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

The simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]

The expression is given as:

[tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex]

Factor the numerator

[tex]\frac{x^{2}(x-8)}{x^2-64}[/tex]

Express the denominator as a difference of two squares

[tex]\frac{x^{2}(x-8)}{(x-8)(x + 8)}[/tex]

Cancel out the common factor

[tex]\frac{x^2}{x + 8}[/tex]

Hence, the simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Answer:

You must graph the two equations and find the point of intersection (x,y)

Point of intersection: (-4, -3)

Step-by-step explanation:

I can not provide a picture, but if you know how to graph these linear functions on the graph properly, you will find a point where the linear functions intersect at (x,y).

The value P price they charges for shirts is (-0.008n) + 38

According to the statement

we have given that the 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $14 .

And we have to find the linear equation.So,

Let p = price

n = number of shirts

m = slope of the line   (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

And they gives us the two points like here (1000, $30) and (3000, $14) which have to be on our line.

To find the slope m, you use m = (p₁-p₂)/(n₁-n₂)

Filling in from our points       m = (30-14)/(1000-3000)

                                         m = 16/-2000

                                         m = -0.008

Now that we have the slope and a point, we can find our equation

p-p₁=m(n-n₁)

p-30=(-.008)(n-1000)

p-30= (-.008n) + 8

p=(-.008n) + 38

So, The value P price they charges for shirts is (-0.008n) + 38

Learn more about linear equation here

https://brainly.com/question/4074386

#SPJ1

The second option saves time and cleaning elements, so that one is better.

We know that every day you sell a total of 50 bowls, and each one needs 8 oz of onion, this means that you need:

50*8 oz = 400 oz

So you need 400 ounces of onion per day.

If you buy at $1.99 per pound (1 lb = 16 oz)

Then the cost per ounce is:

c = $1.99/16

And the cost of 400 ounces is:

C = ($1.99/16)*400 = $49.75

In the case of the pre-sliced onions, the total cost would be:

C' = ($2.99/16)*400 = $74.75

So in the first case, each portion costs:

$49.75/50 = $0.995

And in the second case:

$74.75/50 =$1.495

So the extra cost is returned by the extra time and savings in cleaning elements, thus, the second option is better.

Learn more about costs:

brainly.com/question/25109150

#SPJ1

The probability of drawing a red marble and then a green marble is:

P = 1/6.

In the jar we have a total of 16 marbles, such that:

First, the probability of getting a red marble is give by the quotient between the number of red marbles and the total number of marbles:

p = 4/16 = 1/4

Now we need to draw a green one, the probability is computed in the same way, but this time there are 15 marbles, because we already took one.

q = 10/15

The joint probability (first drawing red, then green) is given by the product between the individual probabilities:

P = p*q = (1/4)*(10/15) = 10/60 = 1/6

If you want to learn more about probability:

https://brainly.com/question/25870256

#SPJ1

Thermal energy can be used in the heating systems either at home or in the industries

However, when solar energy is converted to thermal energy, the radiant energy from the sunlight is converted into heat which can then be used as space and hot water heating, power generation and industrial process heat

Energy simply refers to the capacity of doing work. Some forms of energy are:

So therefore, thermal energy can be used in the heating systems either at home or in the industries.

Learn more about energy:

https://brainly.com/question/25959744

#SPJ1

Answer:

2

Step-by-step explanation:

8/3 = 2 with a Remainder of 2

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: scale \: \: factor = \cfrac{new \: \: measure}{original \: measure} [/tex]

[tex]\qquad \sf  \dashrightarrow \: s = \dfrac{6}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: s = 3[/tex]

so, correct choice is D

The amount of money Craig paid more than Tim if the shop has an offer of reduction if a particular amount is spent is £88.

The shop discount:

£5 reduction if you spend more than £100

or

£10 reduction if you spend more than £140

or

£20 reduction if you spend more than £180

Cost of a shirt = £49

Tim buys 3 shirts

Total cost of Tim's shirt = £49 × 3

= £147

Amount Tim paid = £147 - £10

= £137

Craig buys 5 shirts

Total cost of Craig's shirt = £49 × 5

= £245

Amount Craig paid = £245 - £20

= £225

Difference between Tim and Craig's pay = £225 - £137

= £88

Read more on discount:

https://brainly.com/question/7459025

#SPJ2

From the line bisected with the given midpoints, we have been able to prove that; BC = CE by substitution property of Equality

We are given that;

C is the midpoint of BD

D is the midpoint of CE

1) Thus, BC = CD because of definition of Midpoint.

2) Similarly, by definition of midpoint we know that CD = DE.

3)  We can say that BC = DE because of substitution property of equality.

4) We can say that BC + CD = BD because of segment addition postulate.

5) Similarly, by segment addition postulate, we can say that CD + DE = CE.

6) Finally we can say that BC = CE by substitution property of Equality

Read more about Bisection of Line at; https://brainly.com/question/7299811

#SPJ1

The average number of hours worked per week drop from 2009 to 2010 dropped by 1.16%

The average work weeks are given as:

Year 2009 = 43 hours

Year 2010 = 42 hours 30 minutes

Rewrite as:

Year 2010 = 42.5 hours

The percentage change is then calculated as:

Percentage change= (Final - Initial)/Initial * 100%

So, we have:

Percentage change= (42.5 - 43)/43* 100%

Evaluate

Percentage change= -1.16%

Hence, the average number of hours worked per week drop from 2009 to 2010 dropped by 1.16%

Read more about percentage change at:

https://brainly.com/question/11360390

#SPJ1

Answer:

b) - 10

Step-by-step explanation:

To find the average rate of change, we have divide the change in y of f(x) , by the change in x(input).

   [tex]\sf \boxed{\text{\bf Average rate of change = $\dfrac{f(b)-f(a)}{b-a}$}}[/tex]

 a = 4 ; f(a) = -17

b = 6 ;   f(b) = -37

     [tex]\sf Average \ rate \ of \ change = \dfrac{-37-[-17]}{6-4}[/tex]

                                         [tex]\sf =\dfrac{-37+17}{2}\\\\=\dfrac{-20}{2}\\\\=-10[/tex]

The measure of D, perimeter and area of a parallelogram are 150°, 82cm and 200 square centimeters respectively. Option A

For the parallelogram ABCD, it can be deduced that

Line AB and CD are parallel and AD is a transversal so the angles A and D is co-interior , Co-interior angles are said to be supplementary whose sum is 180 degrees

A + D = 180°

30° + D = 180°

D = 180° - 30°

D = 150°

Perimeter = 2 ( a + b)

a = 16cm, b = 25cm

Perimeter = 2 (  16 + 25) = 2 ( 41)

Perimeter = 82 cm

Area = b × h

base = 25cm , h = 8cm

Area = 25 × 8

Area = 200 square centimeters

Thus, the measure of D, perimeter and area of a parallelogram are 150°, 82cm and 200 square centimeters respectively. Option A

Learn more about a parallelogram here:

https://brainly.com/question/970600

#SPJ1

There are 720 ways through which 3 numbers can be selected from 10 numbers to open a keypad lock.

Given that there are 10 numbers are 3 numbers are required to open a keypad lock.

Permutations are the number of ways in which objects can be selected without replacements to form subsets.

It is expressed as n[tex]P_{r}[/tex]=n!/(n-r)!.

Factorial of a number is the product of consecutive numbers less than the number.

Total numbers available=10

Numbers to be selected=3

Number of ways can be found by using permutations.

Number of ways =10[tex]P_{3}[/tex]

=10!/(10-3)!

=10!/7!

=10*9*8*7!/7!

=10*9*8

=720 ways.

Hence there are 720 ways through which 3 numbers can be selected from 10 numbers.

Learn more about permutations at https://brainly.com/question/1216161

#SPJ1

The place value in thousands for the 0 in 10000 is 0 thousands

From the question, we are to the determine the place value in thousands for the 0 in the given number

The given number is

10000

The place value in thousands for the 0 in 10000 is 0 thousands

Hence, the place value in thousands for the 0 in 10000 is 0 thousands

Learn more on Place value here: https://brainly.com/question/627658

#SPJ1

The proof that the diagram is a square is that; D: slopes are perpendicular where the sides meet

We know that a square is a quadrilateral that has 4 sides. Now, the 4 sides of a square are all equal and at right angles.

Since all sides of the square are equal, then it means that 2 consecutive sides must be perpendicular to each other. Thus, this means that the slope of 2 consecutive sides must be perpendicular to each other.

Read more about Square proof at; https://brainly.com/question/4471785

#SPJ1

The data given illustrates that there's a constant ratio of 2 and y = 600(2)^x; 38400

The ratio based on the information given will be:

= 1200/600

= 2

Therefore, the constant ratio is 2.

In 6 years, the population will be:

= 600 × 2^6

= 600 × 64

= 38400

Learn more about ratio on:

brainly.com/question/2328454

#SPJ1

[tex]\cos \left(\frac{3\pi}{2}-x \right)=\sin x \\ \\ =\cos \left(\frac{3\pi}{2} \right)\cos x -\sin \left(\frac{3\pi}{2} \right) \sin x \\ \\ =0\cos x -(-1)(\sin x) \\ \\ =\sin x[/tex]

Answer:

8.1

Step-by-step explanation:

[tex]\sqrt{(-1-0)^2 + (5-(-3))^2}=\sqrt{65} \approx 8.1[/tex]

The mean length of the 6 people's index finger is 11.55

The given parameters are:

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{3 * 9.9 + 3 * 13.2}{3 + 3}[/tex]

Evaluate

[tex]\bar x = \frac{69.3}{6}[/tex]

Divide

[tex]\bar x = 11.55[/tex]

Hence. the mean length of the 6 people's index finger is 11.55

Read more about mean at:

https://brainly.com/question/14532771

#SPJ1

From the line theorems explained below and when we apply it to the given image, we have; X║Y, A║B, Z ⊥ A

The perpendicular transversal theorem states that in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.

Now, since we are told that Line X is perpendicular to Line A, then it means that Line X is also perpendicular to line B.

The inverse of perpendicular transversal theorem states that if there are two perpendicular lines to a straight line, they're parallel to each other. Thus, it means that Line X is parallel to Line Y and similarly, line A is parallel to Line B.

Read more about Transverse Line Theorem at; https://brainly.com/question/12834964

#SPJ1

Answer:

14 and please Mark me brainlist

Answer:

There are four lines of symmetry in this figure.

Step-by-step explanation:

First look at the mainframe, it has 2 lines of symmetry. And if you look at it diagonally, it has another 2 more lines.

So therefore there is 4 lines of symmetry in this H figure.

Please mark me the Brainliest!

The number of solutions there are for the functions, -f(x) and f(-x) are; 2 and 2 respectively.

According to the task content, the function given initially is; f(x).

Hence, the function -f(x) represents a reflection of the function f(x) over the x axis. And in this case scenario, the reflection also has 2 solutions as it only cuts the x-axis at two points.

Also, the function f(-x) represents a reflection of the function f(x) over the y-axis. And in this case scenario, the reflection also has 2 solutions as it only cuts the x-axis at two points.

Read more on functions and reflection;

https://brainly.com/question/2220797

#SPJ1

Answer:

A

Step-by-step explanation:

9|x-8|<36

|x-8|<4

-4<x-8<4

add 8

-4+8<x-8+8<4+8

4<x<12

The blank space to form a linear pair with m∠BPD is m∠APD.

Linear pair of angles are formed when two lines intersect each other at a single point.

Linear pair angles are adjacent to each other.

Therefore, the sum of a linear pair angles is equals to 180 degrees.

This means linear pair angles are supplementary.

Hence,

m∠APD + m∠BPD = 180°

learn more on linear pair angles here: https://brainly.com/question/26555759

#SPJ1

The number of people who how many most likely purchased crunchy-flakes cereal is 1000 customers.

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).

The first step is to determine the ratio of people who preferred crunchy-flakes cereal:

Ratio of people who preferred crunchy-flakes cereal : 5 - 3 = 2

Now, multiply the ratio of those who prefer crunchy-flakes cereal by the total number of customers: (2/5) x 2500 = 1000  customers.

To learn more about ratios, please check: https://brainly.com/question/25927869

#SPJ1

Hello,

If we want to factor the expression, we have to solve

3x² + 10x + 8 = 0

a = 3 ; b = 10 ; c = 8

∆ = b² - 4ac = 10² - 4 × 3 × 8 = 4 > 0

x1 = (-b - √∆)/2a = (-10 - 2)/6 = -12/6 = -2

x2 = (-b + √∆)/2a = (-10 + 2)/6 = -8/6 = -4/3

Factor :

a (x - x1)(x - x2)

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

= (x + 2)(3x + 4)

The probability of a meerkat living smaller than 16.1 years exists at 99.85%.

The empirical rule notes that for a normal distribution most of the data lose within three standard deviations (σ) of the mean (µ). That exists 68% of the data lose within the first standard deviation (µ ± σ), 95% loses within the first two standard deviations (µ ± 2σ), and 99.7% declines within the first three standard deviations (µ ± 3σ).

68% declines within (10.4 ± 1.9). 68% declines within 8.5 years to 12.3 years.

95% declines within (10.4 ± 2[tex]*[/tex]1.9). 95% declines within 6.6 years to 14.2 years.

99.7% declines within (10.4 ± 3 [tex]*[/tex]1.9). 68% declines within 4.7 years to 16.1 years.

Probability of a meerkat living less than 16.1 years

= 100% - (100% - 99.7%)/2

= 100% - 0.15%

= 99.85%

Therefore, the probability of a meerkat living less than 16.1 years exists at 99.85%.

To learn more about empirical rules refer to:

https://brainly.com/question/23179842

#SPJ9

Answer:

x^4-3x+2

Step-by-step explanation:

There are several different ways to divide algebraic expressions. Here the most simple way to do it (and good idea to try first) is to FACTOR and CANCEL.

see image.

Factor an x from the top. Cancel that x with the bottom x. See image.

(***Also, note: never "cancel" anything connected by a + or a - )

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{x^{5}+(3\times x^{2}) +(2\times x) }{x}} \end{gathered}$}[/tex]

Takes into account expressions that have not yet been taken into account.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{\red{\not{x}}(x-1)(x^{3}+x^{2} +x-2) }{\red{\not{x}} } } \end{gathered}$}[/tex]

Cancel x in both the  numerator and the denominator.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{(x-1)(x^{3}+x^{2} +x-2) } \end{gathered}$}[/tex]

The expression expands

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x^{4}-3x+2 } \end{gathered}$} }[/tex]