The expression below is a sum of cubes.

125x3 + 144
A.True
B.False ...?

Answer:

Option C is correct

[tex]x+y = 425[/tex]

[tex]y = 2x-70[/tex]

Step-by-step explanation:

Here, x represents Kathryn's score and y represents Michael's score.

As per the statement:

Michael and Kathryn bowl together and their combined total score for one game was 425 points.

⇒[tex]x+y = 425[/tex]

It is also given that Michael's score was 70 less than twice Kathryn's.

⇒[tex]y = 2x-70[/tex]

Therefore, the system of equations models the problem is:

[tex]x+y = 425[/tex]

[tex]y = 2x-70[/tex]

Final answer:

To find the amount for the monthly payments for a plasma-screen TV, subtract the down payment from the total cost and divide by the number of installments. The equation is: Monthly Payment = (Total Cost - Down Payment) / Number of Installments, which calculates to $195.75.

Explanation:

The student is seeking to find an equation that represents the cost of a plasma screen television being paid off with a down payment and equal monthly installments. Given the total cost of the television is $5250 and the down payment is $552, we can start by calculating the remaining balance after the down payment, which will be paid in 24 equal monthly payments.

First, subtract the down payment from the total cost to find the balance that needs to be paid in installments:

Next, we divide the balance by the number of monthly payments to find the amount of each payment:

Therefore, the equation that represents the monthly payment after the down payment is:

Monthly Payment = (Total Cost - Down Payment) / Number of Installments

Applying the given numbers we get:

Monthly Payment = ($5250 - $552) / 24

Plugging in the values:

Monthly Payment = $4698 / 24 = $195.75

Answer:

Solution is (2,1)

Step-by-step explanation:

In order to graph both lines ,we need to find the X and Y intercepts for both equations

Lets take equation  y =2x -3

               To find y intercept ,we plug x =0 ,we get y =2(0)-3 = 0-3 =-3

                         Y intercept is (0,-3) Which is point  'C' in the graph

              To find X intercept ,we plug y =0 ,we get 0 = 2x-3 or x = 3/2 or 1.5

                        X intercept is (1.5,0) Which is point D in the graph.

Lets take equation y =-2x+5

                   To find y intercept ,we plug x =0 ,we get y = -2(0)+5 = 0+5 = 5

                       Y intercept is (0,5) which is point A in the graph .

              To find X intercept ,we plug y =0 ,we get 0 =-2x+5 or x = 5/2 or 2.5

                     X intercept is (2.5,0) which is point B on the graph

         After getting intercept of both lines ,we plot both lines

In the graph Blue line shows  y=2x-3 and Red line shows y =-2x+5

both lines intersect at point E which is called the solution of both equation

which is given to be (2,1)

Answer:

The correct option is:   C.  Add the two bags together, multiply by .80, and then subtract $1.00.

Step-by-step explanation:

First you need to add the prices of two bags for getting the total sales price.

Now, the store is offering 20% off, that means you need to pay 80% of the total sales price. For finding the amount, we need to multiply the total sales price by 0.80

Then, you have a manufacturers coupon for a $1.00 off. So, for fining the final price, you need to subtract that $1.00 from the last result.

Thus, the correct option will be......

C. Add the two bags together, multiply by .80, and then subtract $1.00.

To find the number of white pieces when the ratio of black pieces to white pieces is known, set up a proportion and solve for the missing variable. In this case, the number of white pieces is 9.

To find the number of white pieces, we can use the proportion 3/4 = W/12, where W represents the number of white pieces.

Cross multiply to get 3*12 = 4*W

Therefore, 36 = 4W

Divide by 4 to find that W = 9.

Answer:

x = 6

Step-by-step explanation:

The given equation is [tex]f(x)=-(x+9)(x-21)[/tex]

We write the equation in standard form of parabola [tex]f(x)=ax^2+bx+c[/tex] using FOIL

[tex]f(x)=-(x+9)(x-21)\\\\f(x)=-(x^2-21x+9x-189)\\\\f(x)=-x^2+12x+189[/tex]

Now, we know that the axis of symmetry passes through the vertex. Hence, in order to find the vertex of the parabola, we find the x coordinate of the vertex.

x coordinate of the vertex is [tex]-\frac{b}{2a}[/tex]

Here, a = -1 b = 12

[tex]-\frac{b}{2a}\\\\=-\frac{12}{2\cdot(-1)}\\\\=-(-6)\\\\=6[/tex]

Therefore, the axis of symmetry is x = 6

The Answer:

356+56y=-832

The equation relating W to T is W = 600 + 25T.

Given:

The initial amount of water in the pond is 600 liters.

The water is being added at a rate of 25 liters per minute.

As time (T) increases, the amount of water in the pond (W) will increase due to the constant addition of 25 liters per minute.

The equation can be written as follows:

W = 600 + 25T

In this equation, 600 represents the initial amount of water in the pond (at T = 0), and 25T represents the additional water added for each minute of time (T).

Learn more about Linear Equation here:

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To simplify √24, we find its prime factors, pair them up, and bring one number from each pair outside the square root. The remaining numbers stay under the square root. The correct answer is 2√6. The options provided in the question are all incorrect.

The problem is asking us to simplify √24, which is a typical Mathematics question in Middle School. Here are the steps we need to take:

Therefore, √24 simplifies to 2√6.

All the options provided (A √38, B √212, C √26, D √46) are incorrect.

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To maximize revenue for John Deere's heavy-duty tractors, the optimal unit price is found by determining the vertex of the provided quadratic revenue function R(p). Using the vertex formula, the unit price p that maximizes revenue is $1520.

Maximizing Revenue for John Deere Heavy-Duty Tractors

To find the unit price that maximizes revenue for John Deere heavy-duty tractors, we need to analyze the revenue function R(p) provided, which follows a quadratic format:

R(p) = [tex](-1/2)p^2[/tex]  + 1520p

To find the maximum revenue, we can use the fact that the vertex of a parabola described by a quadratic equation y = ax^2 + bx + c provides the maximum or minimum value of the function. Since our equation is in the form of a parabola opening downwards (because the coefficient of p^2 is negative), the vertex will give us the maximum revenue point.

The formula for the p-coordinate (horizontal axis) of the vertex of a parabola is given by -b/(2a). In this case, a = -1/2 and b = 1520, therefore:

p = -b/(2a) = -1520/(2 * (-1/2)) = -1520/(-1) = 1520

Hence, the unit price p should be set at $1520 to maximize revenue for the sale of heavy-duty tractors. This value is already an integer, so rounding to the nearest dollar is not necessary.

Answer:

-40

Step-by-step explanation:

Answer:

The answer is:  [tex]x^3-9x^2+14x+24[/tex]

Step-by-step explanation:

The given expression is:  [tex](x-4)(x^2-5x-6)[/tex]

For getting the product, we need to distribute [tex](x-4)[/tex] with each term in the second parenthesis. So.....

[tex](x-4)(x^2-5x-6)\\ \\ =x^2(x-4)-5x(x-4)-6(x-4)\\ \\ =x^3-4x^2-5x^2+20x-6x+24 \ [using\ distribution\ rule]\\ \\ =x^3-9x^2+14x+24\ [combining\ like\ terms][/tex]

So, the answer is:  [tex]x^3-9x^2+14x+24[/tex]

Answer:

Step-by-step explanation:

Given that there is a cone and cylinder with equal radius and height.

Recall volume formula for cone and cylinder as

Volume of cone = [tex]\frac{1}{3} \pi r^2 h[/tex]

Volume of cylinder =[tex]\pi r^2 h[/tex]

Thus we find that cylinder has a greater volume and ratio is 3:1

Hence 3 times if filled up with a cone the cylinder will be completely full

Note:

Images with coordinates or original and translated triangles are attached.

Answer:

The coordinates for the given triangle are A(6,3), B(6,-3) and C(-2,-3), respectively.

Let us translate this triangle by -6 units along the x-axis and +3 units along the y-axis. This means that 6 will be subtracted from each of the abcissas (x-points) and 3 will be added to each ordinates (y-points). Hence, our translated triangle will have the following coordinates: A'(0,6), B'(0,0) and C'(-8,0), respectively.

Now to prove that both triangles are congruent, we use the SSS postulate, which states that:

"If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent."

Distance between two point P1 and P2 will be:

[tex]|P_1P_2|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Now using distance formula to find sides of triangle ABC and triangle A'B'C'.

For Triangle ABC:

|AB| = [tex]\sqrt{(6-6)^2+(-3-3)^2} =\;6\;units[/tex]

|AC| = [tex]\sqrt{(-2-6)^2+(-3-3)^2} =\;10\;units[/tex]

|BC| = [tex]\sqrt{(-2-6)^2+[-3-(-3)]^2} =\;8\;units[/tex]

For Triangle A'B'C':

|A'B'| = [tex]\sqrt{(0-0)^2+(0-6)^2} =\;6\;units[/tex]

|A'C'| = [tex]\sqrt{(-8-0)^2+(0-6)^2} =\;10\;units[/tex]

|B'C'| = [tex]\sqrt{(-8-0)^2+(0-0)^2} =\;8\;units[/tex]

Hence, as the distances are equal, the two triangles are congruent by SSS postulate.

Answer:

89; the mode

Step-by-step explanation:

Final answer:

The best measure of central tendency for the student's test scores is the mode, which is 89. The mean and median are 86 and 87 respectively, but the mode gives the highest score, hence it is the most favorable for determining the student's final grade.

Explanation:

The question asks for the most favorable measure of central tendency for a student's test scores to determine their final grade. The test scores provided are 89, 81, 85, 82, 89, and 89.

To find the most favorable measure, we need to calculate the mean (average), median, and mode of the test scores. The mean is calculated by adding all the scores together and dividing by the number of tests. The median is the middle number when the scores are listed in order, and the mode is the number that appears most frequently.

Calculating the mean: (89 + 81 + 85 + 82 + 89 + 89) / 6 = 85.83, which we round to the nearest whole number as 86.

To find the median, we order the scores: 81, 82, 85, 89, 89, 89. Since there are an even number of scores, the median is the average of the two middle numbers, in this case, 85 and 89. Thus, the median is (85 + 89) / 2 = 87.

The mode is the most frequent score, which is 89.

Out of the mean, median, and mode, the mode is the highest and most favorable measure of central tendency for the student, resulting in a final grade of 89 when rounded to the nearest whole number.

The volume of the cylindrical water tank with a radius of 5.5 feet and a height of 8 feet is 760 cubic feet after rounding to the nearest whole number.

To calculate the volume of a cylindrical water tank, we use the formula V = , where V represents volume, is the constant Pi, approximately equal to 3.14, r is the radius of the cylinder, and h is its height.

Given that the radius r is 5.5 feet and the height h is 8 feet, substituting these values into the formula gives us:

V = 3.14 * (5.5ft) * 8ft

First calculate the radius squared:

5.5ft * 5.5ft = 30.25ft

Now, calculate the volume:

V = 3.14 * 30.25ft * 8ft = 3.14 * 242ft = 759.88ft

After rounding to the nearest whole number, the volume is 760 cubic feet.