Given the polynomial f(x) = 2x3 + 7x2 + x − 10, which of the following is true?
a (x + 2) is a factor since f(2) = 0.

b (x − 2) is a factor since f(2) = 0.

c (x + 2) is a factor since f(−2) = 0.

d (x − 2) is a factor since f(−2) = 0.

Answers

Answer 1

Answer:

Step-by-step explanation:

Given:

2[tex]x^{3}[/tex]+7[tex]x^{2}[/tex]+x-10

factor it

I used MatLab   roots(x)  to find these so I kinda cheated :P

-2.5,  -2 ,  1

so we know  -2 is a factor and,  then

x+2=0    is a factor

so the "x+2"  answer C)


Related Questions

If the quotient is 0 , what is the dividend?

Answers

Answer: 0

Step-by-step explanation:

If the dividend and the divisor are the same, the quotient is always 1. If the dividend is the, then the quotient would always be 0. A division equation with 0 dividend and 0 divisor is not valid.

Answer: All real numbers

Step-by-step explanation: Anything that's being divided by 0, is always going to be 0. For example, 0/7 is always 0.

write the equation of the line that is perpendicular to the line y=-2 and passes through (4,-2)

Answers

the equation of the perpendicular line is x = 4, as the line vertical and the slope is undefined

What is the equation of the line that passes through the given point and is perpendicular to the given line?

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

The slope intercept formula is expressed as;

y = mx + b

Where m is the slope and b is y-intercept.

Given the data in the question;

Equation: y = -2Point (x,y) : (4,-2)

First, we determine the slope of the initial line by comparing to the slope intercept form y = mx + b

y = -2

Hence

Slope of initial line m = 0

Slope of the perpendicular line will be negative reciprocal of the initial line

m = -1/0

Slope m is undefined

Therefore, the perpendicular line is vertical and the slope is undefined

Hence.

x = 4.

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Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= A(x−A )( x− B) and how they can be identified from the equation.

Answers

The features of the functions when a quadratic function is given in the form: y = a (x − p) (x − q)

y = value in the y coordinates

a = constant in the equation

p and q = zeros or roots

x = value in the x coordinates

How to identify features in the equation

When quadratic equation is written of the form y = a (x − p) (x − q), it is called the factored form of quadratic equation

The other form is ax^2 + bx + c and called standard form of quadratic equation

a in both cases are same and it helps to da if the curve opens upward or downward

when a is positive the curve opens upward but when it is negative the curve opens downward

Expanding the factored form of quadratic equation brings the equation to the standard form

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The ratio of boys to girls in a class is 2:3 if there are 48 pupils in the class.How many boy and girls are there?

tysm po​

Answers

2/3 × 48 =32 boys

48-32=16 girls

1.You need to earn at least $90. You earn $7 for each hour you work.
Which inequality represents the number of hours h that you need to
work?
(Look at the picture for options for the answer)

2. Write a graph that represents the solution

Answers

Answer:

Inequality:

Graph choice:

Step-by-step explanation:

Inequality

It says at least 90, which means we have to use the greater than or equal to sign

Our inequality so far: 90≥______

Now it says you earn 7 dollars per hour, which means 7 times the number of hours you work or 7h. Our inequality now looks like this:

90≥7h

The answer choice that matches is A (90≥7h = 7h≤90)

For the second question on the bottom, I added an image.

(Answer is B)

9x^7/3x^2=3x^9 true or false

Answers

Answer:

False

Step-by-step explanation:

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

given

[tex]\frac{9x^7}{3x^2}[/tex]

= [tex]\frac{9}{3}[/tex] × [tex]\frac{x^7}{x^2}[/tex]

= 3 × [tex]x^{(7-2)}[/tex]

= 3[tex]x^{5}[/tex]

SOMEONE HELP GEOMETRY THXX

Answers

The lines p and q are parallel.

What are alternate exterior angles?

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines, but on opposite sides of the transversal.

Given a figure,

Since, ∠ 1 ≅ ∠ 5 and they are alternate exterior angles, then we can conclude that p║q by alternate exterior angles theorem.

Hence, The lines p and q are parallel.

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Two rockets are to be launched at the same time from NASA headquarters in​ Florida, and are to meet at a space station many miles from Earth. The first rocket is to travel at 19,200 miles per hour and the second rocket will travel at 18,000 miles per hour. If the first rocket is scheduled to reach the space station 0.5 of an hour before the second​ rocket, how far is the space station from NASA​ headquarters?

Answers

By solving a linear equation, it can be calculated that

The space station is at a distance of 144000 miles from NASA headquarters

What is linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let the space station be d miles from NASA headquarters

Speed of the first rocket = 19200 miles/hour

Speed of the second rocket = 18000 miles /hour

Time taken by the first rocket to reach the space station = [tex]\frac{d}{19200}[/tex]

Time taken by the second rocket to reach the space station = [tex]\frac{d}{18000}[/tex]

By the problem,

[tex]\frac{d}{18000} - \frac{d}{19200} = 0.5\\\\\frac{16d - 15d}{288000} = 0.5\\\\\frac{d}{288000} = 0.5\\\\d = 288000 \times 0.5\\\\d = 144000 \ miles[/tex]

The space station is at a distance of 144000 miles from NASA headquarters

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please help me i never learned divison im sorry87,628÷931= ​

Answers

Answer:

94.1224489796

this is the answer

What is the measure of each angle of a regular 22-gon? If necessary, round to the nearest tenth.

Answers

The measure of each angle of a regular 22-gon is 163.6 degrees.

How to find the sum of angles of a polygon?

In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.

Polygon can be named base on the number of sides they possess. For example pentagon has 5 sides, hexagon has 6 sides, heptagon has 7 sides, octagon has 8 sides, nonagon has 9 sides and decagon has 10 sides.

Therefore, a regular polygon is one which sides and angles are congruent.

A regular  22-gon has 22 sides.

The measure of each angle of 22-gon can be found as follows;

angle= 180(n - 2) / n

where

n = number of sides

angle = 180 (22 - 2) / 22

each angle = 180(20) / 22

each angle = 3600 / 22

Therefore,

each angle =  163.636363636

each angle = 163.6 degrees.

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how are the zeros of a polynomial function related to the equation and graph of a function

Answers

The way that zeros of a polynomial function is related to the equation and graph of a function because they act as solutions to the equation and also x-intercepts of a graph.

What graphing relationship does a zero have?

When the quadratic equation's graph crosses the x-axis, those points are known as the zeros of the equation.

The graph's x-intercepts and a function's zeros are the same thing. If the zero of f has an odd multiplicity, the graph of f will cross the x-axis at that x value. The x-axis will be touched by the graph of f if it has an even multiplicity zero.

Hence, A polynomial's zeros are the answers to any equation such as p(x) = 0, where p(x) stands for the polynomial. Since the values of x where y = 0 if we graph this polynomial as y = p(x). In other words, these are the graph's x-intercepts.

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If y varies directly as x, find the constant of variation and the direct variation equation for the situation.
y = 0.1 when x = 0.2

Answers

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em} \textit{we know that} \begin{cases} y=0.1\\ x=0.2 \end{cases} \\\\\\ 0.1=k(0.2)\implies \cfrac{0.1}{0.2}=k\implies 0.5=k\hspace{5em}\boxed{y=0.5x}[/tex]

Please help, i dont understand

Answers

The equation of lines are (a) x - 2y + 6 = 0

                                          (b) 2x - y - 4 = 0

                                          (c) x - y + 1 = 0

                                          (d) 4x + 3y + 4 = 0

Slope-intercept form of the equation -> y = mx + c

Slope = m = [tex]\frac{y2-y1}{x2-x1}[/tex]

(a) A(0,3) and B(6,6)

    m = [tex]\frac{6-3}{6-0}[/tex]

        = 3/6

        = 1/2

    Putting the value in equation,

     3 = (1/2)*0 + c

     c = 3

   Equation -> y = (1/2)x + 3

                     2y = x + 6

          x - 2y + 6 = 0  

(b) A(0,-4) and B(5,6)

    m = [tex]\frac{6+4}{5-0}[/tex]

        = 10/5

        = 2

    Putting the value in equation,

     -4 = (2)*0 + c

     c = -4

   Equation -> y = (2)x - 4

          2x - y - 4 = 0  

(c) A(-4,-3) and B(2,3)

    m = [tex]\frac{3+3}{2+4}[/tex]

        = 6/6

        = 1

    Putting the value in equation,

     3 = (1)*2 + c

      3 = 2 + c

      c = 3 - 2

      c = 1

   Equation -> y = (1)x + 1

                       y = x + 1

             x - y + 1 = 0  

(d) A(-6,4) and B(3,-8)

    m = [tex]\frac{-8-4}{3+6}[/tex]

        = -12/9

        = -4/3

    Putting the value in equation,

     -8 = (-4/3)*3 + c

     -8 = -4 + c

      c = -8 + 4

      c = -4

   Equation -> y = (-4/3)x - 4

                     3y = -4x - 4

       4x + 3y + 4 = 0  

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Here is the histogram of a data distribution. All class widths are 1

Which of the following numbers is closest to the mean of this distribution?

Answers

The number that is closest to the mean of the distribution is 4 (option C)/

What is the mean?

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is the product of the frequency of the rectangle and the width of the rectangle.  

Mean is the average of a set of numbers. It is determined by multiplying each bar in the histogram by its height, add the multiplication value for all the bars together and dividing it by the total frequency of the bars.

Mean = [(1 x 1) + (2 x 2) + (3 x 3) + (4 x 4) + (5 x 3) + (6 x 2) + (7 x 1)] / (1 + 2 + 3 + 4 + 3 + 2 + 1)

Mean = (1 + 4 + 9 + 16 + 15 + 12 + 7) / 16

Mean = 64 / 16

Mean = 4

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Work out the values of a, b, c and d.
Justify each of your answers.

Answers

In the given circle, the values of required angles are as follow:

a = 51°, b = 28° , c = 31°, and d = 70°.

As given in the question,

In the given circle,

As we know by theorem , angles formed in the same arc are congruent.

Angle a° and angle 51° is formed in the same arc XY .

Value of a = 51°

Angle b° and angle 28° is formed in the same arc ZY .

⇒ Value of b = 28°

Angle c° and angle 31° is formed in the same arc WX .

⇒ Value of c = 31°

Angle d° and angle 70° is formed in the same arc WZ .

⇒ Value of d = 70°

Therefore, in the given circle the values of required angles are as follow:  a = 51°, b = 28° , c = 31°, and d = 70°.

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7th grade math: can you help? i only need help on 1, 2, 3, & 4

Answers

By using percentage, it can be calculated that

1) Percentage increase in area = 25 %

2) Percentage increase in area = 60 %

3) Percentage decrease in area = 25 %

4) Percentage decrease in area = 40 %

What is percentage?

Sometimes there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100

1) Original area = 12 sq. yard

   New area = 15 sq. yard

   Increase in area = 15 - 12 = 3 sq. yard

   Percentage increase = [tex]\frac{3}{12}\times 100 \\[/tex]

                                       = 25 %

1) Original area = 15 sq. yard

   New area = 24 sq. yard

   Increase in area = 24 - 15 = 9 sq. yard

   Percentage increase = [tex]\frac{9}{15}\times 100 \\[/tex]

                                       = 60 %

1) Original area = 12 sq. yard

   New area = 9 sq. yard

   Increase in area = 12 - 9 = 3 sq. yard

  Percentage decrease = [tex]\frac{3}{12}\times 100 \\[/tex]

                                       = 25 %

1) Original area = 10 sq. yard

   New area = 6 sq. yard

   Increase in area = 10 - 6 = 4 sq. yard

   Percentage increase = [tex]\frac{4}{10}\times 100 \\[/tex]

                                       = 40 %

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If f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55, then find the
value of f(-1), to the nearest hundredth.

Answers

The value of the exponential function (-1) will be equal to f(-1) = -0.02.

What is an exponential function?

The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects.

Given that f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55. The value of the exponential function will be calculated as,

[tex]y=ax^b[/tex]

[tex]11=a(-3)^b\\55=a(4)^b[/tex]

Calculate the value of constants,

log5 = blog(4 / 3)

b = 0.7 / 0.125

b = 5.6

The value of 'a' will be,

11 = a(-3)⁵°⁶

a = -0.02

The exponential function f(-1) will be calculated as,

f(-1) = -0.02(-1)⁵°⁶

f(-1) = -0.02

Therefore, the value of the exponential function (-1) will be equal to f(-1) = -0.02.

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A caterer charges a $40 fee plus an additional $6.25 per person. She determines the total cost, C, for x people by using the equation shown above. How much will a party cost for 80 people?

Answers

As its $6.25 for each person and it’s 80 people we would do $6.25x80 getting you $500 and with the fee added it would be $540 and the expression would be
$40+$6.25(80)=c

The polynomial P(x) of degree 4 has
a root of multiplicity 2 at x = 4
• a root of multiplicity 1 at x = 0 and at x = -1
• It goes through the point (5,21)
Find a formula for P(x).
P(x) =
Question Help: Message instructor

Answers

Answer:

P(x) = 0.7 [tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x

Step-by-step explanation:

given a polynomial with roots x = a and x = b , then the factors are

(x - a) and (x - b)

If x = a is of multiplicity 2 then factor is (x - a)²

the polynomial is then the product of the factors

p(x) = a(x - a)(x - b) ← a is a multiplier

give x = 4 is a root with multiplicity 2 then (x - 4)² is the factor

x = 0 has factor (x - 0) , that is x

x = - 1 has factor (x - (- 1)) , that is (x + 1)

the polynomial is then the product of the factors

P(x) = ax(x + 1)(x - 4)² ← expand squared factor using FOIL

       = ax(x + 1)(x² - 8x + 16)

       = a(x² + x)(x² - 8x + 16) ← distribute

       = a([tex]x^{4}[/tex] - 8x³ + 16x² + x³ - 8x² + 16x)

      = a([tex]x^{4}[/tex] - 7x³ + 8x² + 16x)

to find a substitute (5, 21 ) into P(x)

21 = a([tex]5^{4}[/tex] - 7(5)³ + 8(5)² + 16(5))

21 = a(625 - 875 + 200 + 80)

21 = 30a ( divide both sides by 30 )

0.7 = a

then

P(x) = 0.7([tex]x^{4}[/tex] - 7x³ + 8x² + 16x) ← distribute parenthesis

P(x) = 0.7[tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x

1: A middle School had a school spirit day
In one class the ratio of students who wore
School colors to the number of students who
Didnt was 8 to 5 Ten students didn't wear school
Colors, Determine the number of students who wore School
Colors.
Answer:

Answers

The number of students who wore School colors are 8/13. If, Ratio of  students who wore School colors to the number of students who didn't are given.

Define ratio.

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division. A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given,

Ratio of  students who wore School colors to the number of students who didn't

8:5

Total number of student = 13

Number of students who wore school colors = 8/13

The number of students who wore School colors are 8/13. If, Ratio of  students who wore School colors to the number of students who didn't are given.

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a football team travels to an away game in cars that seat five players and vans that can hold nine players. If there are 47 players on the team find the equation for this situation

Answers

The equation to illustrate the information when the football team travels to an away game is 5c + 9v = 47.

What is an equation?

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let cars = c

Let van = v

The equation will be 5c + 9v = 47.

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What is the solution to -4(8-3x) ≥ 6x - 8?
O
4
x²--1/32
O x≤
xs--1/72
Ox≥4
Ox≤4

Answers

Answer:

x ≥ 4

Step-by-step explanation:

-4 ( 8 - 3x ) ≥ 6x - 8

First, solve the brackets.

- 32 + 12x ≥ 6x - 8

Subtract 6x from both sides.

- 32 + 12x - 6x ≥ - 8

- 32 + 6x ≥ - 8

Add 32 to both sides.

6x ≥ - 8 + 32

6x ≥ 24

Divide 6 by both sides.

x ≥ 4

How do I solve this question​

Answers

The partial fraction is proved.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=3x²+8x+4/(x²-4)(3x-2)

=3x2+8x+4/(x2-4)(3x-2)

= 3x2+6x+2x+4/(x2-4)(3x-2)

=3x(x+2)+2(x+2)/(x2-4)(3x-2)

Hence proved, l.h.s = r.h.s

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What is the expression 9-z when z=8

Answers

When z=8:

9-(8)=1

Since z is equal to 8, it can be substituted in and solved

1/3[6y+3]-24=3[1/3y-6]
y-3=y-7
x+2x=1/3x-8
y-9=y-2
x-5=6x-5



step by step explanation please

Answers

Answer:

Step 1: Simplify both sides of the equation.

1/3(6y+3)−24 = 3(1/3y−6)

1/3(6y) + 1/3(3) -24 = 3(1/3y) + 3(-6)

2y +1 −24 = y−18

2y −23 = y −18

Subtract y from both sides.

2y−23−y=y−18−y

y−23=−18

Step 3: Add 23 to both sides.

y−23+23 = −18+23

y = 5

Step-by-step explanation:

Zack and his friends went to a movie on Thursday afternoon. It took 25 minutes to drive to the theater. They arrived at the theater 1 hour and 15 minutes before the movie started. Once it started, the movie lasted for 1 hour and 20 minutes and ended at 4:20 P.M. What time did Zack and his friends leave for the movies

Answers

Answer:

2:20

Step-by-step explanation:

The movie started at 3:00 PM they got there at 2:45. and it took them 25 mins to get there meaning they left at 2:20.

Answer: 1:20 P.M.

Minutes: 25 + 60 + 15 + 60 +20 =180minutes
180/60=3
3hours
4:20 - 3h= 1:20
So they left at 1:20 P.M.

If Ø (theta) is an angle in standard position and its terminal side passes through the point (-9,5), find the exact value of sec Ø (theta) in simplest radical form.​

Answers

For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.

As given in the question,

For the given angle ∅ (theta) in standard position:

Terminal side of ∅ is passes through the point ( -9, 5 )

( -9 , 5 ) represents ∅ is in the second quadrant.

In second quadrant sine in positive and cosine is negative.

Base is negative and altitude is positive.

Base = -9

Altitude = 5

Using Pythagoras theorem,

Hypotenuse² = (-9)² + (5)²

⇒ Hypotenuse = √106

cos ∅ = -9 / √106

sec ∅ = 1/ cos ∅

         = - √106/9 ( simplest radical form )

Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of

sec∅= ( - √106/ 9 )  in simplest radical form.

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) Nike deposits N5,000.00 in a savings bank account. If she is paid an interest rate of 5% per annum for 2 years, how much is the simple interest? NOO. O​

Answers

The simple interest that Nike will receive after 2 years is $500.

The principal amount =$5000

Rate = 5% = 0.05

Time = 2 years

Now simple interest = PRT = 5000 × 0.05 × 2 = 500

Hence the simple interest earned by Nike is $500

Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.

Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.

A loan is a sum of money that a person obtains from a bank or another type of financial institution in order to pay bills. A few types of loans are personal, student, auto, and mortgage loans.

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wats the slope?ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answers

the slope is 2/3
rise over run

Select the correct answer.
Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.

Answers

The statement which is true about the y-values of the graph of the function as required is; Choice B; The y-values are all greater than or equal to 2.

Which statement is true regarding the y-values?

It follows from the task content that the statement which is true regarding the y-values of the graph defined by; f(x) = lx-5l +2 is to be determined.

Therefore, we must recall that expressions enclosed in the absolute value sign upon evaluation are always greater than or equal to zero.

Hence, it can be concluded that we the y-values of the resulting graph to be greater than or equal to 2 (on the occasion that; lx-5l = 0).

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