connell. Then, wet with sweat and aching with tiredness, he crouched behind the stump of a lightning-charred tree. He knew his pursuer was coming; he heard the padding sound of feet on the soft earth, and the night breeze brought him the perfume of the general's cigarette. It seemed to Rainsford that the general was coming with unusual swiftness; he was not feeling his way along, foot by foot. Rainsford, crouching there, could not see the general, nor could he see the pit. He lived a year in a minute. What conclusion can a reader draw about Rainsford based on a visualization of the excerpt? He is relieved. He is lost. He is frightened. He is confused. What are two strengths and two weaknesses of the Americans at the start of the war for independence