Activity: Factor Theorem
Use the Remainder Theorem and Factor Theorem to determine whether the given
binomial is a factor of P(x).
P(x) = 9x³+ 6x - 40 - 2x² + 2x4; binomial: x + 5
the given problem.

Answers

Answer 1

The given polynomial is a factor of P(x) because P(-5)=0.

From the remainder theorem, how do you derive the factor theorem?

The Remainder Theorem states that if a synthetic division of a polynomial by x = a results in a zero remainder, then x = an is a zero of the polynomial (thanks to the Remainder Theorem), and x an is also a factor of the polynomial (courtesy of the Factor Theorem).

How can you tell if P(x) is a factor of X C?

The Factor Theorem states that x - c is only a factor of P(x) when P(c) = 0.

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Related Questions

An unusually wet spring has caused the size of a mosquito population in some city to increase by 7 â% each day. If an estimated 18â0,000 mosquitoes are in the city on May 6. Find how many mosquitoes will inhabit the city on May 17 . Use y =18â0,000(1.07 )^ x where x is number of days since May 6 .

Answers

Answer:

378873

Step-by-step explanation:

Using the relation :

y = 180000(1.07)^x

x = Number of days since May 6 ;

y = Number of mosquitoes after x days

x = May 17- May 6 = 11 days

Therefore, number of mosquitoes inhabiting the city on May 17 will be :

y = 180000(1.07)^11

y = 180000 * 2.1048519522998348950643

y = 378873.351413970281111574

y = 378873 (nearest whole number).

Is the set of rational expressions closed under division

Answers

Answer:

Step-by-step

Closure property is true for division except for zero.

Which point is a reflection of (-4, -3) across the y-axis?

Answers

Answer:

(4,-3)

Step-by-step explanation:

The y coordinate stays the same, and the x changes from positive to negative

Find a polynomial that represents the perimeter of the rectangle.

Answers

Hi there!

[tex]\large\boxed{P = 4x^2 + 12x + 22}[/tex]

The perimeter of a rectangle is:

P = 2l + 2w

Thus, plug in the given length and width:

P = 2(2x² + 5x + 8) + 2(x + 3)

Distribute:

P = 2(2x²) + 2(5x) + 2(8) + 2(x) + 2(3)

Simplify:

P = 4x² + 10x + 16 + 2x + 6

Combine like terms:

P = 4x² + 12x + 22

Answer:

[tex]4x^2+12x+22[/tex]

Step-by-step explanation:

The perimeter of a rectangle is equal to [tex]2l+2w[/tex] where l is the length and w is the width. So, this rectangle would be equal to [tex]2\left(x+3\right)+2\left(2x^2+5x+8\right)[/tex]. Then, to find the polynomial simplify the expression. To do this first distribute the two 2s. This equals [tex]2x+6+4x^2+10x+16[/tex]. Then, add like terms to finish simplifying. This gives you the final answer of [tex]4x^2+12x+22[/tex].

Solve Using substitution 3x+5y=-28 Y=x+4

Answers

Answer:

(-6, -2) x=-6, y=-2

Step-by-step explanation:

3x + 5(x+4) = -28

3x + 5x+20=-28

8x+20=-28

8x=-48

x=-6

Y=-6+4

y=-2

HELPPP PLEASE ASAPPP 20 POINTS!

Answers

It is 1/3

Have a good day :D

A parent function is a linear function of the form y=b true of false

Answers

Answer:

False

Step-by-step explanation:

The parent function is the simplest function within a family of functions that defines the general form of that family.

Parent Functions

Parent functions are given in terms of y and x, where y is the output and x is the input. In linear functions, b represents a constant, specifically the y-intercept. Since the form y=b does not have an input it cannot be the parent function of linear lines. The graph of y=b would be a horizontal line with no slope. This does not define the general form of most linear functions. Additionally, since the slope has been changed to zero, it is not considered the simplest form of linear functions.

Linear Parent Function

The true parent function of linear functions is y=x. This function is the simplest linear function and has no transformations. Additionally, when graphed it is a diagonal line that defines the general shape of lines.

To create new linear functions the parent function, y=x, can be transformed by changing the coefficient of x to change the slope or by adding a constant to shift the graph vertically.

Find the area of the irregular figure below.

Answers

Answer:

20

Step-by-step explanation:

5 x 4 = 20

take both numbers and multiply them .


16. The side length of a square ABCD is 18 inches. What is the side length of the square formed by joining the
midpoints of the sides of ABCD, to
the nearest tenth?

Answers

Therefore , the solution of the given problem of square comes out to be the ABCD  square is 18 inches

what is the side of length of square ABCD?

The side length of a square ABCD is 18 inches Each side of square ABCD is 18 inches The midpoints of ABCD are joined to form a square MNOP The figure is attached below

Here,

We need to find the side length of square MNOP

AMN form a Right angle triangle

We know AM =9  and AN= 9

To find MN , use Pythagoreans theorem

MN2=AM2+AN2

MN2=9square+9 square

MN2=162

Take square root on both sides

MN=9 root 2

so the side of the square MNOP is  9 square root 2 inches

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Which of the following points are solutions to the equation 3x - 4y - 8 = 12?
Select all that apply.
(0-5)
(4-2)
(8.2)
(-16-17)
(-1.-8)
(-40,-34)

Answers

I got 0-5
Sorry if I’m wrong I try

Please get it right

Answers

Answer:

Y intercept is where x=0. Plug it in the original function find the y intercept

Step-by-step explanation:

Graph?

Pls help. Cindi wants to cover the top and sides of this box with glass tiles that
are 1 cm square. How many tiles will she need?

Answers

Answer:

300 square centimeters

Surface area of box:

= 2(lb + bh +hl)

= 2(20×15 + 15×9 + 9×20)

= 2(300 + 95 + 180)

= 2 × 575

= 1,150 cm³

Area of tiles:

= 1 × 4 = 4 cm

No of tiles:

= 1,150/4

= 287.5 = 288

Total 288 tiles will be needed

In the figure below, ABCD is a square.

Points are chosen on each pair of adjacent sides of ABCD to form 4 congruent right triangles, as shown below.

What is the area of the shaded regions?

A. 16
B. 32
C. 48
D. 64
E. 72

Answers

Answer:

D . 64

Step-by-step explanation:

Explanation attached as photo

Peter received a $40 gift card to Starbucks for his birthday. He
spends the same amount every time he goes and has gone 5
times so far. On one of his trips he also got a $3 drink for his
brother. What is the most he could have spent per trip? Choose
the inequality that describes his situation. Let xramount per trip

Answers

Answer:

xr ≤ 7

Step-by-step explanation:

He must spend less than or equal to 7$ to account for 5 trips and 3 extra dollars for 1 trip.

#6 for the function f(x) = x² what is the
Max. domain if y is restricted to; f(x) = 144 and
f(x) =1286?

Answers

Answer:

Step-by-step explanation:

or the function f(x) = x² what is the

Max. domain if y is restricted to; f(x) = 144 and

f(x) =1286?

please help guys ASAP

Answers

Answer:

180

Step-by-step explanation:

You do 24 x 4 + 64 which is = to 176 then rounded is 180

This is the graph of a quadratic function i need help

Answers

Answer:

vertex: (-1,-2)

roots: (-3,0);(1,0)

axis of symmetry is: x=-1

Find the mean of the following numbers:
8
0
3 3
17
4
1
4
4​

Answers

Answer:

10.14

Step-by-step explanation

The numbers sum equals 71

and there are 7 # so

71/7

=

Ans.

Set X is the set of all multiples of 6 between 15 and 70.
Which set is equivalent to set X?
A. {6, 12, 18, 24,...}
B. {6, 12, 18, ...,66}
C. {18, 24, 30, 36,...}
D. {18, 24, 30, ..., 66}
E. {18, 24, 30, ..., 70}

Answers

Answer:

D

Step-by-step explanation:

we have 2 conditions

1. to be a multiple of 6

2. to be between 15 and 70

A and B are not correct because have numbers les than 15

C is not correct because the numbers keep on going passed 70

E is not correct because 70 is not a multiple of 6

D is correct because has both conditions meet

X+X+X+Y+Y=

im doing algebra and cant understand the above question

Answers

Answer:

3x + 2y

Step-by-step explanation:

X+X+X+Y+Y=

you simply count equal letters and add them x+x+x is 3x and y + y = 2y.

x + x + x + y + y =

3x + 2y

not knowing the value of x or y we stop here

I need help please I would appreciate if someone can help and god bless you

Answers

4,7,6! You have to halve x to get y on the first two, then times y by two to return to x

If 3n+5=23 what is the value of 2n-3

Answers

Answer:

3n + 5 = 23,

3n = 18

n = 6

since "n" = 6,

2n - 3

= 2×6 - 3

12 - 3

= 9

please help middle school math​

Answers

Answer:

Step-by-step explanation:

1)√320=8√5

(√125+√45)=8√5

(√500-√20)=8√5

ABC is an equilateral triangle.

2) area=1/2 lengh * h

1/2 * 4√15 * 8√5

=2√15 * 8√5

=80√3

A person is using a new teenis ball launching machine that is 15 inches by 14. Assuming the machine uses tennis balls that are spherical and 2.7 inches in diameter, how many tennis balls should fit in one of the top of the machine?

Answers

The number of tennis ball  fit in the machine are 305 balls.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

given dimensions of  machine 15 x 15 x 14

volume of machine is 15 x 15 x 14 = 3150 cubic inches

and shape of ball is spherical,

with dia = 2.7 inches

radius of ball = 2.7/2 = 1.35 inches

volume of sphere is 4/3πr³

V = 4/3πr³

V = 4/3(3.14)(1.35)³

V = 4/3(3.14)(2.46)

V = 10.30 cubic inches

the area covered by 1 ball is 10.30 cubic inches

the number of ball in machine is 3150/10.30

the number of ball in machine  = 305.82 = 305 approx

Hence  305 balls can be fit in machine.

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there is a safety fence around a circular pool with a gate the gate is 150cm wide ​

Answers

Answer:

The length of the fence is 6.28x-150 cm.

Step-by-step explanation: ... Since the pool is in a circular shape so the circumference will be the length of the fence.

The U.S. produces 9.08 million barrels of crude oil per day. It consumes 19.7 million barrels per day. How many barrels of oil have to be imported each day from other oil-producing countries?

help me pls if you cant and dont help me then. no links or report. pls help me giving brainless. ​

Answers

Answer:

pls give brainless

Step-by-step explanation:

How many barrels of oil does the US use per year?

The U.S. uses about 6.6 billion barrels per year. That is only enough oil to last the U.S. about three and a half years without importing oil from other countries. 84% of the reserves are concentrated in four states.

If a pair of shoes was discounted from an original price of P5000 to P2800 what is the percent decrease or discount

Answers

Answer:  44% decrease

Work Shown:

a = old price = 5000

b = new price = 2800

c = change in price

c = b-a

c = 2800-5000

c = -2200

The value of c is negative to indicate a price decrease.

d = percent change

d = (c/a)*100%

d = (-2200/5000)*100%

d = -44%

There is a 44% decrease or discount.

Here thy go in the name of chubbyeti 35+points

Answers

Answer:

okay.................................

On one day at a local minigolf course, there were 320 customers who paid a total of $2,900. If the cost for a child is $7 per game and the cost for an adult is $10 per game, write a system of equations to model this scenario, where x represents the number of children and y represents the number of adults who played that day.

7x + 10y = 2900
x + y = 320

7x + 10y = 320
x + y = 2900

10x + 7y = 2900
x + y = 320

10x + 7y = 320
x + y = 2900

Brainiest for correct answer

Answers

A system of equations to model this scenario is given as follows -

x + y = 320

7x + 10y = 2900

What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.The general equation of a straight line is → y = mx + c

        {m} - slope                 {c} - intercept along the y - axis.

Given is that on one day at a local minigolf course, there were 320 customers who paid a total of $2,900. The cost for a child is $7 per game and the cost for an adult is $10 per game.

Let {x} represents the number of children and {y} represents the number of adults who played that day. We can write the given system of equations as -

x + y = 320

7x + 10y = 2900

Therefore, a system of equations to model this scenario is

x + y = 320

7x + 10y = 2900

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Hey guys! I need some help

Answers

Answer:

D

Step-by-step explanation:

8x+12y-2y+3x=11x+10y

Answer:

answer D

Step-by-step explanation:

8x+12y-2y+3x

11x+ 10y

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