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Part 1
The length of a rectangular park is six times its width. The park is surrounded by a ​3-foot-wide path. Let x denote the width of the park. Write a quadratic function to represent the total area of the park and the path.

The equation |x| = 9 has two solutions: x = 9 and x = -9. The shaded region includes all points to the left of -9 and all points to the right of 9.

The equation is given as follows:

|x| = 9

The equation |x| = 9 has two solutions: x = 9 and x = -9.

To check these solutions, we can substitute them back into the original equation and see if they satisfy it:

|x| = 9

|9| = 9 --> True

|-9| = 9 --> True

Therefore, the solutions x = 9 and x = -9 are both valid.

To graph the solution(s), we can draw a number line and mark the points x = 9 and x = -9 with closed circles (since the absolute value of x is equal to 9 at those points).

We can then shade the parts of the number line where the absolute value of x is greater than or equal to 9.

This includes all points to the right of 9 and all points to the left of -9.

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Answer

[tex]\large\textrm{There are two solutions: 9 and -9.}[/tex]

Further explanation

If we have the absolute value of x, that means x could be positive or negative.

This means that, in |x| = 9, x could be 9 or -9.

 Plug the answers into the original equation.

You should get a true statement.

because the absolute value of 9 is 9 so that's a solution

the absolute value of -9 is also 9 so that's also a solution

therefore, the solutions are 9 and -9.

The side x of the triangular base prism is 0.4 centimetres.

The diagram above is a triangular prism. The triangular base of the prism is a right triangle. Therefore, the unknown side x can be found using Pythagoras's theorem,

c²= a² + b²

where

Therefore,

x² = 0.5² - 0.3²

x² = 0.25 - 0.09

x = √0.16

x = 0.4 cm

Therefore,

x = 0.4 centimetres.

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Answer: 28.3

Step-by-step explanation:

The question is just asking for the area of a circle with a diameter of 6. The equation for that is [tex]A = \pi r^{2[/tex].

Since the Radius (r) is half the diameter, your equation will look like this: [tex]A=\pi 3^2[/tex].

When plugged into a calculator, 28.27443 is the answer. Rounded to the nearest tenth would be 28.3. Hope this helps!

The quotient of the long division of the polynomial (6x³ - 4x² + 11)/(x+3)  is 6x² - 22x + 66.

The quotient of the polynomial divided by a factor of x + 3 is determined by applying long division method as shown below;

6x³ - 4x² + 11 ÷  x + 3

                   6x² - 22x + 66

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

  x + 3   √ 6x³ - 4x² + 11

               - (6x³ + 18x²)

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

                         -22x² + 11

                    -   (-22x² - 66x)

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

                                  66x + 11

                            -  (66x + 198)

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

                                      -187

Thus, the quotient of the long division of the polynomial is obtained as   6x² - 22x + 66.

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Find the quotient of the polynomial using long division

6x3 − 4x2 + 11/x + 3

Answer: the price of the item 8 years from today is approximately $1475.

Step-by-step explanation:

The given exponential function to model the future price of the item is:

P(t) = P(0) * (1.026)^t

Here, P(t) represents the price of the item t years from today, and P(0) is the current price of the item.

1. To find the current price, we need to find P(0):

P(0) = 1200 * (1.026)^0

Since any number raised to the power of 0 is 1:

P(0) = 1200 * 1

P(0) = $1200

So, the current price of the item is $1200.

2. To find the price 8 years from today, we need to find P(8):

P(8) = 1200 * (1.026)^8

Using a calculator:

P(8) ≈ 1200 * 1.229057

P(8) ≈ $1474.87

Rounded to the nearest dollar:

P(8) ≈ $1475

So, the price of the item 8 years from today is approximately $1475.

The number of days required to complete the job in exponent form is 10¹ = 10.

The exponent form of the number of days is calculated as follows;

number of pages that can be printed by all machines = n x P

where;

N = 100 x 104

N = 10400 pages/day

However, the Ted's company needs 10 days to print 106 pages, our equation is formed as follows;

x = log(y)

where;

10ˣ = y

10ˣ = 10

x = 1

so the exponential form = 10¹ = 10

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The measure of the unknown angles in the parallel lines AC and DF with transversal HJ are as follow,

m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.

Two lines AC and DF are parallel to each other  in the attached figure

Transversal HJ cut  lines AC and DF at point B and E respectively.

Measure of ∠ABE = 63°.

Using the result based on corresponding angles, alternate interior angles , and vertically opposite angles of a parallel lines we get,

Measure of ∠ABE ≅ Measure of ∠DEH ( corresponding angles)

⇒Measure of ∠DEH = 63°

Measure of ∠ABE ≅ Measure of ∠BEF ( alternate interior angles)

⇒Measure of ∠BEF = 63°

Measure of ∠ABE ≅ Measure of ∠CBJ ( vertically opposite angles)

⇒Measure of ∠CBJ = 63°

Using the result of linear pair angles,

Measure of ∠ABE + Measure of ∠CBE = 180°

⇒ Measure of ∠CBE = 180° -63°

⇒  Measure of ∠CBE = 117°

Measure of ∠CBE ≅ Measure of ∠FEH ( corresponding angles)

⇒Measure of ∠FEH = 117°

Measure of ∠CBE ≅ Measure of ∠BED ( alternate interior angles)

⇒Measure of ∠BED = 117°

Measure of ∠CBE ≅ Measure of ∠ABJ ( vertically opposite angles)

⇒Measure of ∠ABJ = 117°

Therefore, the measure of the seven unknown angles formed in the parallel line are given by m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.

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The above question is incomplete, the complete question is:

Lines AC and DF are parallel. They are cut by transversal HJ with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E.

In the attached figure.

In a case wherby new bicycle sells for $300 It is on sale for 1/4 off the regular price all the expressions that represent the sale price of the bicycle in dollars are

From the option B)300•3/4, we cam see that (300*3)/4 = 225

From the option C)300•(1-1/4),   (300*3)/4 = 225

From the E.)300 - 1/4•300, 300 - 75 = 225

Therefore, the correct options are the option BCE as listd below because they are seen as the one that gives the  regular price all the expressions hence they are correct.

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Here are the steps to use the double number line diagram to find a percentage:

It should be noted that the double number line diagram is a visual tool that is used to represent two equivalent sets of values, and it can be useful to find percentages in a given context.

In this case, the steps are given above.

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This statement defines the concept of left and right sets of elements x of G with respect to the subgroup H of G.

The left set of x in G, denoted by xH, is the set of all elements of G obtained by multiplying x to the left by all elements of H. Formally xH = {xh: h ∈ H}, where "xh" denotes the product of x and h in G.

Similarly, the right-hand set of x in G, denoted Hx, is the set of all elements of G obtained by multiplying x on the right by all elements of H. Formally Hx = {hx: h ∈ H}, where "hx" denotes the product of h and x in G.

Generally, left and right sets are different sets and may contain different numbers of elements. However, if the group G is commutative (ie the order of multiplication does not matter), then the left and right sets are equal.

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Since ΔJKL was transformed to create ΔMNO, the sequence of transformations that were used include the following:

Reflection over the y-axis.

(x, y) → (x, y - 9).

In Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to the coordinate of the given triangle JKL, we have the following coordinates:

Coordinate J = (3, 7)   →  Coordinate J' = (-(3), 7) = (-3, 7).

Next, we would apply a vertical translation by shifting triangle J'K'L' down by 9 units to produce ΔMNO;

(x, y)                   →         (x, y - 9).

J' (-3, 7)               →        (-3, 7 - 9) = M' (-3, -2).

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The probability of passing at least one will be 0.70.

We know that,

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

here, we have,

Probability of passing history course = 0.59

Probability of passing math course = 0.60

Probability of passing both courses = 0.49

so, we get,

Probability of passing at least one will be

⇒ 0.59 + 0.60 – 0.49

⇒ 0.70

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complete question:

A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?

The amount of sand in each vase is 2.8 pounds by dividing the total amount by the number of vases.

Given that,

Raj combined white sand with black sand to make 14 pound mixture of sand.

Total amount of sand = 14 pounds

Number of vases to which sand is put = 5 vases

Amount of sand in each vase can be found by dividing the total amount by the number of vases.

Amount of sand in each vase = 14 / 5 = 2 4/5 pounds = 2.8 pounds

Hence the total amount of sand is 2.8 pounds.

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The equation that best models the data from the table after the data has been linearized is y=294755 * 1.21728^x. This equation follows an exponental model.

Looking at the data, it is very evident that it is not increasing linearly but rather exponentially.

An exponential equation has the general pattern of formula which y = ab^x, where a is the main value and b is the growth factr.

The question below is as seen in the picture, and the above answer is dependent on it.

What is the equation that best models the data from the table after the data has been linearized?

X                                 y

2                                4.4

7                               18.2

13                              120.0

19                              715.4

22                            1,768.3

26                            5,775.9

30                           10.508.5

(1 point)

logy=0.12502x+0.427231

y=1,350 76x+1,350.76

y=294755 * 1.21728^x

y=5,927 281og x-3,880 59

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Answer:

To find the missing side of a right triangle given an angle and a side, you can use trigonometric functions. In this case, we have the angle opposite the missing side, so we can use the sine function.

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can set up the following equation:

sin(34°) = opposite / 12

To solve for the opposite side, we can multiply both sides by 12:

opposite = 12 * sin(34°) ≈ 6.60

Therefore, the missing side of the triangle is approximately 6.60 units long.

Step-by-step explanation:

Dingaka took out a loan of R12650 with a simple annual discount rate of 12.5%. He has to repay R11595.83 in eight months, after deducting the simple discount of R1054.17.

To find the amount that Dingaka has to repay, we can use the formula for simple discount

Simple Discount = Principal * Rate * Time

Where Principal is the original amount borrowed, Rate is the annual simple discount rate, and Time is the time period in years.

We know that Dingaka received R12650 as the principal amount and the annual simple discount rate is 12.5%, which is equivalent to 0.125 as a decimal. The time period is 8/12 = 2/3 years, since the loan has to be repaid in eight months' time.

Plugging these values into the formula, we get

Simple Discount = 12650 * 0.125 * 2/3

= 12650 * 0.08333333

= 1054.166625

Therefore, the amount that Dingaka has to repay is the principal minus the simple discount, which is

Amount to Repay = Principal - Simple Discount

= 12650 - 1054.166625

= 11595.833375

So, Dingaka has to repay R11595.83 after eight months.

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Answer:

6.7 = π(r^2)(33.5/12)

r = .874

75/(2 × .874) = 42.9 = 42 barrels

6.7 = (3.14)(r^2)(33.5/12)

r = .874

75/(2 × .874) = 42.9 = 42 barrels

1) For the following set of test scores for a history class, 100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40, it would be better for the teacher to consider D) The mean because it is higher and the teacher wants to feel good about the students.

2) The mode of these data about the high temperatures in Orlando for the past 8 days would be 90.

3) The median of these data about the high temperatures in Orlando for the past  8 days would be 80.

The mean, mode, and median are three centers of measurement.

The mean refers to the average value in the data set, obtained as the quotient of the total value divided by the number of items.

The mode refers to the value that occurs most in the data set.

Lastly, the median is the middle value for a data set arranged in descending or ascending order.

1. Test Scores:

100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40

Total value = 660

Number of data items = 11

Mean = 60 (660 ÷ 11)

Median = 55

Mode = 60

2. High Temperature:

91, 90, 90, 90, 84, 82, 81, 90

Total Value = 698

Number of data items = 8

Mean = (87.25 (698 ÷ 8)

Median = 90

Mode = 90

3. High Temperature:

91, 90, 90, 90, 84, 82, 81,90

Median = 80 (81, 82, 84, 90, 90, 90, 90, 91)

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Answer:

To find the probability of an event occurring, you need to divide the number of ways the event can occur by the total number of possible outcomes. The probability is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

For example, if you want to find the probability of rolling a 3 on a standard six-sided die, there is only one way to roll a 3 and six possible outcomes (1, 2, 3, 4, 5, 6). So, the probability of rolling a 3 is 1/6 or approximately 0.17.

Keep in mind that the probability of an event occurring is not a guarantee that the event will happen. It only indicates the likelihood of the event happening based on the available information.

The sales after 5 months is 36,000 units (since f(t) is given in thousands of units).

The given function f(t) represents the sales of a gaming product in thousands of units after t months. To find the sales after 5 months, we need to substitute t = 5 in the function f(t) and evaluate the expression. f(5) = 5(5) + 11

= 25 + 11

= 36

Therefore, the sales of the gaming product after 5 months is 36 thousand units. This means that the company has sold 36 thousand units of the gaming product within the first 5 months since the launch of the product. It also indicates that the sales are increasing by 5 thousand units every month.

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-- The given question is incomplete, the complete question is

"Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11. Find the sales after 5 months."

The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.

We have,

From the given data, we can see that the number of mice is being multiplied by 2 every month.

That means the growth is exponential.

We can use the formula for exponential growth:

[tex]m(t) = a \timesr^t[/tex]

where m(t) is the total number of mice after t months, a is the initial number of mice (when t = 0), and r is the common ratio

From the given data, we can see that when t = 0, there are 3 mice.

So, a = 3.

Also, we can see that the common ratio is 2 (i.e., the number of mice is being multiplied by 2 every month).

Now,

The equation that models how many mice there will be in the lab after 10 months is:

m(10) = 3 × 2^10

Simplifying this equation gives:

m(10) = 3 × 1024

m(10) = 3072

Therefore,

The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.

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Answer: 24 minutes and 30 seconds after the meeting as started

Step-by-step explanation:

110 minutes into 2 equal parts = 55 minutes in each section.

In the middle of 55 minutes = subtract the 10 minutes for a break from the 55 minutes that leaves you with 45 minutes. 24 minutes and 30 seconds before and after the 10 minute break.

Total session minutes - 110

Two equal parts of session: 55 minutes in each session

10 minute break in each session: 55-10 =45.

24 minutes and 30 seconds + 10 min break (in middle) + 24 minutes and 30 seconds

After 50 minutes the break will start.

The metting is 110 minutes long. According to the Question the metting have 'a'(only one) break of 10 minutes in between of two equal parts of metting.

so, duration of metting without the break=100 minutes

                                 duration of each part=50 minutes

Now, the break should be after First part which is of 50 minutes.

=> The break should 50 minutes after the starting of metting.

There is 1 smaller can that will be put on the shelve.

Given that, a clerk is placing cans of soup on an 8-ft long shelf, we need to find how many more of the smaller cans will fit on the shelf than the larger cans,

Volume of small cans = 127.2 in³

Therefore,

127.2 = 3.14 × 4.5 × r²

r² = 127.2 / 14.13

r² = 9

r = 3

Similarly, the volume of the large can = 301.6 in³

301.6 = 3.14 × 6 × r²

r² = 16

r = 4

The number of small cans that can be out on the shelve = 8/3 ≈ 9

The number of larger cans that can be out on the shelve = 8/4 = 2

Hence, there is 1 smaller can that will be put on the shelve.

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Financial aid letters display aid and attendance costs for one year only. Some schools offer a financial aid letter for four years of undergrad, aiding in budget planning for the program.

A few schools may give a budgetary help letter that ventures aid and costs for all four a long time of an undergrad program. This could offer assistance understudies arrange and budget for their whole undergrad instruction.

In a few cases, Financial aid letters  may show aid and costs for a single semester, instead of the complete scholarly year. This could be valuable for understudies who are as it were going to part-time or who got to take a semester off.

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The answers are 1) 360,000, 2) 217,060, 3) 37,140 and 4) 180,080.

1) To calculate the amount of premium paid by the employee and the employer =

Consider employee medical insurance payable, and employee life insurance payable.

The journal entries for accrual payroll, including employee deductions, consider sales salaries expense office salaries expense, social sec taxes payable Medicare tax payable, employee income taxes, life insurance payable, union dues, salaries payable.

2) Journal entry for cash payment of net payroll for month of July consider salaries payable and cash.

3) Calculate the unemployment tax amount, consider state unemployment taxes and federal unemployment taxes,

Journey Entries for accrued employer payroll taxes,

Payroll taxes expenses, social taxes, Medicare taxes, state unemployment taxes, federal unemployment taxes, employee medical and life insurance.

4) Journal entries for cash payment of all libraries, consider, social medical taxes, employee fed, medical, life and state income taxes payable.  

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The coordinates of point B are given as follows:

B(-7, 6).

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

For this problem, we have that M(-6,2) is the midpoint of A(-5,-2) and B(x,y).

Then the x-coordinate of point B is obtained as follows:

(x - 5)/2 = -6

x - 5 = -12

x = -7.

The y-coordinate of point B is obtained as follows:

(y - 2)/2 = 2

y - 2 = 4

y = 6.

Hence the coordinates of B are given as follows:

B(-7, 6).

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An expression that represent PS include the following: C. (NP + NQ + QR)/NR - NR.

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to this circle, we have the following:

NP × PS = NQ × QR

PS = (NQ × QR)/NP

In terms of line segment NR, the expression can be rewritten as follows;

(NP + NQ + QR)/NR - NR

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Answer:

not sure sorry -(1,0)and (2,0)

a) The probability that the student was female is 43/76

b) The probability that the student was female AND got a "C" is 9/38

c) The probability that the student was female OR got a "C" is 45/76

We have,

             A   B   C  

Male     16  15  2  33

Female 14  11  18  43

Total     30 26 20 76

a) The probability that the student was female

= 43/76

b) The probability that the student was female AND got a "C"

= 18/76

= 9/38

c) The probability that the student was female OR got a "C"

= 43 /76 + 20/76 - 18/76

= 45/76

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Selective serotonin reuptake inhibitors (SSRIs) are drugs that A. prevent unused neurotransmitters from being transported back to the neuron.

By inhibiting the serotonin transporter, SSRIs prevent the reuptake of serotonin into neurons after synapse release, thereby increasing available serotonin in the brain. Such changes help to alleviate symptoms associated with anxiety, depression and other mood disorders.

Overall, a rise in serotonin activity is significant in transforming an individual's mood pattern. When more serotonin remains within synapses, it binds with and activates its receptors, leading to increased levels of hormonal activity proven to be effective in treating various mood imbalances in patients.

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