1) Divide using synthetic division, and write a summary statement in fraction form.
two x to the fifth minus x to the fourth plus three x squared minus x plus five divided by quantity x minus one

a. 2x4 + x3 + 4x2 + 3x + eight divided by quantity x minus one
b. 2x4 + x3 - x2 + 2x + 1 + six divided by quantity x minus one
c. 2x4 + x3 + x2 + 4x + 3 + eight divided by quantity x minus one
d. 2x4 - 3x3 + x + six divided by quantity x minus one

2) Divide f(x) by d(x), and write a summary statement in the form indicated.
f(x) = x4 - 4x3 + 2x2 - 4x + 1; d(x) = x2 + 1

a. f(x) = (x2 + 1)( x2 + 4x + 1)
b. f(x) = (x2 + 1)( x2 - 4x + 1) + 12x + 3
c. f(x) = (x2 + 1)( x2 + 4x + 1) + 12x + 3
d. f(x) = (x2 + 1)( x2 - 4x + 1)

3) Find the remainder when f(x) is divided by (x - k).
f(x) = 3x3 - 4x2 - 3x + 14; k= 3

a. 50
b. 68
c. -12
d. 112

4) Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f.
k = -1; f(x) = 4x3 - 2x2 + 2x + 4; Lower bound?

a. yes
b. no

5) Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.
f(x) = -2x4 + 4x3 + 3x2 + 18

To calculate the number of days between two dates, subtract the start date from the end date and add 1.

To find the number of days between two dates, you can use the formula:

Number of days = (End date) - (Start date) + 1

For example, if the start date is July 10, 2022, and the end date is July 15, 2022, the number of days between them would be:

Number of days = (15) - (10) + 1 = 6

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Okay, well we start out with the equation P=66, where P is perimeter. You should create equations using variables to explain each piece of information you are given. Follow the equations below and see if you can understand how to do another one like this. In this problem, l is length and w is width.

P = 66                               The perimeter is equal to 66

l = 3 + w                           The length of one side is 3 more than the width

2l + 2w = 66                      A rectangle's perimeter is calculated by adding the lengths and widths

2(3 + w) + 2w = 66           Use what you know about length from step 2 to replace the variable in step 3

6 + 2w + 2w = 66              Multiply

6 + 4w = 66                       Add like terms

4w = 60                            Subtract

w = 15                             Divide

l = 3 + w                         Remember step 2?

l = 3 + 15                       Replace the variable using your value for w

l = 18                             Add

And you're done! Always check your work. It helps to create a picture of a rectangle while you're doing these problems as well. As you get used to these problems more and more, you can show more or less work than I've shown, but try to stay true to what the teacher asks of you. Good luck!

Answer:

49.075 minutes

Step-by-step explanation:

Your welcome :]

slope =

7- - 2 =9

8-0 = 8

slope = -9/8

y intercept = 7

equation: y=-9/8x+7

Final answer:

The area of triangle ΔABC with m∠A = 120°, side b = 13 cm, and side c = 15 cm, when calculated using the formula for area ½ bc sin A, is approximately 84.2 cm² when rounded to the nearest tenth.

Explanation:

To find the area of triangle ΔABC with m∠A = 120°, side b = 13 cm, and side c = 15 cm, we will use the formula for the area of a triangle when two sides and the included angle are known:

Area = ½ bc sin A

First, we need to find the sine of angle A, which is sin(120°). Using a calculator, we find that sin(120°) ≈ 0.866. Now, we can plug in the values into the area formula:

Area = ½ × 13 cm × 15 cm × sin(120°)

Area = ½ × 13 cm × 15 cm × 0.866

Area ≈ ½ × 13 cm × 15 cm × 0.866 ≈ 84.225 cm²

Rounding to the nearest tenth, the area is approximately 84.2 cm².

Answer:

1.25x>35

Step-by-step explanation:

If x is the number of times you must ride the subway and the monthly pass is $35, we must determine the expression where the cost per ride is greater than $35. Therefore:

1.25x>35

We can solve x to determine the number of rides you must ride for the monthly pass to be a better deal.

x>35/1.25

x>28

The student must take more than 28 rides for the mothly pass to be a better deal.

The measure of the angle ∠ABC will be 95 degrees.

A quadrilateral is a shape made up of four sides having the sum of the angles 360 degrees. The given shape is like a parallelogram in which two sides are equal and at the same angles.

Given that angle A in the quadrilateral is 85 degrees. The value of the angle B will be calculated as:-

∠A + ∠B +∠C + ∠D = 360

85 + ∠B + 85 + ∠B = 360        ∠B = ∠D

170 + 2∠B = 360

2∠B = 360 - 170

2∠B = 190

∠B = 190 / 2

∠B = 95

Therefore, the measure of the angle ∠ABC will be 95 degrees.

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 4d +13.00 -6.00 = 13.20

4d = 7.00 = 13.20

4d = 6.20

d - 6.20/4 =1.55

 answer is B

The US Constitution requires that there be a census every ten years in order to apportion the seats in the House of Representatives among the states. Census information is also used by federal, state, and local governments to assess needs and allocate funding, by academics to study the changing population, by individuals to trace their genealogy, and for many other purposes.

To determine the number of one-dollar decreases that would yield a revenue of $55,000, set up the equation (1,700 + 200y) * (25 - x) = 55,000 and solve for x.

To determine the number of one-dollar decreases, x, that would yield a revenue of $55,000, we can set up an equation based on the given information.

Let y be the number of one-dollar decreases and (1,700 + 200y) be the number of tickets sold. The revenue can be calculated by multiplying the number of tickets sold by the price of each ticket. So in this case, the equation can be written as:

(1,700 + 200y) * (25 - x) = 55,000

Now we can solve this equation to find the value of x.

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1 lb / 0.45 = 2.22

 so approximately 2.22 kilograms per pound

 divide price per pound by kilometers per pound

1.44 / 2.22 = 0.648

 round to 0.65, so it costs $0.65 per kilogram

Answer:

1 lb / 0.45 = 2.22

so approximately 2.22 kilograms per pound

divide price per pound by kilometers per pound

1.44 / 2.22 = 0.648

round to 0.65, so it costs $0.65 per kilogram

Step-by-step explanation:

got it right on the quiz

Acceleration determines whether an object speeds up or slows down, which can be positive or negative based on the direction of motion and the chosen coordinate system. Negative acceleration occurs when an object slows down while moving in the positive direction or speeds up while moving in the negative direction. Positive acceleration occurs when an object speeds up in the positive direction or slows down in the negative direction.

Acceleration is the rate of change in velocity, and it can be characterized as positive or negative depending on its direction relative to a chosen coordinate system. Understanding acceleration involves recognizing how it affects an object's speed in relation to its direction of motion. Let's clarify which statements describe acceleration correctly.

It is important to distinguish between speeding up, slowing down, and the sign of acceleration. For example, if we assume rightward motion is positive:

Summarizing these principles:

This understanding can help distinguish between deceleration, which always indicates slowing down, and negative acceleration, which may increase speed if the velocity is also negative.

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Final answer:

To measure 1 liter, one could fill a 500 mL cup twice, or fill a 300 mL cup once, a 500 mL cup once, and a 100 mL cup twice, summing to a total of 1,000 mL which equals 1 liter.

Explanation:

To measure exactly 1 liter using cups of 100 mL, 300 mL, and 500 mL, we can use two different methods. It's important to note that 1 liter (L) equals 1,000 milliliters (mL). Here are the steps for each method:

Method 1:

Fill the 500 mL cup twice and pour the contents into another container. (500 mL + 500 mL = 1,000 mL)

This gives you exactly 1 liter, since 1,000 milliliters is equivalent to 1 liter.

Method 2:

First, fill the 300 mL cup and pour it into an empty container.

Then, fill the 500 mL cup and add it to the same container. (300 mL + 500 mL = 800 mL)

Lastly, fill the 200 mL remaining by using the 100 mL cup twice. (100 mL + 100 mL = 200 mL)

Combining all the measurements gives you 1,000 mL, which is exactly 1 liter. (800 mL + 200 mL = 1,000 mL)

The domain of the given function f(x)= -6x+11 for the given range is

{2,4,6,8}

Given :

The function f(x)= -6x+11  

range given by {-37,-25,-13,-1)

Range is the f(x) values . Domain are the x values .

To find out domain , we substitute the values of f(x) that is range and solve for x

First we substitute -37 for f(x) in the given function and solve for x

[tex]f(x)= -6x+11 \\x=-37\\-37=-6x+11\\-37-11=-6x\\-48=-6x\\x=8[/tex]

Now substitute -25 for f(x)

[tex]x=-25\\-25=-6x+11\\-25-11=-6x\\-36=-6x\\x=6\\\\\\x=-13\\-13=-6x+11\\-13-11=-6x\\-24=-6x\\x=4\\\\\\x=-1\\-1=-6x+11\\-1-11=-6x\\-12=-6x\\x=2[/tex]

x values are the domain

Domain is {2,4,6,8}

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The equation that describes Emily's robot's movement is y = -mx + c where 'm' is the number of steps per second the robot climbs down, and 'c' is the initial number of steps. The equation would be negative because the number of steps decreases over time.

In the given context, Emily's robot is being tested for its ability to climb down steps. As it performs this task, the number of steps it needs to climb down decreases over time. This relationship could be described by a linear equation. If every second the robot climbs down a fixed number of steps, this would translate to a constant rate of change or slope in the graph. Therefore, the equation would be of the form y = mx + c, where 'm' is the slope (representing the number of steps per second the robot climbs down) and 'c' is the y-intercept (representing the initial number of steps).

For instance, if the robot climbs down 1 step per second, and we started with 10 steps, the equation would be y = -x + 10 (negative because the number of steps is decreasing).

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The TDC's net profits for the year were -$24,000 if TDC, Inc's. net profits were $-2000 each month last year option (A) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

TDC, Inc.'s net profits were $-2000 each month last year.

Let x be the net profit for the year

As we know there are 12 months in 1 year.

So the net profit:

x = $-2000×12

x = -$24,000

Thus, the TDC's net profits for the year were -$24,000 if TDC, Inc. net profits were $-2000 each month last year option (A) is correct.

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The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.

Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10,which is even.