Review Questions

1. A washer and a dryer cost $1004 combined. The washer costs $54 more than the dryer. What is the cost of the dryer?

Please use your work.

In ΔRST, the overline{RT} RT is extended through point T to point U, Therefore the value of x = 10.

The sum of angles in a triangle is 180 degrees, we have:

m∠RST + m∠STU + m∠TRS = 180

We substitute the given values, and have:

(3x + 17) + (8x + 1) + (3x + 18) = 180

We simplify  and solve  for x, we get:

14x + 36 = 180

14x = 144

x = 10.

A triangle in geometry is descried a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most important  characteristic.

This characteristic is known as the triangle's angle sum property.

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The area of the semi-circle patio is approximately 17.91 square feet.

To find the area of the semi-circle patio, we need to use the formula for the area of a circle, which is A = πr^2, where π is 3.14 and r is the radius of the circle.

However, since we only have a semi-circle, we need to divide the result by 2 to get the area of the half-circle.

In this case, the radius of the semi-circle is half of the diameter, which is given as 6.75 feet. So, the radius is 6.75/2 = 3.375 feet.

Now, we can plug this value into the formula:

A = (π)(3.375)^2 / 2

A = (3.14)(11.390625) / 2

A = 35.81765625 / 2

A = 17.908828125 square feet

Therefore, the area of the semi-circle patio is approximately 17.91 square feet.

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1. The value of d is 10

2. measure of angle BSR is 120°

3. measure of angle RSM is 60°

The sum of angles on a straight line is 180°. This angles are adjascent angles.

angle BSR and RSM are on a straight line, therefore;

10d+20+6d = 180

16d = 180-20

16d = 160

d = 160/16

d = 10

therefore the value of d is 10

angle BSR = 10d+20 = 10×10+20

= 100+20 = 120°

angle RSM = 6d = 6 × 10

= 60°

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The ∠EBC and ∠FCD are corresponding angles.Option(C) is Crrect.

Corresponding angles are angles that are in matching or corresponding positions when two parallel lines are intersected by a transversal. In other words, corresponding angles are pairs of angles that occupy the same relative position at each intersection of a transversal and parallel lines.

More specifically, if two parallel lines, line AB and line CD, are intersected by a transversal, line EF, at point G, then the angles that are opposite each other (one on each line) are corresponding angles. The corresponding angles are denoted by the same letter or symbol.

So, ∠EBC and ∠FCD are corresponding angles.Option(C) is Correct.

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The percent increase in Patti's hourly wage is 23%.

Percent​ increase is aimply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.

It is expressed as:

percent increase = ((new value - old value) / old value) × 100%

Given that, the old hourly wage was $10.00 and the new hourly wage is $12.30.

Substituting the values into the formula, we get:

percent increase = ((new value - old value) / old value) × 100%

percent increase = (($12.30 - $10.00) / $10.00) × 100%

percent increase = ($2.30 / $10.00) × 100%

percent increase = 0.23 × 100%

percent increase = 23%

Therefore, the percent increase is 23%.

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The maximum profit is $1,892,250.

The profit function is given by[tex]P(x) = -x^2 + 15x + 72x - 300 = -x^2 + 87x - 300.[/tex]

To find the number of hundred thousands of tires that must be sold to maximize profit, we need to find the value of x that maximizes P(x).

We can do this by finding the critical point of P(x) and then checking whether it corresponds to a maximum or a minimum.

The derivative of P(x) is:

P'(x) = -2x + 87

Setting this equal to zero to find critical points, we get:

-2x + 87 = 0

Solving for x, we get:

x = 43.5

Since the problem specifies that x must be at least 5, we know that the critical point x = 43.5 corresponds to a maximum.

Therefore, the number of hundred thousands of tires that must be sold to maximize profit is 43.5.

To find the maximum profit, we substitute x = 43.5 into the profit function:

[tex]P(43.5) = -43.5^2 + 87(43.5) - 300 = 1892.25[/tex]

Therefore, the maximum profit is $1,892,250.

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The slope of desired parallel line is undefined.

Given two points [tex](-4, 3)[/tex] and [tex](-4, 7)[/tex], we can see that both points have the same x-coordinate, which means that they lie on a vertical line parallel to the y-axis. Since the slope of a vertical line parallel to the y-axis is undefined, we can say that the slope of line m is undefined.

To find the slope of a line that is parallel to line m, we can use the fact that parallel lines have the same slope. Since the slope of line m is undefined, any line parallel to it will also have an undefined slope.

Therefore, the slope of the line that is parallel to line m is undefined.

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The equation that represents the Ferrells' savings after x months is y = 150x

In this equation, x represents the number of months that the Ferrells have been saving, and y represents the amount of money they have saved after x months.

The coefficient 150 represents the amount of money the Ferrells save each month, and it is multiplied by the number of months x to get the total savings y. For example, after 5 months of saving, the Ferrells would have saved:

y = 150(5) = $750

This equation can be used to calculate their savings at any point in time, as long as they continue to save $150 each month.

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The dimensions of the square are 6 inches by 6 inches.

Let's assume that the side of the square is equal to x inches. Then, the area of the square can be expressed as x^2 square inches. The perimeter of the square is equal to 4 times the length of the side, or 4x inches.

According to the problem, the area of the square is 12 more than its perimeter, so we can write:

x^2 = 4x + 12

This is the equation we can use to find the dimensions of the square. To solve for x, we can rearrange the equation:

x^2 - 4x - 12 = 0

Then, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -4, and c = -12.

Plugging in these values, we get:

x = (-(-4) ± √((-4)^2 - 4(1)(-12))) / 2(1)

x = (4 ± √64) / 2

x = (4 ± 8) / 2

Therefore, the two possible solutions are:

x = 6 or x = -2

Since the side of a square cannot be negative, the only valid solution is x = 6.

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Answer:

Step-by-step explanation:

The independent variable in the study is the  temperature of the water

The variable that the experimenter consciously modifies or changes is known as the independent variable.

The variable that is supposed to have an impact on the dependent variable is this one. After then, the dependent variable is assessed and recorded to see if it changes as a result of the independent variable's manipulation.

The temperature was changed before each trial hence the temperature was manipulated and that is the independent variable.

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a. The two companies charge the same for 14 tons of sugar.

b. The cost when the two companies charge the same is $7953.50.

a. Let's represent the amount of sugar as x, and the total cost as C. Then we can set up the following equations for each company:

Company 1: C = 5143 + 200.75x

Company 2: C = 5500 + 175.25x

To find the amount of sugar for which the two companies charge the same, we can set the two equations equal to each other and solve for x:

5143 + 200.75x = 5500 + 175.25x

25.5x = 357

x = 14

So the two companies charge the same for 14 tons of sugar.

b. To find the cost when the two companies charge the same, we can plug in x = 14 into either equation. Let's use Company 1's equation:

C = 5143 + 200.75x

C = 5143 + 200.75(14)

C = 5143 + 2810.50

C = 7953.50

Therefore, the cost when the two companies charge the same is $7953.50.

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A system of inequalities to model this situation is 4x + 9y ≥ 720 and x + y ≤ 110.

The two possible solutions are (80, 40) and (100, 20).

In order to write a linear equation to describe this situation, we would assign variables to the number of student tickets sold and the number of adult tickets sold respectively, and then translate the word problem into a linear equation as follows:

Since each student ticket was sold for $4 and each adult ticket sales to cover the show's costs sells for $9 in order to make a minimum of $720 from show's expenses, a linear equation which can be used to model the situation is given by;

4x + 9y ≥ 720

Additionally, the auditorium can hold no more than 110 people;

x + y ≤ 110

Next, we would use an online graphing calculator to plot the above system of linear equations in order to determine its solution as shown in the graph attached below.

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All real numbers will be the function's domain. D is the right answer in this case.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set(x).

A function's range is the collection of values it can take as input.

After we enter an x value, the function outputs this sequence of values.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

Let a be the leading coefficient and the parabola's vertex be the point (h, k).

The parabola's equation will then be provided as,

y = a(x - h)² + k

The graph shows where the vertex of the parabola will be. (-1.5, -4.5). The equation is then presented as:

y = a(x + 1.5)² - 4.5

Therefore, all real numbers will be the function's domain. D is the right answer in the case.

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Correct question:

The graph of the quadratic function f is shown in the grid. Which of these best represents the domain of f?

A: y>=4.5

B: All real numbers less than -4 or greater than 1

C: -4<=x<=1

D: All real numbers ​

To find the length of border needed to put around a rectangular room, you can follow these steps:

Measure the length and width of the room using a tape measure or ruler. Let's say the length is L and the width is W.

Determine the type and width of the border you want to put around the room. Let's say you want to use a wallpaper border that is 6 inches wide.

Calculate the length of the border needed for the top and bottom of the room.

This can be done by adding the width of the room to twice the width of the border. So the length of the top and bottom borders would be:

Length of top/bottom borders = 2(W + 6 inches)

Calculate the length of the border needed for the left and right sides of the room. This can be done by adding the length of the room to twice the width of the border. So the length of the left and right borders would be:

Length of left/right borders = 2(L + 6 inches)

Add up the length of all four borders to get the total length of border needed to put around the room:

Total length of border = 2(W + 6 inches) + 2(L + 6 inches)

Simplifying the above equation, we get:

Total length of border = 2L + 2W + 24 inches

So the total length of border needed to put around the room is 2L + 2W + 24 inches.

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If 1/6 of the boys joined the basketball team, there are 160 boys in the soccer team.

If 1/6 of the boys joined the basketball team, then 5/6 of the boys did not join the basketball team. Similarly, if 2/9 of the boys joined the soccer team, then 7/9 of the boys did not join the soccer team.

Let's first find out how many boys did not join the soccer team:

7/9 x 540 = 380

Therefore, 380 boys did not join the soccer team.

To find out how many boys did join the soccer team, we can subtract the boys who did not join from the total number of boys:

540 - 380 = 160

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Answer:

Solution: (x-3)(x+1)

Step-by-step explanation:

1) Using Mid term break:

x²-2x-3

x²+x-3x-3

2) Take Common Factors from the two pairs

(x²+x) + (-3x-3)

x(x+1) -3(x+1)

3) Rewrite in Factored Form:

(x-3)(x+1)

1)  The domain of Y = 3x⁴ + 4x³ is (-∞, ∞).

2) The x-intercepts are (0, 0) and (-4/3, 0) and the y-intercept is (0, 0)

3)  The horizontal asymptote is y = infinity.

4) Function does not exhibit any symmetry with respect to the y-axis or origin.

5)  The critical points are x = 0 and x = -1.

6)  The critical points are x = 0 and x = -1.

7) The function is concave down on the interval (-∞, -2/3) and concave up on the intervals (-2/3, 0) and (0, ∞).

1) The domain of a polynomial function is all real numbers, so the domain of Y = 3x⁴ + 4x³ is (-∞, ∞).

2) To find the x-intercepts, we set Y equal to zero and solve for x:

0 = 3x⁴ + 4x³

0 = x³(3x + 4)

x = 0 or x = -4/3

Therefore, the x-intercepts are (0, 0) and (-4/3, 0).

To find the y-intercept, we set x equal to zero and solve for Y:

Y = 3(0)⁴ + 4(0)³

Y = 0

Therefore, the y-intercept is (0, 0).

3) Polynomial functions do not have vertical asymptotes. However, as x approaches positive or negative infinity, the function approaches infinity. Therefore, the horizontal asymptote is y = infinity.

4) The function Y = 3x⁴ + 4x³ is neither even nor odd. Therefore, it does not exhibit any symmetry with respect to the y-axis or origin.

5) To find the critical points, we take the first derivative of Y and set it equal to zero:

Y' = 12x³ + 12x²

0 = 12x²(x + 1)

Therefore, the critical points are x = 0 and x = -1.

6) To determine whether the critical points are maxima or minima, we take the second derivative of Y and evaluate it at each critical point:

Y'' = 36x² + 24x

At x = 0, Y'' = 0, which means that the second derivative test is inconclusive. To determine whether x = 0 is a maxima or minima, we look at the sign of the first derivative to the left and right of the critical point. We find that Y' is negative to the left of x = 0 and positive to the right, so x = 0 is a local minimum.

At x = -1, Y'' = 12, which is positive. Therefore, x = -1 is a local minimum.

7) To determine the concavity of the function, we look at the sign of the second derivative:

Y'' = 36x² + 24x

When Y'' > 0, the function is concave up, and when Y'' < 0, the function is concave down.

At x < -2/3, Y'' is negative, so the function is concave down.

At -2/3 < x < 0, Y'' is positive, so the function is concave up.

At x > 0, Y'' is positive, so the function is concave up.

Therefore, the function is concave down on the interval (-∞, -2/3) and concave up on the intervals (-2/3, 0) and (0, ∞).

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The representativeness of a sample depends on how it is selected and whether it accurately reflects the characteristics of the larger population. Without more information about the sampling method used, it is difficult to determine if the sample of 16 politicians is likely to be representative of the citizens of the state.

If the sample was selected randomly from a diverse pool of politicians that accurately represents the political landscape of the state, there is a higher likelihood that the sample would be representative. However, if the sample was obtained through convenience sampling or if it disproportionately represents certain political affiliations or demographics, it may not be representative of the entire population of citizens in the state.

To assess the representativeness of the sample, it is important to consider factors such as the sampling method, sample size, diversity of the sample, and the specific characteristics being studied.

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Answer:

Step-by-step explanation:

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No, quadrilaterals ABCD and EFGH are not similar because the ratio of their corresponding sides is not proportional.

In Geometry, two (2) quadrilaterals are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Additionally, two (2) geometric figures such as quadrilaterals are considered to be congruent only when their corresponding side lengths are congruent (proportional) and the magnitude of their angles are congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The minimum number of dots that could lie on the whole surface of four standard dice glued together is 56.

This can be achieved by placing the faces with 1 dot opposite the faces with 6 dots, the faces with 2 dots opposite the faces with 5 dots, and the faces with 3 dots opposite the faces with 4 dots on all four dice. Since the sum of the numbers on opposite faces of each individual die is always 7, the sum of the numbers on opposite faces of the four glued-together dice is also always 7. Therefore, the minimum number of dots on the whole surface is 7 times the number of faces, which is 7 x 8 = 56.

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Since 24.8 minutes is less than 36.4 minutes, you would still meet your goal because your total running time added to your swimming and biking times is less than 100 minutes.

The inequality that represents how many minutes x you can take to finish the running event and still meet your goal is: 18.2 + 45.4 + x < 100. To solve for x, we need to isolate it on one side of the inequality:

18.2 + 45.4 + x < 100
x < 100 - 18.2 - 45.4
x < 36.4

Therefore, you can take no more than 36.4 minutes to finish the running event and still meet your goal of finishing with an overall time of less than 100 minutes.

For question 3, if it takes 8 minutes to run a mile and the running event is 3.1 miles long, it would take you 24.8 minutes to complete the running event. This time is less than the maximum time of 36.4 minutes that you can take to still meet your goal, so yes, this time would allow you to reach your goal.

For question 4, the statement is just reiterating the goal mentioned in the first sentence, that your overall time for all three events must be less than 100 minutes. It confirms that you have met your goal by stating that your total running time added to your swimming and biking times is less than 100 minutes.

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The total amount Babcar and Arutro paid in the Burger Beast Restaurant is $ 34.56.

Total bill = $36

Discount coupon = 20 %

The price paid after the discount coupon = 36 - (20% of 36 )

Price paid = 36 - (36 × 20/100)

The price paid = 36 - 7.2

Price paid = 28.8

The tip paid is 20 % the discounted price

The tip paid = 20% of 28.8

The tip paid = 28.8 × 20/100

The tip paid = 5.76

The total price paid = price paid after discount coupon + Tip paid

The total price paid = 28.8 + 5.76

The total price paid = 34.56

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Note that the light is about 9.17 x 10³ times faster than sound. See the explanation below.

To arrive a the above, we only need to simplify Jakes observation as follows

[tex]\frac{1.1 * 10^{9} km/h }{1.2 * 10^{3}km/h }[/tex]

dividing the coefficients

1.1/1.2 = 0.91666666666

0.91666666666 x 10 ⁹⁻³

= 9.1666667 x 10 ⁵

further simplified, we have
9.17 x 10³

Thus, we can summarize that light is about 9.17 x 10³ faster than the speed of sound going by Jake observation.

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Full Question:

Jake noted that speed of light is approximately 1.1 × 10⁹ km/h;

the speed of sound is approximately 1.2 x 10³ km/h; and

11 + 12 = 0.916.

Using Jake's figures how many times faster is light than speed?

Write your answer in standard form.

Based on the information, the equilibrium price is $56.67

Using the first data point, we have:

25 = a - 40b

Using the second data point, we have:

185 = a - 20b

Solving these two equations simultaneously, we get:

a = 325

b = 5/2

So the demand function is:

Qd = 325 - 5/2 P

the supply function is:

Qs = -100 + 5P

325 - 5/2 P = -100 + 5P

425 = 15/2 P

P = $56.67

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Answer:

Set your calculator to degree mode.

tan(37°) = x/8

x = 8tan(37°) = 6.03

For the given triangle the required value of the x is approximately 6.02 units.

Use the concept of triangle defined as:

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

In the given triangle:

One angle is 37°

Adjacent side = 8 cm

Perpendicular = x

Since we know that,

Tan θ = opposite/adjacent

Therefore,

Tan 37° = x/8

Since Tan 37° ≈ 0.753

Then, 0.753  ≈  x/8

x ≈ 6.02 units

Hence,

The required value of x is approximately 60.2 units.

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An equation that best fits the data is: C. g = -0.019r² + 0.797r + 1.94.

In this scenario, the r (inches) would be plotted on the x-axis (x-coordinate) of the scatter plot while the G (inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the r (inches) and the G (inches), an equation for the line of best fit is given by:

g = -0.019r² + 0.797r + 1.94

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The area of ΔSTU is approximately 6.7 square centimeters.

To find the area of a triangle, we can use the formula A = (1/2)bh, where b is the base of the triangle and h is the height. In this case, we know that u is the base of the triangle, so we need to find the height.

To do this, we can use the sine function, which tells us that sin(6°) = h/u. Rearranging this equation, we get h = usin(6°). We can then substitute u and sin(6°) into the formula for the area to get

A = (1/2)(3.4)(3.4sin(6°)) ≈ 6.7 square centimeters.

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