Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

Answers

Answer 1

A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².

How to interpret the graph?

The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.

This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:

x⁴

x - a

(x - b)²

In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².

Related Questions

evaluate f(x)=4|x|+3 for x=-5

Answers

Subs x = -5 into f(x) = 4

f(-5) = 4 (answer)

You are building a ramp for your grandparent’s house. The ramp will replace the steps that go to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the front door. How long will the ramp need to be?

Answers

Answer:

10.4403 or the square root of 109

Step-by-step explanation:

We do this by finding the height (3) and squaring it then the base (10) and squaring that, this sets up the Pythagorean theorem which is A^2+B^2=C^2 then you square C to find it's value

What is DC to the nearest tenth? I need help, thank you:)

Answers

The measure of the length DC to nearest tenth is 24.1 units

Pythagoras theorem

In order to determine the measure of DC from the figure shown, we will use the pythagoras theorem

Determine the measure of BC

BC² = 22² - 15²

BC² = 259

BC = 16.09

Determine the measure of DC

DC² = 259 + 28²
DC = √583

DC = 24.1 units

Hence the measure of the length DC to nearest tenth is 24.1 units

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1. Which one of the following statements expresses a true proportion? A. 3:49:12 OB. 2:1 1:2 OC. 54:9 = 6:3 OD. 7:98:9

Answers

Answer:

3:4 9:12

Step-by-step explanation:

Rewrite the ratios as fractions. 3:4 becomes 3/4, and 9:12 becomes 9/12, which simplifies to 3:4. Therefore A is a true proportion.

What are the domain and range of g(x)=√x+4?
OD: [4, ∞) and R: [0, ∞)
OD: (-4, ∞) and R: (-∞, 0)
OD: [-4, ) and R: [0, ∞)
OD: (4,) and R: (-∞, 0)

Answers

Answer:

Domain [-4 , +∞)

Range [0 , +∞)

Step-by-step explanation:

the function g such that g(x)=√(x+4) ,is defined

for the values of x that verify :

x + 4 ≥ 0

⇔ x ≥ -4

Then

The domain of g is [-4 , +∞)

………………………………………………

Let x ∈ [-4 , +∞)

then x ≥ -4

then x + 4 ≥ 0

then g(x) = √(x+4) ≥ 0

Therefore, we can affirm that the range of g is [0 , +∞)

A text message plan costs $9 per month plus $0.39 per text. Find the monthly cost for x text message The monthly cost of x messages is dollars. (Use integers or decimals for any numbers in the expression.) *

Answers

Answer:

The monthly cost = $9 + $0.39x

Step-by-step explanation:

Assignment
Slide the green dot from 0 to plot the number at the correct
location.
Plot-1.
-6 -5 4 -3 -2 -1 0 1
2
3 4
5
+
6
Use the interactive number line to find each sum to
complete the table.
A
1
-1
-4
-6
B
2
-2
1
-3
A + B
3
R
S
T

Answers

From the number line, the values which completes the sum in the table are:

R = -3.S = -3.T = -9.

What is a number line?

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

How to find each sum?

From the table of values (see attachment), the values on the number line are represented as follows:

a + b = a + b

R = -1 - 2

R = -3.

a + b = a + b

S = -4 + 1

S = -3.

a + b = a + b

T = -6 - 3

T = -9.

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write the expression 5x(x+9) -7(x+9) in complete factored form.

Answers

5x^2 + 45 - 7x - 63 which simplifies to 5x^2 -7x -18?

Answer:

(5x-7)(x-9)

Step-by-step explanation:

Factoring is the inverse of the distributive property. This means that we want to find the factors, not the product.

Partial Factoring

The expression we are given has already been factored to an extent. Both terms are split into 2 different factors. This was done by factoring out the greatest common factor (GCF) from both terms. In the first term, the GCF was 5x, and in the second, the GCF was -7.

Complete Factoring

Even though it was partially factored, we can factor it more. When given the situation:

a(x + y) - b(x + y)

The expression can be factored into:

(a - b)(x + y)

You can add (subtract in this case because 7 is negative) the values from outside the parentheses together. This term can then be multiplied by the value within the parentheses.

Thus, 5x(x+9) -7(x+9) can be factored into:

(5x-7)(x-9)

Remember this trick only works when both terms share a factor like (x-9).

In which data set is the mean greater than the median?

Answers

One of the basic tenets of statistics that every student learns in about the second week of intro stats is that in a skewed distribution, the mean is closer to the tail in a skewed distribution. So in a right skewed distribution (the tail points right on the number line), the mean is higher than the median.

How do i plot 3 points on a graph when all I am given is "x=4" ? and I need to find "x and y" for 3 points.

Answers

Answer:

(4,-1) (4,0) (4,1)

Step-by-step explanation:

If you graph this, it will be a straight vertical line. No matter what y is, x will always be 4.

Use the chart to find the constant of variation

Answers

As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.

Does the table represent a linear relation?

A table between two variables represents a linear relation if and only if every pair of values (x, y) have the same constant:

k = y/x (1)

Now we proceed to check the existence of the constant of variation:

k₁ = 8/(- 2) = - 4

k₂ = (- 16)/4 = - 4

k₃ = (- 36)/9 = - 4

As k₁ = k₂ = k₃, the table represents a linear relation whose constant of variation is - 4.

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Simplify the following fractions.

Answers

Answer:

The solution for the above fraction is

[tex] \frac{146}{167} [/tex]

Step-by-step explanation:

Greetings!

look at the attachment above for the explanation.

Find the indicated real nth root(s) of a.
n=3, a = - 216

Answers

Answer:

-6

Step-by-step explanation:

A suitable calculator can find this for you directly.

Odd root of a negative number

-1 raised to an odd power is -1. That means an odd-index root of a negative number will be the opposite of the corresponding root of its absolute value:

∛(-216) = -∛216 = -6

Additional comment

Many calculators and spreadsheets do not respond well to requests for roots of negative numbers. A calculator with built-in support for complex numbers is the best choice for this sort of problem.

The second attachment shows a calculator capable of finding the complex roots as well as the real one.

A sience teacher uses an overhead projector to display a diagram of a pulley sytem. the actual diagram is 6'' by 7.2''. The image projected onto the wall is 4' 2'' by 5'' what is the scale factor of the projection

Answers

Answer:

25/36, or .694444

Step-by-step explanation:

First, let's convert 6" to inches.

That gives us 72. After we convert 4'2" into inches, we get 50.

This means that the diagram goes from 72 inches wide to 50. Put this into a proportion to find the scale factor:

50/72 = 25/36 = .6944444

If a diameter of a circle has endpoints (-3,5) and
(5, 7), then the center of the circle is

Answers

Answer:

(1 , 6)

Step-by-step explanation:

the center of the circle is the midpoint of the diameter

Which is the point of coordinates:

[tex](\frac{-3+5}{2} ,\frac{5+7}{2} )[/tex]

Then the center is the point :

[tex](1 , 6)[/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:

[tex]\longrightarrow\bold{(-3,5)}[/tex]

[tex]\longrightarrow\bold{(5, 7)}[/tex]

Calculate the average value between the x-coordinates of the diameter and do the same for the y-coordinates:

[tex]\longrightarrow\sf{C_x=\dfrac{-3+5}{2} = \dfrac{2}{2} =1}[/tex]

[tex]\longrightarrow\sf{C_y= \dfrac{5+7}{2} = \dfrac{12}{2} = 6 }[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\longrightarrow\sf{=(1,6)}[/tex]

Which of the following is the most accurate statement about Spatial Relations?
A- Children understand the spatial world watching movies about animals all over the world.
B- Children Need to know, use and be able to read spatial terms before they can demonstrate spatial awareness.
C-Spatial terms such as above, below, behind, and under are used to describe objects in space from different perspectives and are important for children to understand and express as they understand spatial relations.

Answers

Option C. The correct statement about spatial relationshipo is that Spatial terms such as above, below, behind, and under are used to describe objects in space.

What are spatial relationship?

These are the types of relationships that are used to relate objects to the location of somethings else. It makes use of words like under, above etc.

It is one of the knowledge that children need in the preoperational stage to learn how to use logical operations.

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x+11=35 solve on algebraic equation

Answers

Answer:

x = 24

Step-by-step explanation:

x + 11 = 35

x = 35 - 11

x = 24

x+11=35

Subtract 11 on both sides.

x=35−11

Subtract 11 from 35 to get 24.

x=24 === Answer

Solve the proportion
12
8
=
7.5
x

Answers

Answer:

9.8 is the final anwser

Step-by-step explanation so easy

Solutions greatest to smallest for function
=2+5−7

Answers

The greatest or maximum value for the given function = -8.25

The minimum or smallest value for the given function =-4

Calculation of greatest and smallest functions

The maximum value of a function is the highest value of that function. To calculate the greatest function, the following equation is used,

Formula max = c - (b2 / 4a)

Where,

a = 2

b = 5

C = -7

Therefore maximum function

= -7 -(5*2/4*2)

= -7-(10/8)

= -7 - 1.25

= -8.25

The minimum value of a function is the least value of that function.

Formula for the minimum = c - b^2/4a.

= -7-5^2/4*2

= -32/8

= -4

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Which statement most clearly shows an example of ethos? There is nothing more important than making sure everyone has access to a quality education. O Today, too many recent college graduates are struggling to secure a job in their field of study. O As the CEO of a major technology company, I am constantly making tough hiring decisions. O While a college education isn't everything, it does make a difference on a job application. Mark this and return Save and Exit Next Submit

Answers

The statement that most clearly shows an example of ethos is C. As the CEO of a major technology company, I am constantly making tough hiring decisions.

What is an ethos statement?

An ethos statement establishes the credibility, knowledge, and good moral character of the speaker or writer.

The use of ethos is meant to sound fair or to demonstrate credibility, expertise, education, or pedigree.

Thus, an example of ethos is when this CEO claims they constantly make tough hiring decisions.

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(02.03 MC)

Choose the equation that represents the graph.

graph of a line passing through points negative 2 comma 0 and 0 comma negative 4

y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4

Answers

Answer:

y = - 2x - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, - 4) ← 2 points on the line

m = [tex]\frac{-4-0}{0-(-2)}[/tex] = [tex]\frac{-4}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4

y = - 2x - 4 ← equation of line

Please look at the attachment and answer my question :(

Answers

Answer:

AB / BC = 2 / 3

A equals 9 and C = 13

AC = 13 - 9 = 4

AB + BC = 13

A) AB + BC = 4

B) AB / BC = 2/3 Therefore BC = AB / (2/3)

B) BC = 1.5 AB

A) BC = 4 - A/B

Multiplying equation A) by -1

A) -BC = -4 + AB then we add equation B)

B) BC = 1.5 AB then adding both equations

0 = 2.5 AB -4

2.5 AB = 4

AB = 1.6

Since A = 9 then the number at B is 9 + 1.6

equals 10.6

Step-by-step explanation:

Answer:

The number at B is 10.6

Step-by-step explanation:

Let the number at B be x.

We know that distance between two points on the number line is the absolute value of the difference of numbers at those points.

Then distances representing the lengths of segments AB and BC are:

AB = x - 9BC = 13 - x

We are given the ratio of segments:

AB/BC = 2/3

Substitute and solve for x:

(x - 9)/(13 - x) = 2/33(x - 9) = 2(13 - x)3x - 27 = 26 - 2x3x + 2x = 26 + 275x = 53x = 53/5x = 10.6

Represent each expression as a power of a, a cannot be equal to 0

Answers

Answer:

a^-27

Step-by-step explanation:

(a^3)^-3)^3)

(a^-9)^3)

a^-27

When we represent the expression ((a³)⁻³)³ as a power of a, the result obtained is a⁻²⁷

How to represent the expression as a power of a?

The following data were obtained from the question:

Expression: ((a³)⁻³)³Representation as power of a =?

We can represent the expression ((a³)⁻³)³ as a power of a by using the power law of indices as illustrated below:

((a³)⁻³)³

Recall

(Bᵐ)ⁿ = Bᵐⁿ (i.e multiply the power)

Thus,

((a³)⁻³)³ = (a⁻⁹)³

= a⁻²⁷

Thus, we can conclude from the above calculation that the representation of the expression ((a³)⁻³)³ as a power of a is a⁻²⁷

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convert this into a standard number
[tex]10^{6}[/tex]

Answers

Answer:

1,000,000

Step-by-step explanation:

The attached place value chart shows the power of ten associated with each number place in a decimal number.

Application

You have ...

1 × 10⁶ = 1,000,000

(Put the multiplier digit in the appropriate number place, and fill the remaining spaces with zeros. The digits 32,465 on the chart can be ignored.)

Additional comment

For powers of 10, the exponent (6 in this case) tells you the number of zeros to the right of the digit 1. That is, 10^6 is 1 followed by 6 zeros:

1,000,000

A customer's stock value seems to be rising exponentially. The equation for
the linearized regression line that models this situation is log(y) = 0.30x +0.296,
where × represents number of weeks. Which of the following is the best
approximation of the number of weeks that will pass before the value of the
stock reaches $600?

Answers

Answer:

B: 8.3

Step-by-step explanation:

We will substitute 600 to the y, since our final answer will be a number that makes the value of the stock reach $600.

log (y) = 0.30x + 0.296

Replacing y with 600, the equation becomes:

log (600) = 0.30x + 0.296

2.78 = 0.30x + 0.296

To move all the x and real numbers to different sides, we take 0.296 away from both sides to form:

2.78 - 0.296 = 0.30x

2.484 = 0.30x

x = 8.28

The approximation of 8.28 will be rounded to 8.3.

Then our final answer will be B: 8.3

Two friends, Jamie and Devin, are working together at the Sparrowtown Cafe today. Jamie works every 2 days, and Devin works every 7 days. How many days do they have to wait until they next get to work together?

Answers

Answer:

14 days

Step-by-step explanation:

let assume they both work on Monday (today)

devin works every 7 days,that is devin works every Monday.

jamie has to work for 14 days inorder to work with devin again

Question 3(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following tables shows the correct steps to transform x2 + 6x +8=0 into the form (x-p)² =q?
[p and q are integers]

Answers

The correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;

x^2 + 6x +8 +1 = 0 + 1

x^2 + 6x +8 +1 = 1

x^2 + 6x + 9 = 1

(x+3)² = 1

Vertex form of a quadratic equation

The vertex form of a quadratic equation is expressed as:

a(x-h)² + k

Given the quadratic equation

x^2 + 6x +8=0

Subtract 8 from both sides

x^2 + 6x +8 - 8 = 0 - 8

x^2 + 6x = -8

Complete the square

(x^2+6x+3^2) = -8 + 9

(x+3)² = -8 + 9

(x+3)² = 1

Hence the correct steps to transform x^2 + 6x +8=0 into the form (x-p)² =q are;

x^2 + 6x +8 +1 = 0 + 1

x^2 + 6x +8 +1 = 1

x^2 + 6x + 9 = 1

(x+3)² = 1

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What is the radian measure of central angle AOB in the circles? Write down the answer in the lowest terms

Answers

5pi/12 radians

The arc measure is 75, so theta must also be the same. if theta is 75, and 75 in radians is 5pi/12 radians, then the answer is that.

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 316 people entered the park, and the admission fees collected totaled 924.00 dollars. How many children and how many adults were admitted

Answers

Answer: pretty sure

There were 108 children and 175 adults.

Simplify the following expression.x-[tex]\frac{2}{3}[/tex] x[tex]\frac{6}{7}[/tex]

Answers

Keeping the bases and adding the exponents, the simplified expression is:

[tex]x^{\frac{4}{21}}[/tex]

How to solve a product of two terms with the same base and different exponents?

We keep the bases and add the exponents.

Hence:

[tex]x^{-\frac{2}{3}} \times x^{\frac{6}{7}} = x^{-\frac{2}{3} + \frac{6}{7}} = x^{\frac{-14 + 18}{21}} = x^{\frac{4}{21}}[/tex]

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