A store sells a floor lamp for 73.99. The store is having a sale that reduces the lamps price by 35%.How much does the lamp cost during sale?

The root of the function is such point [tex]x_0,[/tex] for which [tex]f(x_0)=0.[/tex]

The attached graph of the function  [tex]f(x) = 2x^3 - 19x^2 + 57x - 54[/tex] shows, that the graph of the function intersects the x-axis in three points (2,0), (3,0) and (4.5,0).

This means that for

Thus, x=2, x=3 and x=4.5 are rational roots of the polynomial function f(x).

Answer: three rational roots.

The polynomial function f(x) = 2x^3 - 19x^2 + 57x - 54 has three rational roots at x=2, x=3, and x=4.5, as confirmed by the graph intersecting the x-axis at these points.

The graph of the function f(x) = 2x^3 - 19x^2 + 57x - 54 intersects the x-axis at three points: (2,0), (3,0), and (4.5,0). This implies that x=2, x=3, and x=4.5 are the roots of the polynomial function.

Since these values are rational, the function has three rational roots. Rational roots occur when the function evaluates to zero for specific rational input values.

In this case, f(2) = 0, f(3) = 0, and f(4.5) = 0. The graph crossing the x-axis at these points confirms their status as roots. The polynomial f(x) has three rational roots, which are x = 2, x = 3, and x = 4.5.

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"+" & "=" button key Tom will press in the calculator.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

To calculate Tom's pay raise, he can perform the following calculation on his calculator:

= 40.85 x 0.06

= 2.4510

So Tom's pay raise is $2.45 per hour.

To calculate Tom's new hourly rate, he can perform the following calculation:

= 40.85 + 2.45

= 43.30

So Tom's new hourly rate is $43.30.

Here is how the calculation can be done on most calculators:

Enter 40.85 and then press the "+" button.

Enter 2.45 and then press the "=" button.

The result should be 43.30, which is Tom's new hourly rate with a 6% pay raise.

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Answer:

Option C

Step-by-step explanation:

Equation of any line is of the form y=mx+b where m is the slope and b the y intercept.

The given line has y intercept [tex]\frac{-1}{2}[/tex] and slope as [tex]\frac{1}{2}[/tex]

Hence equation of given line is :

[tex]y= \frac{1}{2}x-\frac{1}{2}[/tex]

Taking point (0,0) to check the inequality we have:

0≥[tex]\frac{-1}{2}[/tex]

The statement is true so option C [tex]y\geq \frac{1}{2} x-\frac{1}{2}[/tex] is right .

Answer:

      [tex]2x^2+4x+2[/tex]

Step-by-step explanation:

[tex]2x^3+6x^2+6x+2[/tex] divide by x+1

Divide the first term of numerator by the first term of denominator and put it at the top. then multiply the answer by x+1 . write the expression at the bottom and subtract it. Repeat the process till we get remainder.

                                         [tex]2x^2+4x+2[/tex]

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

          [tex]x+1[/tex]            [tex]2x^3+6x^2+6x+2[/tex]

                                [tex]2x^3+2x^2[/tex]

                                     -----------------------------------------(subtract)

                                                   [tex]4x^2+6x[/tex]

                                                    [tex]4x^2+4x[/tex]

                                            -------------------------------------------Subtract

                                                            [tex]2x+2[/tex]

                                                           [tex]2x+2[/tex]

                                             ------------------------------------------Subtract

                                                                 0

Answer:

Option 3 - [tex]m=-\frac{3}{4}[/tex]

Step-by-step explanation:

Given : P(-2, 4), Q(6, -2)

To find : The slope of a line parallel to the line through the given points?

Solution :

First we find the slope of the line passes through given points P(-2, 4), Q(6, -2)

The slope formula is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-2-4}{6-(-2)}[/tex]

[tex]m=\frac{-6}{8}[/tex]

[tex]m=-\frac{3}{4}[/tex]

When two lines are parallel then there slope are equal.

Therefore, The slope of a line parallel to the line through the given points is

[tex]m=-\frac{3}{4}[/tex]

So, Option 3 is correct.

Since Ned's truck suffered body damage due to a hailstorm, the components of Ned's insurance policy will take care of the damage done to Ned's truck during the hailstorm is comprehensive damage.

A comprehensive coverage is an insurance policy which covers the cost of damages to a vehicle which has been involved in an accident that is not caused by a collision.

Comprehensive insurance covers losses such as:

Therefore, the components of Ned's insurance policy will take care of the damage done to Ned's truck during the hailstorm is comprehensive damage.

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Final answer:

The remainder of 4^31 when divided by 10 is 4, determined by examining the repeating last-digit pattern of powers of 4.

Explanation:

To find the remainder of 4^31 when divided by 10, we can use the concept of powers and properties of numbers related to modulo arithmetic. Specifically, we look at the last digit pattern that emerges when calculating powers of 4, since the remainder when dividing by 10 depends solely on the final digit of the number.

The powers of 4 have a cycle: 4^1 ends with 4, 4^2 ends with 6, 4^3 ends with 4 again, and so on. This cycle repeats every two powers, so we only need to consider the power of 4 modulo 2 to determine the last digit of 4^31. Since 31 is an odd number, we know that 4^31 will end with a 4. Hence, the remainder of 4^31 divided by 10 is 4.

The net change in elevation from the Atacama trench to the Mariana trench is 2.968km.

We know that the deepest part of Mariana trench is at -11.033 km, while the deepest part of the Atacama trench is -8.065km.

To find the net change, we need to find the difference between the largest value and the smallest value.

So we get:

D = -8.065km - (-11.033 km) = 2.968km

Then the correct option is the second one.

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The planning value for the population standard deviation can be found by dividing the range by 4.

To estimate the population standard deviation, we can use the planning value formula. The planning value for the population standard deviation is equal to the range divided by 4. Thus, in this case, if the range is estimated to be 36, the planning value for the population standard deviation would be 9.

Answer: width = 18.5 ft; area = 342.3 ft2

Step-by-step explanation:

you plug in the width with the function , where ever there is an x replace it with the width for the maximum area

To determine Daniel's rate per lawn mowing, we would need to divide his total earnings by the total number of lawns mowed. The answer can also be found by evaluating the slope of a graph with earnings on the y-axis and lawns mowed on the x-axis as the slope would represent his earnings per mow.

Without the graph provided, we can't determine the exact answer to this problem. However, conceptually, Daniel's rate per lawn would be calculated by dividing the total amount he earned by the total number of lawns he mowed. For example, if he earned $60 from mowing 4 lawns, his rate would be $15 per lawn.

To find the answer using a graph, you would need to evaluate the slope of the line if the y-axis represents earnings and the x-axis represents lawns mowed. The slope of the line provides the rate, which is Daniel's earnings per mow.

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To solve the equation 5x + 5 = 25 + 3x, subtract 3x from both sides, subtract 5 from both sides, and divide by 2 to find x = 10.

To solve the equation 5x + 5 = 25 + 3x, you need to isolate the variable x. First, subtract 3x from both sides of the equation to combine like terms: 5x - 3x + 5 = 25. Simplify: 2x + 5 = 25. Next, subtract 5 from both sides of the equation to isolate the variable: 2x = 20. Finally, divide both sides of the equation by 2 to solve for x: x = 10.

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To earn $500 in interest at a 4% annual rate, you need to leave $2000 in the account for approximately 6.25 years.

The formula for simple interest is given by:

[tex]\[ I = P \times r \times t \][/tex]

Where:

- I is the interest earned,

- P is the principal amount (initial deposit),

- r is the annual interest rate (expressed as a decimal), and

- t is the time the money is invested or borrowed in years.

In this case, you want to find t, so rearrange the formula to solve for t:

[tex]\[ t = \frac{I}{P \times r} \][/tex]

Given that P = $2000, r = 0.04 (4% as a decimal), and I = $500, plug these values into the formula:

[tex]\[ t = \frac{500}{2000 \times 0.04} \][/tex]

Calculate the result to find out how long you must leave the money in the account to earn $500 in interest.

[tex]\[ t = \frac{500}{2000 \times 0.04} \]\[ t = \frac{500}{80} \]\[ t = 6.25 \][/tex]

Therefore, you must leave the money in the account for approximately 6.25 years to earn $500 in interest at a simple annual rate of 4%.

Answer:

x+x+x+x = 4x.

Step-by-step explanation:

x + x + x + x can represent 4x since there are 4 x’s. Those 4 x’s represent x being multiplied by 4, since there are 4 x’s.

Therefore, your answer is 4x.