When fractions share the same number on the bottom what is it called?

x+1 is not a factor of f(x).

A polynomial can be factored and its roots can be discovered using the factor theorem. The polynomial remainder theorem is a special instance of this one. A polynomial f(x) has a factor (x-a), as was mentioned in the introduction, if and only if f(a) = 0.

Given:

ƒ(x) = 2x³ – 9x² + 13x – 6.

if x+1 is factor of 2x³ – 9x² + 13x – 6.

So, x= -1.

Then, 2x³ – 9x² + 13x – 6.

f(-1) = 2(-1)³ – 9(-1)² + 13(-1) – 6.

f(-1)= -2 - 9 - 13 - 6

f(-1) = -33.

Hence, x+1 is not a factor of f(x).

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Final answer:

The rate of change for the equation y=9x+4 is 9, representing a constant slope where for every unit increase in x, y increases by 9 units.

Explanation:

The rate of change in the linear equation y=9x + 4 is the coefficient of the x term, which represents the slope of the line. In this case, the rate of change is 9. This means that for every one unit increase in x, the value of y increases by 9 units. Since this is a linear equation, the rate of change is constant, meaning it does not change regardless of the value of x.

To find the common ratio and general term equation of the geometric sequence, we analyze the given graph and use the formula for the general term of a geometric sequence. By solving the equations (-16)(r)^(n-1) = -8 and (-8)(r)^(n-2) = -16, we find that the common ratio is 1/2 and the general term equation is an = -16(1/2)^(n-1).

Explanation:

To determine the common ratio and general term equation of the geometric sequence, we can examine the given graph.

From the graph, we can see that the first term is -16. Let's identify two points on the graph that correspond to consecutive terms. We can choose the points (-1, -8) and (-2, -16) as the graph passes through these points.

Using the formula for the general term of a geometric sequence, an = a1(r)^(n-1), we can substitute the given values (-16, r) and (-8, r^2) to find the common ratio and the general term equation.

By solving the equations (-16)(r)^(n-1) = -8 and (-8)(r)^(n-2) = -16, we find that the common ratio is 1/2 and the general term equation is an = -16(1/2)^(n-1).

Answer:

The sales price is $31.49

Step-by-step explanation:

If the toaster has a marked down of $8.50 means that is a discount and you need to subtract this value from the originally costing, as follows:

Sales price = Original cost - Discount value

Sales price = [tex]39.99-8.50[/tex]

Finally, the sales price is $31.49

Answer:

The answer C

Step-by-step explanation:

To find the average number of car rentals processed per day, we first calculate that 70% of the 200-car fleet equates to 140 cars. Each car is rented for 4 days, so, therefore, the total number of cars rented in four days is 560. Hence, the average daily rentals are 140 cars.

To calculate the average number of car rentals processed per day, we need to consider that the company rents 70% of their 200-car fleet daily. That is, 70/100 * 200 = 140 cars.

Since each car is rented for an average of 4 days, each day's rentals represent 1/4 of the number of cars that will be rented over the next four days. Therefore, the total number of cars rented in four days would be divided by 4 to get the daily average. In this case, it's 140 * 4 = 560, and 560 / 4 = 140 car rentals per day.

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Answers are 2, 3, and 4 on    e d g e n u i t y

LCM 14 & 24 = 168

then use the highest exponents for the variables

 answer = 168x^6y^6z^8

     Original equation 
     4 = √-6-2x+√31-3x

     Isolate
     -√-6-2x = -4+√31-3x

      Tidy up 
     √-6-2x = 4-√31-3x

     Raise both sides to the second power
     (√-6-2x)2 = (4-√31-3x)2

     After squaring 
     -6-2x = 31-3x+16-8√31-3x

     Current equation 
     -6-2x = 31-3x+16-8√31-3x

     Isolate radical on the left hand side
     8√31-3x = 6+2x+31-3x+16

      Tidy up 
     8√31-3x = 53-x

     Raise both sides to the second power
     (8√31-3x)2 = (53-x)2

     After squaring 
     1984-192x = x2-106x+2809

     Rearranged equation
     x2  + 86x  + 825 = 0

     This equation has two rational roots:
       {x1, x2}={-11, -75}
 

     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x

     Plug in  -11 for  x 
      √-6-2•(-11) = 4-√31-3•(-11)

      Simplify
      √16 = -4
      Solution does not check 
      4 ≠ -4 

     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x

     Plug in  -75 for  x 
      √-6-2•(-75) = 4-√31-3•(-75)

      Simplify
      √144 = -12
      Solution does not check 
      12 ≠ -12 

Hopefully this helped You

The value of [tex]w[/tex] is [tex]24[/tex].

Given:

The equation is:

[tex]1000^8=10^w[/tex]

To find:

The value of [tex]w[/tex].

Explanation:

We have,

[tex]1000^8=10^w[/tex]

[tex](10^3)^8=10^w[/tex]

[tex]10^{24}=10^w[/tex]         [tex][\because (a^m)^n=a^{mn}][/tex]

On comparing the exponents of the same bases, we get

[tex]24=w[/tex]

Therefore, the value of [tex]w[/tex] is [tex]24[/tex].

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Using the Pythagorean theorem and defining the shorter leg as 'x', we solve the equation x² + (x + 3)mm² = (x + 6)mm² to find that the shorter leg is 9 mm, the longer leg is 12 mm, and the hypotenuse is 15 mm.

To solve for the lengths of the sides of a right triangle when given the difference in length between the legs and the hypotenuse, we can use the Pythagorean theorem, which states that for a right triangle with legs 'a' and 'b', and hypotenuse 'c', the relationship is a² + b² = c².

Let's define the length of the shorter leg as 'x'. According to the problem, the other leg is 'x + 3 mm' (3 millimeters longer than the shorter leg), and the hypotenuse is 'x + 6 mm' (6 millimeters longer than the shorter leg).

Applying the Pythagorean theorem, we get the equation:

x² + (x + 3)mm² = (x + 6)mm²

Expanding the squares and solving for 'x', we get:

This means the shorter leg is 9 mm, the longer leg is 9 mm + 3 mm = 12 mm, and the hypotenuse is 9 mm + 6 mm = 15 mm.

To find the measure of angle MNQ, we can set up an equation using the fact that ray NP is an angle bisector. Solving the equation gives us the value of x, and substituting that value back into the equation gives us the measure of angle MNQ.

To find the measure of angle MNQ, we can use the fact that ray NP is an angle bisector of angle MNQ. This means that angle PNQ is half of angle MNQ.

We are given that angle PNQ = 2x + 1, so we can set up the equation 2x + 1 = (1/2)(x^2 - 10) to find the value of x.

Solving this equation, we get x = 5. Therefore, the measure of angle MNQ is 5^2 - 10 = 15 degrees.

Answer:

The volume of the U-shape will be half the volume of the original  right cylinder.

Step-by-step explanation:

If we are given a right cylinder and it was bent into a U shaped then this U-shaped figure could also be considered as a half cylinder.

We could see from the figure attached how this shape looks like.

and now the volume of this half cylinder will be half the volume of the actual right cylinder.

Answer:

B) There is not enough information to tell since they are not between parallel planes.

Step-by-step explanation:

In order for Cavalieri's principle to be true, both cylinders must have the same cross section. They may or may not. The requirement of being between parallel planes was broken. Therefore -- There is not enough information to tell since they are not between parallel planes

The length of a rectangle is 33 inches.

The rectangle is a 2D shape having four sides and the opposite sides of the rectangle are equal and parallel. The sum of all angles of the rectangle is 360°.

We have,

The perimeter of the rectangle = 88 inches

And,

The length is 2 inches more than the width.

Now, Let,

Width of the rectangle = a

So,

Length of the rectangle = 3a

Now,

Using the formula of the perimeter of the rectangle,

i.e.

The perimeter of the rectangle = 2(Length + Width)

Now,

According to the question,

i.e.

88 = 2( 3a + a)

i.e.

8a = 88

We get,

a = 11,

i.e.

Width of the rectangle = a = 11 inches

So,

Length of the rectangle = 3a = 3 * 11 = 33 inches

Hence, we can say that the length of a rectangle is 33 inches and the width of the rectangle is 11 inches.

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Answer:

<−10

Step-by-step explanation:

Answer: The phrase is "The time it takes to read a book depends on the number of pages in the book"

so the time is the dependent variable and the pages are the independent variable.

Then you will have a function of the form Time(pages) in which you introduce a number of pages (the total number of pages in a book, in this case) and returns the time it takes to read them all. So the correct answer is A.

Answer:

523.33 cubic inches

Step-by-step explanation:

Using the equation for distance, which is the product of rate and time, the distance to Grandmother's house is calculated to be 234 miles.

To solve this problem, you can use the given equation

               d = rt,

where d stands for distance,

r indicates rate (or speed), and

t is the time.

In the question, the rate is given as 52 mi/hr and the time as 4.5 hr.

Substituting these values into the equation gives:

             d = 52 mi/hr * 4.5 hr = 234 mi.

So, Grandmother's house is 234 miles away.

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The limit as x approaches zero of sin3x all over x is indeed 3.  

Below is a step by step display of how to derive this answer.