Alyssa was given a gift card for a coffee shop each morning Alyssa uses the gift card to buy one cup of coffee let a represent the amount of money of money remaining on the card after buying X cups of coffee that the table below has selected values showing the liner relationship between X and a determine the original amount of money on the gift card

The value of 'y' is 32. 5 degrees . Option B

It is important to note that If two chords intersect inside a circle,

The measure of the angle formed is half the sum of the measure of the arcs intercepted by the angle and its vertical angle

From the diagram, it is shown that the both the chords at 'y' and the angle '65' intersect in the circle

We then have that;

[tex]y = 65[/tex] × [tex]\frac{1}{2}[/tex]

[tex]y = 65[/tex] × [tex]0. 5[/tex]

y = 32. 5 degrees

We can see that the value of 'y' in the given figure is 32. 5 degrees which is half the angle at the vertex of the intersecting chords.

Thus, the value of 'y' is 32. 5 degrees . Option B

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Answer: 1

Step-by-step explanation:  It's subtraction and add ion look at the right side

Answer: B. (-1, -5)

Step-by-step explanation:

Given equations

2x + y = -7

x - y = 4

Concept

[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

[tex]A*A^{-1}=A^{-1}*A=I~(Which~is~basically~1)[/tex]

Convert into matrix

[tex]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]

Calculate the inverse of the matrix

[tex]A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right][/tex]

[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

[tex]A^{-1}=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right][/tex]

Solve by multiplying the inverse of the matrix

[tex]A*A^{-1}=A^{-1}*A=I[/tex]

[tex]-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]

[tex]1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3}\left[\begin{array}{ccc}3\\15\\\end{array}\right][/tex]

Simplify by multiplication

[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right][/tex]

Therefore, the answer is [tex]\Large\boxed{(-1,~-5)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x = 31

Step-by-step explanation:

Given:

f(x) =

[tex]2 {x}^{2} - 1[/tex]

g(x) = x + 2

We will first find g(2).

g(2) = 2 + 2 = 4

Next we will find f(g(2)).

f(g(2))= f(4) =

[tex]2( {4}^{2} ) - 1 \\ = 2(16) - 1 \\ = 32 - 1 \\ = 31[/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\small\leadsto\bold{Substitute:}[/tex]

[tex]\longrightarrow\sf{ \dfrac{6}{7}= Ce^{k*0}}[/tex]

[tex]\longrightarrow\sf{\dfrac{6}{7}= C*e^0}[/tex]

[tex]\longrightarrow\sf{e^0=1}[/tex]

[tex]\therefore\sf{C= \dfrac{6}{7} }[/tex]

[tex]\therefore\sf{5=Ce^{k*5}}[/tex]

[tex]\\[/tex]

[tex] \bold{Solve \: to \: find \: k:}[/tex]

[tex]\longrightarrow\sf{5 = \dfrac{6}{7} *e^{k5}}[/tex]

[tex]\longrightarrow\sf{ \dfrac{7*5}{6} *e^{5k}}[/tex]

[tex]\longrightarrow\sf{In=( \dfrac{35}{6} ) = 5k}[/tex]

[tex]\longrightarrow\sf{1.76=5k}[/tex]

[tex]\longrightarrow\sf{k=\dfrac{1.76}{5} = 0.352}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\sf{\boxed{\sf \dfrac{6}{7}= e^{0.352*t}}}[/tex]

Answer:

1/6 p - 4/5 or -4/5 + 1/6p They both mean the same thing.

Step-by-step explanation:

You have two sets of like terms.  You have 2 terms that have the variable p as part of the term and you have 2 terms with no variable that are called constants.

-2/3p + 5/6p  Are two terms that you want to combine.  We need common denominators to add.  The common denominator would be 6, so we will make an equivalent fraction with -2/3 with 6 as the denominator.

-2/3 = -4/6  We just multiple the top (numerator) and the bottom (denominator of the first fraction (-2/3) by 2 to the get the second faction (-4/6).  Now we can add the 2 terms with p together.

-4/6p + 5/6p  The denominators stays the same (6) and we add the numerators -4 + 5 = 1,  So our p term is 1/6p

Now we have to combine the constant terms of 1/5 and - 1.  Another name for -1 is 5/5.  We are going to use this form so that our denominators are the same.

1/5 - 5/5 = -4/5

Based on the amount that both Salesmen A and B earn per sale, the number of sales they both had was 12 sales.

Sales commission is a key aspect of sales compensation. It's the amount of money a salesperson earns based on the number of sales they have been able to make.

We are told that;

Salesman A gets $65 per sale.

Salesman B gets $300 and $40 per sale.

Assuming the number of sales to take them both to the same amount is x, the relevant formulas would be:

65x = 300 + 40x

Rearranging gives;

65x - 40x = 300

25x = 300

x = 300/25

x = 12 sales

The amount that salesman A earned is = 65 * 12 = $780

The amount that salesman B earned is = 300 + (40 * 12) = $780

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Answer:Sanjay has 8

Step-by-step explanation: Because 8x4 equals 32 so thats how much tanya has a 32+8 equals 40. This is what I did I knew 10x4 is 40 so that couldn't be it so then I tried 8 because nine x four is 36 which would be to high so I tried 8 and it was perfect hope this helps.

If Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, then Sanjay have 8 pens.

Two or more expressions with an equal signs is called as Equation.

Given that Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, We need to find how many pens sanjay has.

Let sanjay has x number of pens.

Tanya has four times as many pens as Sanjay

So 4 times means four multiple of sanjay pens.

Tanya has four times as many pens as Sanjay can be write as 4x.

Combined of tanya and sanjay has 40 pens.

Combined means adding.

x+4x=40

Add the like terms

5x=40

Divide both sides by 5.

x=8

So Sanjay has eight pens and Tanya has 4(8)=32 pens.

Hence Sanjay have eight pens.

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The trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

In the question, we are asked to derive the trigonometric identity, cos x + cos y = 2 cos (x + y/2) cos (x - y/2), using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

We are given the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

Substituting a = x + y/2 and b = x - y/2 in this, we get:

cos (x + y/2) cos (x - y/2) = 1/2[cos (x + y/2 + x - y/2) + cos (x + y/2 - x - y/2)],

or, cos (x + y/2) cos (x - y/2) = 1/2[ cos (2x/2) + cos (2y/2) ],

or, 2 cos (x + y/2) cos (x - y/2) = cos x + cos y, which on inter-changing the sides, gives us:

cos x + cos y = 2 cos (x + y/2) cos (x - y/2), which is the required trigonometric identity.

Thus, the trigonometric identity cos x + cos y = 2 cos (x + y/2) cos (x - y/2), is derived using the trigonometric identity cos a cos b=1/2 [cos (a + b) + cos (a-b)].

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The provided question is incorrect. The correct question is:

"Use cos a cos b=1/2 [cos (a + b) + cos (a-b)]to derive cos x + cos y = 2 cos (x + y/2) cos (x - y/2) ."

Answer:

choice C. Yes, this image proves the pythagorean theorem is true because 9 + 16 = 25

Step-by-step explanation:

Proportionately, if they do half and half of 50% and 80% of the two bags, Bob is correct.

A proportion is a mathematical measure that compares two variables or numbers.

Proportions can be stated in percentages or ratios, as decimals or fractions.

Content of 16-ounce bag of nuts = 60% chocolate-covered nuts

Content of first bag = 50/50 plain and chocolate-covered nuts

Content of second bag = 80% chocolate-covered nuts

A mixture of half of 50% bag with half of 80% bag will result in 65% (50% + 80%)/2.

Thus, since the promise for each 16-ounce bag is for at least 60% chocolate-covered nuts, Bob is correct.

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Is Bob correct?

Answer:

It is a rational number.

Step-by-step explanation:

A number is only irrational if it has a decimal that never ends and doesn't have a pattern. So a number like Pi (3.141592653589...) is irrational while a number like 1/3 (0.33333333...) is rational.

Hi :)

Below is the difference between rational & irrational numbers

Evidently,

Let's test the given number, [tex]\boldsymbol{3\dfrac{1}{4}}[/tex]

Well isn't it already in [tex]\sf{\dfrac{p}{q}}[/tex] form? It is.

Thus

[tex]\longrightarrow\darkblue\boldsymbol{3\dfrac{1}{4}\:is\:rational}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

Answer:

  x = {π/6, π/2, 5π/6, 3π/2}

Step-by-step explanation:

The equation can be solved using a double-angle trig identity and factoring.

Dividing the equation by 7 and substituting for sin(2x), we have ...

  7sin(2x) = 7cos(x)

  sin(2x) = cos(x)

  2sin(x)cos(x) = cos(x)

  2sin(x)cos(x) -cos(x) = 0

  cos(x)(2sin(x) -1) = 0

The product of factors is zero when one or more of the factors is zero.

  cos(x) = 0   ⇒   x = {π/2, 3π/2}

  2sin(x) -1 = 0   ⇒   x = arcsin(1/2) = {π/6, 5π/6}

Solutions in the given interval are ...

  x = {π/6, π/2, 5π/6, 3π/2}

__

Additional comment

When the equation is of the form f(x) = 0, then the x-intercepts of f(x) are its solutions. We can rearrange this one to ...

  sin(2x) -cos(x) = 0

The solutions identified above match those shown in the graph.

Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion estimate and the sample size are given as follows:

p = 0.45, n = 437.

Hence the mean and the standard error are:

The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.

Hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (0.42 - 0.45)/0.0238

Z = -1.26

Z = -1.26 has a p-value of 0.1038.

2 x 0.1038 = 0.2076.

0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

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The answer is Pedro.

The cost to rent each chair is $1.5 and cost to rent each table is $6.5

From the question, we are to determine the cost to rent each chair and each table

Let c represent chair

and

t represent table

From the given information,

The total cost to rent 5 chairs and 3 tables is $27

That is,

5c + 3t = 27 ------------ (1)

Also,

The total cost to rent 2 chairs and 12 tables is $81

That is,

2c + 12t = 81 ---------- (2)

Now, solve the equations simultaneously

5c + 3t = 27 ------------ (1)

2c + 12t = 81 ---------- (2)

Multiply equation (1) by 2 and multiply equation (2) by 5

2 × [5c + 3t = 27 ]

5 × [2c + 12t = 81 ]

10c + 6t = 54        ------------- (3)

10c + 60t = 405   ------------- (4)

Subtract equation (4) from equation (3)

10c + 6t = 54        

10c + 60t = 405

---------------------------

-54t = -351

t = -351/-54

t = 6.5

Substitute the value of t into equation (2)
2c + 12t = 81

2c + 12(6.5) = 81

2c + 78 = 81

2c = 81 - 78

2c = 3

c = 3/2

c = 1.5

∴ The cost of chair is $1.5 and cost of table is $6.5

Hence, the cost to rent each chair is $1.5 and cost to rent each table is $6.5

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See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1

From the question, the given parameters are:

Amplitude, A = 5

Vertical shift, D = -1

Period, T = 4

A cosine function is represented as:

f(x) = A cos(B(x + C)) + D

Where

Amplitude = A

Period = T

Horizontal shift = C

Vertical shift = D

Since the horizontal shift is not stated in the question, we can assume that the horizontal shift is 0

i.e. C = 0

So, the equation of the cosine function becomes

f(x) = A cos(Bx) + D

Calculate the value of B using

B = 2π/T

So, we have:

B = 2π/4

Evaluate

B = π/2

So, we have:

f(x) = A cos(π/2x) + D

Substitute the known values of A and D in the above equation

f(x) = 5 cos(π/2x) - 1

Next, we plot the graph of the cosine function on a graphing tool

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Answer:

400$

Step-by-step explanation:

Let C.P. of the watch = Rs. 100

When profit =5%; S.P. = Rs. (100+5)

= Rs. 105

and when profit = 11%;

S.P. = Rs. (100+11)

=Rs.111

Difference of two selling prices

= Rs. 111-Rs.105 = Rs.6

When watch sold for Rs. 6 more; then C.P. of the watch = Rs.

100

6

When watch sold for Rs. 24 more; then C.P. of the watch = Rs.

100

6

×

24

= Rs.

100

×

24

6

=400

Answer:

  (x, y) = (-√3/2, 1/2)

Step-by-step explanation:

The terminal point for that angle can be read from a unit circle chart.

On the attached chart, the point of interest is the first one above the -x axis on the left side. The chart tells you the coordinates are ...

  (x, y) = (-√3/2, 1/2)

Solving a system of equations, we can see that:

Let's define the variables:

With the given information, we can write:

P*8h = D

C*7h = D

C = 2*P - 144mi/h

So we have a system of 3 equations, where D is the distance in the problem.

With the first and second equations we can write:

P*8h = D = C*7h

Isolating P, we get:

P = C*(7/8)

Now we can replace that in the last equation:

C = 2*P - 144mi/h

C = 2*C*(7/8) - 144mi/h

And now we can solve that for C.

C - 2*(7/8)*C = - 144mi/h

C*(1 - 14/8) = -144mi/h

C*(8/8 - 14/8) = - 144mi/h

C*(6/8) = 144mi/h

C = (8/6)*144mi/h = 192mi/h

Now that we know the speed of the commercial jet, we can find the speed of the private jet.

P = C*(7/8) = 192mi/h*(7/8) = 168 mi/h

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The total income and expenditure in September are "Income is R 106 360.00 and expenditure is R 4 850.00." Option C. This is further explained below.

Generally, the equation for  Insurance and investment  is  mathematically given as

II= 42% of the balance

II = 0.42*0.64A

II= 0.2688A

Generally, the equation for Total After All other exp is  mathematically given as

Texp = 0.64A – 0.2688A

Texp= 0.3712A

Total After All other exp = 111210

subbing ahead and equating we have

111210 = 0.3712 A

Therefore

A = 299596

The total income is 299596

Therefore, the calculation for the expense is given as

Expense = 0.25A + 0.11A + 0.2688A + 4850

Expense= 0.6288A + 4850 = (0.6288*299596) + 4850

Expense= 193236

The Expense is 299596

In conclusion,  At the end of September, Agri-Small Business's minimal spending on gasoline for their fleet amounted to R 4 850.00, and they still had a balance of R106 360.00 in their account. The majority of the remaining revenue was allocated to insurance and investments by the business, which accounted for 42% of the total. Wages and salaries accounted for 25% of the company's income in September. The overall revenue and expenses for the month of September were as follows: the income was R 106 360.00, and the expenses were R 4 850.00. Option C.

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The limit of j (x) as x approaches 3 is 4.

According to the question, A line begins at an open circle (2, 6) on a coordinate plane and descends through ( -2, 2). At, a complete circle is (3, 6). From a solid circle (2, 3), a curve leads to an open circle (3, 4). From the open circle to the closed circle, a line runs (6, 5).

From the graph, it can be seen that the limit of the function j(x) as the value of x approaches 3 is 4.

A diagram or pictorial representation that organizes the depiction of data or values is known as a graph.

The relationships between two or more items are frequently represented by the points on a graph.

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Answer:

4

Step-by-step explanation:

egg 2023

The third decile is 58.

Decile is a statistical term that divides the data into groups of ten. The third decile is the third group of the data set.

Third decile = 3/10 x (n + 1 )

3/10 x 16 = 4.8th term  = 58

Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.

The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.

Given that angle ADE ≅ angle ABC, we also know that:

Angle EAD ≅ CAB.

Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.

Thus, the ratios that are equal to each other would be:

AE/EC = AD/DB.

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The mass of the CO2 produced IS 630 Kg

Gasoline is a kind of fuel that is composed mostly of isooctane. In most engines, gasoline is widely used hence the demand for the product is high. We know that the combustion of an alkane (of which gasoline is one) would produce carbon dioxide and water according to a balanced reaction equation.

The balanced reaction equation for the combustion of gasoline is shown in the image attached to this answer.

Since  a Puerto Rico hospital uses 3 gallons of gasoline per hour, and there are 24 hours in a day, it the follows that 72 gallons of gasoline are used per day. This 72 gallons is the equivalent of 272.88 L

Now;

Given that the density of gasoline = 748.9 g/L

Mass of gasoline = 748.9 g/L * 272.88 L = 204 Kg

Number of moles of gasoline =  204 * 10^3/114 g/mol = 1789.5 moles

If 2 moles of gasoline produces 16 moles of CO2

1789.5 moles produces  1789.5 moles * 16 moles/2 moles = 14316 moles

Mass of CO2 =  14316 moles * 44 g/mol = 630 Kg

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Answer:

26 units^2

Step-by-step explanation:

the area of a kite is (d1 * d2)/2

d1 = 2 + 2 = 4

d2 = 6 + 7 = 13

4 * 13 = 52

52 / 6 = 26

26 units^2 is your answer

Answer: 26

Step-by-step explanation:

[tex]f(x) = 2 {}^{x} \\ g(x) = f(x + 2) = 2 {}^{x + 2} \\ g(x) = 2 {}^{x + 2} =2 {}^{x} .2 {}^{2} = 4.2 {}^{x} [/tex]

[tex]a.b {}^{x} = > horizontal \: asymp \: y = 0[/tex]

[tex]4.2 {}^{0} = 4 = > vertical \: int \: (0,4)[/tex]

[tex]a.b {}^{x} = > x ∈ \: ] -∞ , ∞ [[/tex]

The horizontal asymptote of the function f ( x ) = 2ˣ is y = 0 and the y-intercept is ( 0 , 4 )

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be denoted as f ( x )

Now , the value of f ( x ) is

f ( x ) = 2ˣ   be equation (1)

The y-intercept of the function is when x = 0

So , when x = 0

f ( 0 ) = 2⁰

f ( 0 ) = 1

So , the y-intercept of the function is at ( 0 , 4 )

And , when the function f ( x ) is tending to zero , the horizontal asymptote is y = 0

Therefore , the horizontal asymptote is y = 0

The domain of the exponential function is { -∞ < x < ∞ }

Hence , the horizontal asymptote of the function f ( x ) = 2ˣ is y = 0

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Answer:

The intervals represent the domain, or the values on the horizontal axis.

When x ≤ -3, the graph should form a straight line at y = 3. Because the interval includes x = -3, the rightmost part of the line should be capped with a closed dot. The line should continue for infinity to the left.

When -3 < x < 4, the graph should form a line with the equation (2x + 1). Because the interval does not include the endpoints, the endpoints should have open dots.

When x ≥ 4, the graph should form a straight line at y = -4. Because the interval includes x = 4, the leftmost endpoint should be a closed dot. The right of the line should continue for infinity.

**The included graph does not take the endpoints into account

Answer:

See attached for graph.

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases}3 & \textsf{if }x\leq -3\\2x+1 & \textsf{if }-3 < x < 4 \\ -2 & \textsf{if } x\geq 4 \end{cases}[/tex]

Therefore, the function has three definitions:

[tex]f(x)=3 \quad \textsf{when x is less than or equal to 3}[/tex]

[tex]f(x)=2x+1 \quad \textsf{when x is more than -3 and less than 4}[/tex]

[tex]f(x)=-2 \quad \textsf{when x is more than or equal to 4}[/tex]

When graphing piecewise functions:

First piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies f(-3)=3 \implies (-3,3)[/tex]

Place a closed circle at (-3, 3).

As this piece of the function is f(x) = 3 for any value of x that is less than or equal to -3, draw a horizontal straight line to the left from the closed circle.  Add an arrow at the end.

Second piece of function

Substitute the endpoints of the interval into the corresponding function:

[tex]\implies f(-3)=2(-3)+1=-5 \implies (-3,-5)[/tex]

[tex]\implies f(4)=2(4)+1=9 \implies (4,9)[/tex]

Place an open circle at (-3, -5) and (4, 9).

Join the points with a straight line.

Third piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies f(4)=-2 \implies (4,-2)[/tex]

Place a closed circle at (4, -2).

As this piece of the function is f(x) = -2 for any value of x that is more than or equal to 4, draw a horizontal straight line to the right from the closed circle.  Add an arrow at the end.

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The sales last year of the company is 5617

The given parameters are:

Company sales = 6740

Percentage increase = 20%

The sales of the company last year (x) to date is calculated as:

Company sales = (1 + Proportion) * Last year sales

Substitute the known values in the above equation

6740 = (1 + 20%) * x

Evaluate the sum

6740 = 1.2 * x

Divide both sides by 1.2

x = 5617

Hence, the sales last year is 5617

Read more about percentages at:

https://brainly.com/question/843074

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