Using synthetic division, what is the quotient of this expression?

Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.

To calculate the outstanding balance at the end of 13 months, we need to use the declining balance method. This method involves applying the interest rate to the remaining balance after each repayment.

First, let's calculate the interest for the first 4 months. The interest for this period can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the principal is $18,500, the rate is 5.00% per year (or 0.05), and the time is 4 months (or 4/12 years). Thus, the interest for the first 4 months is $18,500 × 0.05 × (4/12) = $308.33.

Next, we subtract the repayment made after 4 months ($5,300) from the outstanding balance ($18,500) and add the interest for the first 4 months ($308.33). This gives us a new outstanding balance of $18,500 - $5,300 + $308.33 = $13,508.33.

Now, let's calculate the interest for the period between 4 and 10 months. The principal remains the same ($13,508.33), the rate is still 5.00% per year (or 0.05), and the time is 6 months (or 6/12 years). Therefore, the interest for this period is $13,508.33 × 0.05 × (6/12) = $337.71.

Subtracting the repayment made after 10 months ($3,800) from the outstanding balance ($13,508.33) and adding the interest for the period gives us a new outstanding balance of $13,508.33 - $3,800 + $337.71 = $10,045.04.

Finally, to determine the last payment required to clear the outstanding balance at the end of 13 months, we subtract the new outstanding balance ($10,045.04) from the principal ($18,500). The last payment is therefore $18,500 - $10,045.04 = $8,454.96.

Therefore, Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.

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The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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In a math class with 19 students, on a day when a test and an assignment were given, there were 10 students who passed the test and 14 students who completed the assignment.

In a math class with 19 students, a test and an assignment were given on the same day.

Out of the 19 students, 10 of them passed the test and 14 students completed the assignment.

This information allows us to analyze the performance and completion rate of the students in the class.

Firstly, we can determine that there are at least 10 students who demonstrated a satisfactory level of understanding and knowledge in the subject matter, as they successfully passed the test.

This indicates that approximately 52.63% (10 out of 19) of the students achieved a passing grade on the test.

Furthermore, we know that 14 students completed the assignment.

This implies that these students fulfilled the requirements and submitted the necessary work within the given timeframe.

Consequently, we can deduce that approximately 73.68% (14 out of 19) of the students in the class completed the assignment.

It's worth noting that there may be overlap between the students who passed the test and those who completed the assignment, as well as students who did both.

However, without additional information, we cannot determine the exact number of students who passed the test, completed the assignment, or did both.

This data provides insight into the performance and diligence of the students in the math class, indicating the proportions of students who met the criteria for passing the test and completing the assignment.

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The ratio of the surface area to the volume of a cylinder is (2rh + 2r²) / (r²h).

The formula for the surface area of a cylinder is:

Surface Area = 2πrh + 2πr²

Volume of Cylinder: The volume of a cylinder is given by the formula:

Volume = πr²h

Ratio of Surface Area to Volume:

Ratio = (2πrh + 2πr²) / (πr²h)

Simplifying the expression, we can cancel out the common factors of π and r:

Ratio = (2rh + 2r²) / (r²h)

So, the ratio of the surface area to the volume of a cylinder is (2rh + 2r²) / (r²h).

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The complete equation is x² + 1/2x -2 = 2 + 2

The given equation can be rewritten as:

x² + (1/2)x + () = 2 + ()

Since the equation involves two missing values, let's consider them one by one.

Solve for the first missing value indicated by (_):

To find the missing value indicated by (_), we equate the quadratic equation to 2:

x² + (1/2)x + (_) = 2

Comparing this with the standard form of a quadratic equation,

ax² + bx + c = 0, we have:

a = 1, b = 1/2, c = (_ - 2)

Using the quadratic formula, x = (-b ± √(b²- 4ac)) / (2a), we can substitute the values:

x = (-(1/2) ± √((1/2)² - 4(1)(_-2))) / (2(1))

x = (-1/2 ± √(1/4 + 8(1)(_-2))) / 2

x = (-1/2 ± √(1/4 + 8(_ - 2))) / 2

Therefore, the first missing value is represented by (_ - 2).

Solve for the second missing value indicated by (_):

To find the missing value indicated by (_), we equate the constant term to 2:

(_) = 2

This indicates that the second missing value is equal to 2.

Putting it all together, the solution to the equation x² + (1/2)x + _ = 2 + _ is:

x = (-1/2 ± √(1/4 + 8(_ - 2))) / 2

with (_ - 2) representing the first missing value, and the second missing value is 2.

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Given the relationship, 9r + 8t = 9, the relationship as a function r = f(t) will be (9 - 8t) / 9.

The relationship 9r + 8t = 9 as a function r = f(t), one is needed to isolate the variable r first on one side of the equation.

Taking with the original equation:

9r + 8t = 9

Subtract 8t from both sides in order to isolate the term with r:

9r = 9 - 8t

Divide both sides by 9 in order to solve for r:

r = (9 - 8t) / 9

Therefore, the relationship 9r + 8t = 9 can be written as the function:

r = (9 - 8t) / 9.

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Your question seems incomplete, the probable complete question is:

Consider the relationship 9r + 8t = 9. a. Write the relationship as a function r = f(t).

Answer:

[tex]x\approx0.39,-3.89[/tex]

Step-by-step explanation:

[tex]\displaystyle 2x^2+7x=3\\2x^2+7x-3=0\\\\x=\frac{-7\pm\sqrt{7^2-4(2)(-3)}}{2(2)}\\\\x=\frac{-7\pm\sqrt{49+24}}{4}\\\\x=\frac{-7\pm\sqrt{73}}{4}\\\\x\approx0.39,-3.89[/tex]

Answer:

[a] 12 units

Step-by-step explanation:

The answer is (D) 44 units

1. The formula for the area of a rhombus is A= [tex]\frac{d_{1} d_{2}}{2}[/tex]

2. Fill in the information we know:

3. Now work backward:

4. Solve it:

Hence 44 units (D) is your answer

Answer:

44 m2

Step-by-step explanation:

The area of the rhombus can be divided into 4 equal triangles.

The area of one triangle is A=bh/2

so:

A = 5.5*2

A = 11 squared m

Since there are four (4) triangles in the rhombus we just need to multiply 11 by 4 so:

A = 11 * 4

A = 44 squared m

Based on the data, we can infer that the park with the highest fee is Coaster City.

To find the value of each park we must take into account the different tables that show the value of each park. In this case we must find the unit value of each park as follows:

Park 1:

Park 2:

Park 3:

In accordance with the above, we can infer that the 2 Coaster City park is the one with the highest rate.

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Answer:

6 m, 24 m

Step-by-step explanation:

area of kite = (diagonal 1 × diagonal 2) / 2

Let the length of the shorter diagonal = x.

The length of the longer diagonal is 4x.

The area is the product of the diagonals divided by 2.

area = 4x × x / 2 = 4x²/2 = 2x²

The area is 72 m².

Therefore, 2x² must equal 72 m².

2x² = 72 m²

Divide both sides by 2.

x² = 36 m²

Take the square root of both sides.

x = 6 m

The short diagonal has length 6 m.

The long diagonal is 4x long.

4x = 4(6 m) = 24 m

Answer: 6 m, 24 m

Answer:

6 metres and 24 metres

Step-by-step explanation:

The kite will be composed of two smaller triangles and two larger triangles.

Let's call the shorter diagonal (across the kite) W.

So the longer diagonal (top to bottom of kite) will be 4W.

area = (L X W)/2

= (4W X W)/2

= 4W²/2

= 2W².

2W² = 72

W² = 36

W = 6 metres.

so the shorter diagonal is 6 metres.

the longer diagonal is 4 X 6 = 24 metres

Answer: Your line should start at (-1,6) then it should cross (0,0) so, straight down and a small curve. Then you should be at (0 -2), continue the small curve you made. DO not make it a parabola. it is basically just a straight line down, then a really long curve. Make sure you make the curve go across the entire graph.

Answer:

Step-by-step explanation:

first, to find if they are perpendicular, we would have to determine their slopes.

y=-2x-1, we know that the slope is -2 (due to y=mx+b, where m is the slope)

y=-2x+6, we also know that the slope is -2.

since the slope is equal, it would be parallel.

However, if the slopes were negative reciprocals, (e.g. 1/2 & -2) they would be perpendicular.

If the slopes were neither negative reciprocals or equal, it would be neither.

Answer:

The median is the middle value in the set. Since there are 5 values in this set, the middle value is the third value, which is 6.

Therefore, the median of the set {2, 4, 6, 8, 10} is 6.

The correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200, option A is correct.

We have two carriers: land carriers and air carriers.

The land carriers can transport 1500 pieces of mail per load, and the air carriers can transport 1250 pieces of mail per load.

The loading equipment at the distribution center can handle up to 200 loads per day.

To represent this situation using a system of inequalities, we can define the variables x and y as the number of loads by land carriers and air carriers, respectively.

The first inequality, 1500x + 1250y ≥ 175,000, represents the total number of pieces of mail transported per day.

The second inequality, x + y ≥ 200, represents the total number of loads.

Hence,  the correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200.

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Answer:

Aprox: 465.4 ms/2

Step-by-step explanation:

To find the magnitude of the acceleration the engine must produce, we'll break down the missile's motion into its horizontal and vertical components.

Given:

Initial velocity (V₀) = 1810 m/s

Launch angle (θ) = 20.0°

Target distance (d) = 19,500 m

Target direction (φ) = 32.0°

Time of flight (t) = 9.20 s

First, let's find the horizontal and vertical components of the missile's initial velocity (V₀x and V₀y).

V₀x = V₀ * cos(θ)

V₀y = V₀ * sin(θ)

V₀x = 1810 m/s * cos(20.0°) ≈ 1712.4 m/s

V₀y = 1810 m/s * sin(20.0°) ≈ 618.8 m/s

Now, let's find the horizontal and vertical displacements (dx and dy) of the missile using the time of flight (t) and the target distance (d).

dx = d * cos(φ)

dy = d * sin(φ)

dx = 19,500 m * cos(32.0°) ≈ 16,402.8 m

dy = 19,500 m * sin(32.0°) ≈ 10,236.8 m

Next, let's calculate the acceleration needed in the x-direction (ax) and y-direction (ay) to cover the horizontal and vertical displacements in the given time.

ax = (2 * dx) / t²

ay = (2 * dy) / t²

ax = (2 * 16,402.8 m) / (9.20 s)² ≈ 391.7 m/s²

ay = (2 * 10,236.8 m) / (9.20 s)² ≈ 257.7 m/s²

Finally, to find the magnitude of the acceleration, we can use the Pythagorean theorem:

acceleration magnitude (a) = √(ax² + ay²)

a = √(391.7 m/s²)² + (257.7 m/s²)² ≈ 465.4 m/s²

Therefore, the magnitude of the acceleration that the engine must produce is approximately 465.4 m/s².

The  names of the siblings from shortest to longest time are:

Rafael= 75min = 1 hour and 15 minutes.

Leanne= 1 hour and 25 minutes

Ray= 1 3/4 =  1 hour and 45 minutes.

To be able to compare 1 hour and 25 minutes with  1 3/4 (1.75 hours), one need convert the minutes to hours. 1 hour is equal to 60 minutes, so 1 hour and 25 minutes is equivalent to 1.42 hours.

1.42 hours is smaller than 1.75 hours. hence Ray has the longest time.

So according to the given information, note that:

Hence, the siblings' names listed from shortest to longest time are Rafael, Leanne, and Ray.

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The total amount of money shared by Lee and Olivia is £132 and  Lee and Olivia shared £84 and £48, respectively.

Lee has 7/11 of the total money, which means Lee has (7/11) × x amount of money.

When Lee gives Olivia £18, they have the same amount of money.

So Olivia's share becomes equal to Lee's share.

Therefore, we can set up the following equation:

(7/11) × x - £18 = (1/2)×x

To solve this equation, we can simplify it:

7x/11 - £18 = x/2

Multiplying both sides of the equation by 22 (the least common multiple of 11 and 2) to eliminate the denominators:

14x - 22 × £18 = 11x

14x - 396 = 11x

Subtracting 11x from both sides:

14x - 11x - 396 = 0

3x - 396 = 0

Adding 396 to both sides:

3x = 396

Dividing both sides by 3:

x = 396/3

x = 132

To find Lee and Olivia's individual shares, we can substitute this value back into the initial conditions:

Lee's share = (7/11)× £132 = £84

Olivia's share = £132 - £84 = £48

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Answer:

The volume is 423.33 cubic millimeters.

Step-by-step explanation:

The formula for volume of a cylinder is given by:

V = πr^2h, where

Step 1:  Find radius, r, of the cylinder:

The diagram shows us the diameter, d, of the circle is 7 mm.  Since the diameter is twice the radius, r, we can find r by dividing the diameter by 2:

r = d / 2

r = 7 / 2

r = 3.5 mm

Thus, the radius of the cylinder is 3.5 mm.

Step 2:  Plug in values and round to the nearest hundredth to find the volume, V, of the cylinder:

Now we can plug in 3.5 for r and 11 for h to find V, the volume of the cylinder.  We can round at the end.

V = π(3.5)^2(11)

V = π(12.25)(11)

V = 134.75π

V = 423.3296101

V = 423.33 mm^2

Thus, the volume of the cylinder is 423.33 cubic millimeters.

Answer:

  (a)  0.75

Step-by-step explanation:

You want the 10th term of the geometric sequence with a1 = 384 and a7 = 6.

The equation for the n-th term can be written ...

  an = a1·b^(n-1)

Using a1 = 384, we can find b from ...

  a7 = 6 = 384·b^(7-1)

  (6/384)^(1/6) = b

Then the 10th term is ...

  a10 = 384·(6/384)^((10-1)/6) = 0.75

The 10th term of the sequence is 0.75.

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Answer:

x intercept at( -2)

y intercept at (4)

The x-intercept and the y-intercept are -2 and 4 respectively.

The X-intercept is the point where the line of an equation intersects the X-axis. While y-intercept is the point where the line of an equation intersects the Y-axis. Here, the X-axis is the horizontal axis, and the Y-axis is the vertical axis.

Since the given graph shows the line intersecting the X-axis i.e. the horizontal axis at -2, the x-intercept of the line would be -2. Whereas, since the line intersects the Y-axis at 4, the y-intercept is 4. The points that show these intercepts are (-2,0) for the x-intercept and (0,4) for the y-intercept.

∴ The intercepts are -2,4 respectively.

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Answer:

x = 12

Step-by-step explanation:

sin45 = x/17         (sin = opposite/hypotenuse)

x = (sin45)(17) = 12.02 ≈ 12

The value of x with the answers in simplest radical form is 18.

We are given that;

The right triangles with dimension

Now,

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2

1. 14^2+14^2=x^2

196+196=x^2

x^2=392

x=19.7

2. x^2+X^2=12^2

2x^2=144

x^2=72

x=8.48

3. 9[tex](\sqrt{2} )^2[/tex]+9[tex]\sqrt{2})^2[/tex]=x^2

162+162=x^2

324=x^2

x=18

Therefore, by pythagoras theorem the answer will be 18.

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Beth and Kelly were on vacation for 6 days.

Let's assume that Beth and Kelly were on vacation for "x" days.

For Beth:

The cost per day for dog sitting at Rover Sleepover is $24.50.

Beth also paid a fee of $90.50 for food and cleaning.

So the total cost for Beth's dog sitting can be expressed as:

Total cost for Beth = (Cost per day × Number of days) + Cleaning fee

Total cost for Beth = ($24.50 × x) + $90.50

For Kelly:

The cost per day for dog sitting at Pet Palace is $32.

Kelly also paid a fee of $45.50 for cleaning.

So the total cost for Kelly's dog sitting can be expressed as:

Total cost for Kelly = (Cost per day × Number of days) + Cleaning fee

Total cost for Kelly = ($32 × x) + $45.50

Since both Beth and Kelly spent the same total amount of money, we can set up an equation:

($24.50 × x) + $90.50 = ($32 × x) + $45.50

Simplifying the equation, we get:

$24.50x + $90.50 = $32x + $45.50

Moving the variables to one side and constants to the other side:

$32x - $24.50x = $45.50 - $90.50

Combining like terms, we have:

$7.50x = $45

Dividing both sides of the equation by $7.50:

x = $45 / $7.50

x = 6

Therefore, Beth and Kelly were on vacation for 6 days.

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The additional information is needed to prove the triangles are congruent by the SAS Postulate is <ACB = <ACD.

We have, CB = CD

As, The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the two triangles are congruent.

In triangle ACB and ACD

AC = AC (common)

CB=  CD (given)

Now, to prove using SAS rule we need only one angle which is in between the two congruent sides then

<ACB = <ACD

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Answer:

The average speed of a particle over a time interval is defined as the total distance traveled divided by the time elapsed. In this case, the average speed of the particle over the time interval [0,4] is represented by options 2 and 3. Option 2 represents the change in position over the time interval [0,4] divided by the time elapsed. Option 3 represents the slope of the secant line connecting the points (0,s(0)) and (4,s(4)), which is equivalent to the average rate of change of position over the time interval [0,4].

the correct answers are, 2 and 3

Answer:

There are 6 countries with more than 60 confirmed cases

Step-by-step explanation:

- Draw your stem and leaf plot

-There is a stem without a leaf (There are no values in this class)

-Count the values in the stem and leaf plot and ensure they are 15. Each value represents the number of confirmed case in a county.

There are six numbers greater than 60 which are 62,63,63,67,65 and 97

Hence, there are 6 countries which have more than 60 confirmed cases