Please help with the attached photo.

Please Help With The Attached Photo.

Answers

Answer 1

The solution to the equation r(1 - 2cosФ) = 1 is given as x² + y² - 4x√(x² + y²)  + 4x² = 1

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

In polar form:

r = √(x² + y²) and cosФ = x / √(x² + y²)

Hence:

r(1 - 2cosФ) = 1

√(x² + y²) [1 - 2(x / √(x² + y²))] = 1

√(x² + y²) - 2x = 1

Take square of both sides:

x² + y² - 4x√(x² + y²)  + 4x² = 1

The solution to the equation r(1 - 2cosФ) = 1 is given as x² + y² - 4x√(x² + y²)  + 4x² = 1

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Related Questions

Find the solutions to x² = 8.
A. x- +4√6
B. x- +4√√2
C. x=+2√4
D. x=+2√2

Answers

Answer:

D. 2√2

Step-by-step explanation:

x² = 8

x = √8

x = √4 x √2

x = 2√2

Step-by-step explanation:

[tex] x {?}^{2} \sqrt{2 \times 2 \times 2} \\ \\ x { }^{2} = 2 \sqrt{2} [/tex]

which relation describes the graph?

Answers

Answer:

A.

Step-by-step explanation:

The other graphs answers have a point at (3, 1) which is not on the graph.

Pls help why did she flip the sign i dont understand

Answers

Answer:

See below

Step-by-step explanation:

When you multiply or divide both sides of an inquality equation by a NEGATIVE number , it reverses the symbol to see this in action:

- 4n >36       Instead of dividing by -4   let's ADD - 4n to both sides

0 > 36 + 4n    now SUBTRACT 36 from both sides

-36 > 4n       re-arrange just a little

4n < -36       <======== see how the symbol has reversed ???

n < -9        

Hii!

___________________________________________________________

Answer:

'Cause both sides were divided by a negative number! ^^

Step-by-step explanation:

The sign of the inequality was flipped because you divided both sides of the inequality by -4, which is a negative number.

When we divide, or multiply, both sides of an inequality by a negative number, we flip the inequality sign.

--

Hope that this helped! Best wishes.

--

4Days 7hours 16 minutes

Answers

Answer:

6190

Step-by-step explanation:

you multiply 4 days by 24 because a day have 24 hrs,then you will multiply the answer by 60 ,then after multiplying by 60 you will add 16 minutes and if you want to put is in seconds you multiply by 60 again that's what I know

which matrix can be used to solve the system

Answers

Answer:

6x + 7y = 14

7x + 8y = 27

6 7. x = 14

7 8. y = 27

option B

A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold. The business manager requires that a profit of at least $100 be earned every hour. The product manager estimates that the expenses for running the machine are $45 per hour. What is the least number of sweaters that must be produced each hour to earn a profit of at least $100?

Answers

The least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.

What is inequality?

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold.

Let x be the number of sweaters that must be produced each hour to earn a profit of at least $100

Total selling price if earns $4 profit for each one sold = 4x

The expenses for running the machine are $45 per hour.

4x - 45 ≤ 100

4x ≤ 145

x ≤ 145/4

x ≤ 36.25

Number of sweater(estimate value) = 37

Thus, the least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.

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Find two functions f(x) and g(x) such that h(x) = ( f∘ g)(x) , if h(x) = √ + 5

f(x) = ____________________

g(x) = ____________________

Answers

If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.

How to find the two functions behind a composed function

Let be f and g two functions, h is a composition of f with respect to g when the input variable of f is equal to g.  The composed function is h(x) = √x + 5 and there may be more than a solution. One of these solutions are f(x) = x + 5 and g(x) = √x.

If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.

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Genesis throws a ball up in the air. The graph below shows the height of the ball hh in meters after tt seconds. Find the interval for which the ball’s height is decreasing.


help please

Answers

We conclude that the interval in which the function decreases is (1.5, 3]

In which interval is the ball's height decreasing?

The ball is decreasing when the graph, reading from left to right, is going downwards.

Particularly, in this parabola that opens downwards, the graph will decrease after the vertex.

And we can see that the vertex is at x = 1.5

And we also see that the graph of the function ends at x = 3.

Then we conclude that the interval in which the function decreases is (1.5, 3]

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What is the surface area of the figure? 9 ft 9 ft 15 ft 15 ft 4 ft

Answers

The surface area of the given composite figure is; 528 ft²

How to find the area of a composite figure?

To get the surface area of the attached composite shape, we will have to break the object down into smaller shapes to get;

Surface area 1 = 2(15 * 4) = 120 ft²

Surface area 2 = 2(9 * 4) = 72 ft²

Surface area 3 = 2(6 * 4) = 48 ft²

Surface area 4 = 2((15 * 15) - (9 * 9)) = 288 ft²

Thus;

Total surface area = 120 + 72 + 48 + 288

Total surface area = 528 ft²

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Briana monitors the number of E. coli infections reported in a certain
neighborhood in a given week. The recent numbers are shown in
this table:

According to her reports, the reported infections are growing at a
rate of 50%.

If the number of infections continues to grow exponentially,what
will the number of infections be in week 6?

Answers

An equation is formed of two equal expressions. The number of infections in 6 weeks is 456.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.


The general equation of an exponential function is written as,

y = A(B)ˣ

Since the infection is increasing at a rate of 50%, therefore, the rate of growth will be,

B = 1.50

Substitute any value then we will get,

40 = A(1.50)⁰

A = 40

Thus, the exponential equation of the growth will be,

y = 40(1.50)ˣ

Now, the number of infections in 6 weeks will be,

y = 40(1.50)⁶

y = 455.625 ≈ 456

Hence, the number of infections in 6 weeks is 456.

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What is the solution to this equation? 2ln4+lnx=3ln2+ln(x+1)

Answers

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Given equation:

[tex]2 \ln 4+\ln x=3 \ln 2+\ln(x+1)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x = \ln x^n[/tex]

[tex]\implies \ln 4^2+\ln x=\ln 2^3+\ln(x+1)[/tex]

Simplify:

[tex]\implies \ln 16+\ln x=\ln 8+\ln(x+1)[/tex]

Subtract ln 8 from both sides:

[tex]\implies \ln 16+\ln x- \ln 8=\ln(x+1)[/tex]

Subtract ln x from both sides:

[tex]\implies \ln 16-\ln 8=\ln(x+1)-\ln x[/tex]

[tex]\textsf{Apply the quotient law}: \quad \ln x - \ln y = \ln \frac{x}{y}[/tex]

[tex]\implies \ln \left\dfrac{16}{8}\right = \ln \left(\dfrac{x+1}{x}\right)[/tex]

Simplify:

[tex]\implies \ln 2 = \ln \left(\dfrac{x+1}{x}\right)[/tex]

[tex]\textsf{Apply the equality law}: \quad \textsf{if }\: \ln x= \ln y\:\textsf{ then }\:x=y[/tex]

[tex]\implies 2=\dfrac{x+1}{x}[/tex]

Multiply both sides by x:

[tex]\implies 2x=x+1[/tex]

Subtract x from both sides:

[tex]\implies x=1[/tex]

find the x intercepts of the following linear function 3x-5y=-15

Answers

Answer:

(-5, 0)

Step-by-step explanation:

The y value of an x intercept is always 0. Therefore, we can substitute 0 for y in the equation to find the x intercept:
3x - 5(0) = -15
3x = -15
x = -5
The x intercept is (-5, 0)

I got (-5,0) not 100% sure it’s right could be (5,0) but I think it’s the first one more!!

Which is the graph of 2x - 4y > 6?
-4 -2
2
-2
2
RUTA
4-2
414
2
O
W
4 -4-2
414
2
-2
O
2
RY
4
-2
2
211

Answers

Answer:

  (d)  see attached

Step-by-step explanation:

There are a couple of quick checks you can do to identify the correct graph.

__

shading and line style

Find a variable with a positive coefficient, and write that in the given relation to the inequality symbol:

  x >

This tells you ...

shading is to the right of the line (where x-values are greater)the line is dashed (the = case is not included)location of the line

The x-coefficient is a factor of the constant, so the x-intercept of the boundary line is easily found. Set y=0, and you have ...

  2x = 6

  x = 3

The boundary line you're looking for has an x-intercept at x=3.

__

The correct graph is shown in the attachment.

A car travels at 80 km an hour. How far will it travel in 2 1/2 hours?​

Answers

200 km
or if it’s miles it’d be approximately 124 miles, or 124.3008079552517 miles

If f(n)= n²-n, then f(-4) is
O-20
12
-12
20

Answers

Answer: 20

Step-by-step explanation:

f(-4) = -4² - (-4)

f(-4) = 16 + 4

f(-4) = 20

pls someone help me asap

Answers

Answer:

Area: 15.53 square inches

Perimeter: 15.71 inches

Step-by-step explanation:

Area:

So the area of the rectangle is pretty easy to find and is just the width * height. In this case it's 4 * 3 which is 12. Now the area of a circle is [tex]\pi r^2[/tex]. But since this is a semi circle it's half of that which is [tex]\frac{\pi r^2}{2}[/tex]. The diameter of the semicircle is 3 as it sits on top of the rectangle. The radius is half of the diameter so the radius is 1.5. Now plug that into the equation and you get [tex]\frac{(3.14) (1.5)^2}{2} = 3.5325[/tex]. Now add that to 12 and you get 15.5325. Round that number to the nearest hundredth and you get 15.53. So that's the area.

Perimeter:

Pi is the ratio of any circle's circumference to the diameter. Or in other words the circumference is equal to the diameter * 3.14. The diameter is 3 which you multiply by 3.14 to get the circumference of a circle. This will get you 9.42 but since it's a semicircle, the circumference is half of this value which is 4.71. The perimeter of the rectangle is just 2 times the width + 2 times the height. This is not completely the case in this shape since one of the sides of the rectangle is not a side of the two shapes joined together. Which is the side that is parallel to the side of length 3 inches. So the perimeter is going to be 2(4) + 3. This gives you 11 which you add to the 4.71 and get 15.71

What are the possible values of x in 8x² + 4x=-1? OA 2+1√2 3 -1±i 16 SOB. OC -1t с. 4 OD. 11 4 OE. 1ti√2 1+1/2 4 What are the possible values of x in 8x² + 4x = -1 ? OA 2 + 1√2 3 -1 ± i 16 SOB . OC -1t с . 4 OD . 11 4 OE . 1ti√2 1 + 1 / 2 4​

Answers

Answer:

4

Step-by-step explanation:

4

The possible values of x are:

x = -1/2 + i/2

x = -1/2 - i/2

What is a quadratic equation?

A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

To find the possible values of x in equation 8x² + 4x = -1, we need to solve for x.

First, we can rearrange the equation to get:

8x² + 4x + 1 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).

In this case, a = 8, b = 4, and c = 1. Substituting these values into the quadratic formula, we get:

x = (-4 ± √(4² - 4(8)(1))) / 2(8)

x = (-4 ± √(16 - 32)) / 16

x = (-4 ± √(-16)) / 16

x = (-4 ± 4i) / 16

where i is the imaginary unit, which is defined as the square root of -1.

Therefore, the possible values of x are:

x = (-4 + 4i) / 16

x = (-4 - 4i) / 16

These values can also be simplified as:

x = -1/2 + i/2

x = -1/2 - i/2

So the possible values of x are complex numbers, specifically x = -1/2 ± i/2.

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Find the value below using your calculator. Round to the nearest hundredth. e³ Find the value below using your calculator . Round to the nearest hundredth . e³​

Answers

The value of e³ = 20.079.

What is Euler's number , e ?

e is an irrational number , It is a numerical constant used in mathematical constant .

The value of e = 2.718

It is asked in the question to determine the value of e³

Therefore

e³ = ( 2.718)³

e³ = 20.079

Therefore the value of e³ = 20.079.

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Select the correct answer. Consider this function. Which graph represents the inverse of function f? The linear function on a coordinate plane passes through (4, 3), and (2, 2) which intercepts the axis at (0, 1), and (minus 2, 0). W. The linear function on a coordinate plane passes through (minus 4, 4), and (2, 1) which intercepts the axis at (4, 0), and (0, 2). X. The linear function on a coordinate plane passes through (3, 4), and (minus 1, minus 4) which intercepts the axis at (1, 0), and (0, minus 2). Y. The linear function on a coordinate plane passes through (minus 1, 4), and (2, minus 2) which intercepts the axis at (0, 2), and (0, 1). Z. A. W B. X C. Z D. Y

Answers

Answer:

A , C , D  , i thinks it another one but ionk

Step-by-step explanation:

Tim earns 96pounds for 16 hours. Tim earns 'time and a half' for overtime. he works 4 hours of overtime in addition to his normal 16 hours. how much does he earn altogether​

Answers

find hourly rate:

96 / 16 = 6 pounds per hour

6 x 1.5 = 9 pounds per hour for overtime.

9 x 4 = 36 pounds


96 + 36 = 132 pounds total

132

196/16 = 6 per hr
overtime = 6*1.5=9
96 + (9*4) = 132

Christina knits a scarf for each of her 7 friends. Altogether, the scarfs had a total length of 39.9 ft. if each scarf has the same length. how long was each scarf? write answer in inches

Answers

The length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft

Length of each scarfNumber of friends = 7Total length of scarf = 39.9 ft

Length of each scarf = Total length of scarf / Number of friends

= 39.9 ft / 7

= 5.7 ft

Therefore, the length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft

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If there are 3500 students in a school and 3/7 of them
are majoring in business, how many of them are majoring in business?

Answers

Answer:

1500

Step-by-step explanation:

3/7 of 3500

=3/7 × 3500

=150

Denise and Stacey went to a carnival. The admission fee was $6 per person. Each ride at the carnival costs c dollars. The game booths charged g dollars for each game. Both Denise and Stacey went on 7 rides each. Stacey played 3 games, while Denise played 2 games. Which expression represents the total amount of money that Denise and Stacey spent at the carnival?

Answers

The total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.

What is total amount?

The amount that you get when you add several numbers or things together.

The total amount of money that Denise and Stacey spent at the carnival will be money spent on admission + ride + game.

Total amount = 2 * 6 + 2 ( 7 * c ) +  ( 3 * g + 2 * g )

                      = 2 * 6 + 14 * c + 5 * g

                      = 12 + 14c + 5g dollars.

Therefore, the total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.

The questions seems incomplete, its option could be:

12 + 14c + 5g 12 + 14g + 5c 12 + 7g + 5c 12 + 7c + 5g.

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Katie divided a drink with a volume
of 3½ cups into ½ cup servings.
How many servings did she have?

Answers

Answer:

Step-by-step explanation:

she has 7 servings. Add 1/2 + 1/2 until you get 3 1/2 and it equals 7

4. Use the formula for the area of a circle to derive the formula for the area of a sector.

Answers

The area of a circle to derive the formula for the area of a sector will be (θ/2π) x (area of the circle).

What is the area of the sector?

Let r be the radius of the circle. Then the area of the circle will be

Area = πr²

Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be

Area = (θ/2π) πr²

Area = (θ/2π) x (area of the circle)

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Solve for x in the triangle. Round your answer to the nearest tenth.
14
x
68
X

Answers

Answer:

x=15.1

Step-by-step explanation:

Side definitions

In a right triangle, the side across from the right angle is always the hypotenuse.

The other two sides are termed "legs".

Once one of the other two angles is chosen as the angle to work from, then the two legs can be defined as the "opposite" and the "adjacent"

The leg touching the angle is the "adjacent" leg (or adjacent side), and the leg across from the angle is the "opposite" leg (or opposite side).

Trigonometric function definitions

[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]

[tex]\cos(\theta)=\dfrac{\text{adjacent side}}{\text{hypotenuse}}[/tex]

[tex]\tan(\theta)=\dfrac{\text{opposite side}}{\text{adjacent side}}[/tex]


The given situation

In this situation, the given angle is in the bottom right.  A value is given for the side opposite the given angle, and the requested value is on the hypotenuse.

So, the two sides of interest are the "opposite" and the "hypotenuse".  The trigonometric function that relates these two sides is the sine function.

Calculating x

[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]

[tex]\sin(68^o)=\dfrac{(14)}{(x)}[/tex]

Evaluating the sine function in a calculator (in degree mode):

[tex]0.9271838546...=\dfrac{14}{x}[/tex]

Multiply both sides by x:

[tex](0.9271838546...)x=\left (\dfrac{14}{x} \right)x[/tex]

[tex](0.9271838546...)x=14[/tex]

Divide both sides by the decimal number:

[tex]\left (\dfrac{(0.9271838546...)x}{0.9271838546...} \right)=\dfrac{14}{0.9271838546...}[/tex]

[tex]x=15.0994864...[/tex]

Rounded to the nearest tenth, x=15.1

In a board game, you gain 1.5x the number of coins in your purse every time you pass start. However, you max out at 300 coins. If you have 5 coins in your purse, how many times must you pass until you reach maximum?

Answers

Answer:

6

Step-by-step explanation:

The requried number of passes to reach the maximum is given as 10 passes.

What is an exponential function?

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,

We have 5 coins in your purse,
We Gain 1.5x the number of coins in your purse every time you pass the start. The maximum number of coins is 300.

According to the quesiton,
5 . 1.5ˣ = 300

Where x is the number of passes,
1.5ˣ = 60
x ≈ 10

Thus, the requried number of passes to reach the maximum is given as 10 passes.

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42+48/6=?
48/6 meaning a fraction not division

Answers

Answer:

50

Step-by-step explanation:

Fractions are division problems. :) You have to complete that first to solve the equation (PEMDAS).

48/6 = 8

42 + 8 = 50

I need helpppppp asap

Answers

Answer:

graph A

Step-by-step explanation:

When looking at a graph, there are two different axes. The vertical values--marked by the center up/down line--are "y-values"; and this is called the "y-axis"

The horizontal values--marked by the left/right line--are "x-values"; and this is called the "x-axis"

For the x-axis, values to the left side of the origin (the place where the y-axis and x-axis intercept) are smaller than 0--they are all negative values.

Values to the right side of the origin are positive--greater than 0.

For the y-axis, positive numbers are on the top half [once again, the midpoint / 0 is where the two lines are both = to 0; the origin] and negative numbers are on the bottom half.

Ordered pairs (points) are written as (x,y)

(x-value, y-value)

We are looking for a graph that decreases (along the y-axis), hits a point below the origin, and goes flat/stays constant.

When a graph is decreasing (note: we read graphs from left to right), the line of the graph is slanted downwards (it looks like a line going down).

So, if we look at the graphs, we can see Graph A descending, crossing the y-axis {crossing the middle line /vertical line / y-axis} at a value of -7, and then staying constant (it is no longer increasing or decreasing because the y-values stay the same)

hope this helps!!

You toss a coin and roll a number cube. The table shows the sample space,
where H means heads, T means tails, and the numbers represent the number
cube roll.
H
T
1
H1
T1
2
H2
T2
3
H3
T3
4
H4
T4
5
H5
T5
6
H6
T6
What is the probability of tossing heads and rolling a number less than 3?

Answers

Probability helps us to know the chances of an event occurring. The probability of tossing heads and rolling a number less than 3 is 1/6.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The number of cases where coins land on heads and a number less than 3 are rolled is 2, which are H1 and H2.

The probability of tossing heads and rolling a number less than 3 is,

Probability = (Outcomes where coins land on heads and a number less than 3 are rolled)/(Total number of cases)

Probability = 2/12 = 1/6

Hence, the probability of tossing heads and rolling a number less than 3 is 1/6.

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Akespeare most often used sonnets to express which emotion between characters? love happiness grief anger help im so confused!!!!! How does a command economy differ from a mixed market economy? Define Relative clouse and subject verb agreement Which situation from Initiation is an example of int What is the length of the hypotenuse? If necessary, round to the nearest tenth. Determine the number of protons, neutrons, and electrons in the following:40 . . X18Ignore the dots im just trying to place the element over between the numbers In theory, what would be the approximate weight gain of a person who consumes an excess of 500 kcal every day for four weeks (e.g., about 28 days) Which product is an example of a consumer good?A. Stock share in a tech company B. dog food for a pet boarding family c. paint sprayer for an autobody shopd. gallon of milk to use in a bowl of cereal Identify how the whiskey rebellion of 1794 was similar to the american revolution. changes in the ______ can begin or end the life of a river. Read the excerpt from The Dark Game.Mr. H. quickly began talking to his contacts in the city. Soon he heard of a British printer in Mexico City who had been falsely arrested for printing counterfeit money. Mr. H. intervened with the British minister, who got the frightened printer released from custody and the charges against him dropped. The printer, overjoyed to be free, told Mr. H. that he would welcome the opportunity to repay the agent for his intervention. As a matter of fact, Mr. H. told him, there was a favor the printer could do for him.Which inference can a reader make based on the information in the excerpt?Mr. H. knew the printer would help them upon release from prison.Mr. H. was very concerned for the falsely imprisoned printer.Mr. H. and the printer had known each other for a long time.Mr. H. originally had not intended to employ the printers help. Why do lunar and solar eclipses not happen every month? Why when I send a message on iOS it says the persons notification is silenced, and the message isnt delivered? Which of the following is a shared cause of the downfall for both the Han and Roman empires? A line intersects the points (8, 2) and (12, -10). What is the slope of the line in simplest form? m = [?] Question 14 of 25Scientists are most likely to change a scientific theory if:A. members of society do not agree with the theory.B. the theory cannot be tested through direct observation.C. new evidence does not support the theory.D. a hypothesis used to test the theory is not supported. Please help me solve problems a - d. Juanitas boss told her that once she has worked with the company for 10 years, her salary will be increased to 3 times what she makes now plus $2,000. If s represents her original salary, which expression represents what her salary will be after 10 years at the company?One-third s + 2,000StartFraction 3 Over s EndFraction + 2,0003 s + 2,0002,000 minus 3 s Read the excerpt from Iqbal.My first impression was that he was handsome. Then I thought, No, he isn't really good-looking. But he had such eyes. They were sweet and deep and they weren't afraid. He was standing at the threshold of the workroom with Hussain Khan's enormous hand gripping his arm and we were all looking at him. The fourteen of us child-slaves plus Karim, all observing another slave. He was one of the many who had come and gone over the years, but we felt that somehow, this new boy was different. He looked around at us, one by one. He was sad, of course, like anyone who has been away from home for a long time, like anyone who is little more than a slave, like anyone who can't imagine what will become of him.But I'm telling you this: He wasn't afraid.Why did the author choose to provide this fictional account of Iqbal Masih, who was a real person? Select 4 options.to interpret and share real eventsto bring Iqbal to life through descriptive detail and dialogueto make the account of Iqbals life more interesting than it actually wasto add details, such as characters thoughts and feelings, to the story since some of these details are not knownto engage the reader by sharing his point of view about the topic