Suppose a function f has an inverse. If f(2)=6 and f(3)=7, find: f−1(6)

Answers

Answer 1

Answer:

[tex]f^{-1}(6) = 2[/tex]

Step-by-step explanation:

Given

[tex]f(2) = 6[/tex]

[tex]f(3) = 7[/tex]

Required

[tex]f^{-1}(6)[/tex]

First, we need to determine the slope of the function using;

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

From the given parameters;

In [tex]f(2) = 6[/tex]

x = 2; y =6 --- Take this as x1 and y1

In [tex]f(3) = 7[/tex]

x = 3; y = 7 --- Take this as x2 and y2

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex] becomes

[tex]m = \frac{6 - 7}{2 - 3}[/tex]

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

[tex]m = 1[/tex]

Next, we determine the equation of the function using

[tex]y - y_1 = m(x - x_1)[/tex]

Substitute the values of x1,y1 and m

[tex]y - 6 = 1(x - 2)[/tex]

Open bracket

[tex]y - 6 = x - 2[/tex]

Add 6 to both sides

[tex]y - 6 + 6 = x -2 +6[/tex]

[tex]y = x + 4[/tex]

Next is to determine the inverse function by swapping the positions of x and y

[tex]x = y + 4[/tex]

Make y the subject of formula;

[tex]y = x - 4[/tex]

Replace y with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x) = x - 4[/tex]

Now, we can solve for [tex]f^{-1}(6)[/tex]

Substitute 6 for x

[tex]f^{-1}(6) = 6 - 4[/tex]

[tex]f^{-1}(6) = 2[/tex]


Related Questions

Determine what type of model best fits the given situation: A model rocket fired straight up from the ground, where h is the height of the rocket and t is the time in seconds. A. none of these B. quadratic C. linear D. exponential

Answers

The type of model best fits the given situation is a quadratic equation

Quadratic equation

Quadratic equations are equation that has a leading degree of 2.

From the given question, the motion of the rocket from the launch point to the landing point will be parabolic in nature and since the graph of a quadratic function is a parabola, hence the type of model best fits the given situation is a quadratic equation

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Match each number with its place in order from smallest (1st) to largest (6th). 1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48

Answers

Answer:

Numbers provided:

-56, 90, -84, 59, -80, 48

The smallest number is -84.

The highest number is 90.

1st: -84

2nd: -80

3rd: -56

4th: 48

5th: 59

6th: 90

Highest number is 90

Mariah bought a shirt for $28.50 and a belt. The total cost was $45.50. Which of the following equations can be used to find the cost of the belt? A. 28.50 + b= 45.50 B. 45.50 + b= 28.50 C. b= 28.50 - 45.50 D. b= 28.50 * 45.50 Please include work!!

Answers

Answer:

a is the answer 28.50 + b = 45.50

Step-by-step explanation:

so if i move 28.50 to the right side then it becomes b=45.50-28.50 and that equals to 17 . hope i helped have a great day

Answer: Choice A)  28.50+b = 45.50

=================================================

Explanation:

28.50 = cost of shirt

b = cost of belt, some unknown value

45.50 = total cost (given)

28.50+b = total cost (add the first two items shown above)

equate the two total cost expressions to end up with 28.50+b = 45.50

Is the function ƒ(θ) = 2cos( θ) an odd or even function?

Answers

Answer:

Even function.

Step-by-step explanation:

An odd function has symmetry with respect to the origin.

[tex]\text{A function is odd }\Leftrightarrow f(-x)=-f(x)[/tex]

The sine function is an odd function:

[tex]\sin(-\theta)=\sin(\theta)[/tex]

An even function has symmetry with respect to the y-axis.

[tex]\text{A function is even}\Leftrightarrow f(-x)=f(x)[/tex]

The cosine function is an even function:

[tex]\cos(-\theta)=\cos(\theta)[/tex]

Is the function [tex]f(\theta)=2\cos(\theta)[/tex] an odd or even function?

It is an even function.

What happens in the function is a vertical stretch by a factor of 2. The y-intercept is equal to 2.  

It’s an Even function

pleeeaaaasseeeee help me!!!
determine the percent of change. round to the nearest whole percent if necessary. original: 250 new: 100

Answers

Answer:

going from new to original would be times 2.5

from original to new would be time 0.4

Step-by-step explanation:

new to original is the 250/100

original to new is 100/250

Answer:

-60%

Step-by-step explanation:

First, find the difference

250 - 100 = 150

Then divide the decrease by the original number

150/250 = 0.6

And to convert this to a percentage all you have to do is multiply it by 100

0.6(100) = 60

The percent of change is -60% which is a decrease since it's negative

Please someone help me!!!!

Answers

Answer:

  4 months

Step-by-step explanation:

The 24% APR corresponds to a monthly rate of 24%/12 = 2%. This finance charge on a balance of $300 is ...

  0.02 × $300 = $6.00

To pay off $300 will take more than 3 payments of $100 because of the finance charge. Because the finance charge is not very large, the last month's payment will not need to be $100, but will be somewhat less.

It will take 4 months to pay off the balance.

_____

Additional comment

The actual finance charge will depend on your credit agreement. It may amount to $4 the second month, and $2.08 the third month, if it is charged on the outstanding balance. That is, the 4th month's payment may only be $6.08. If there is a finance charge on the initial $300 balance, that may cause the last payment to be a little more than $12.

It will take you 4 months to pay the card off.

If 120 is divided into 3 parts which are proportional to 1, [tex]\frac{1}{2} [/tex], and [tex]\frac{1}{6}[/tex], what is the middle part?

Answers

[tex]k+\frac{k}{2}+\frac{k}{6}=120\\\\6k+3k+k=720\\10k=720\\k=72[/tex]

72,36,12

answer: 36

So if we put 120 Into 3 parts 72,36,12 then the answer would be 36

Find the first, fourth, and eighth terms of the sequence. A(n) = −5 ∙ 2x − 1

Answers

Answer:

The answer is option A

Step-by-step explanation:

The rule for the sequence is

[tex]A(n) = 5. {2}^{x - 1} [/tex]

where x is the number of terms

For the first term

x = 1

That's

[tex]A(1) = 5. {2}^{1 - 1} [/tex]

[tex]A(1) = 5. {2}^{0} [/tex]

A(1) = 5(1)

A(1) = 5

For the fourth term

x = 4

[tex]A(4) = 5. {2}^{4 - 1} [/tex]

[tex]A(4) = 5. {2}^{3} [/tex]

A(4) = 5(8)

A(4) = 40

For the eighth term

x = 8

[tex]A(8) = 5. {2}^{8 - 1} [/tex]

[tex]A(8 ) = 5. {2}^{7} [/tex]

A(8) = 5(128)

A(8) = 640

Hope this helps you

Answer:

The first option.

Step-by-step explanation:

The first term of the sequence would be...

A(1) = -5 * 2^(1 - 1)

= -5 * 2^0

= -5 * 1

= -5

The fourth would be...

A(4) = -5 * 2^(4 - 1)

= -5 * 2^3

= -5 * 8

= -40

The eighth would be...

A(8) = -5 * 2^(8 - 1)

= -5 * 2^7

= -5 * 128

= -640

So, the correct answer is the first option.

Hope this helps!

Three faucets fill a 100-gallon tub in 6 minutes. How long, in seconds, does it take six faucets to fill a 25-gallon tub? Assume that all faucets dispense water at the same rate.

Answers

Answer:

see below

Step-by-step explanation:

It would take 3 faucets 6/4 = 1.5 minutes to fill a 25-gallon tub since when the number of faucets stays the same, the volume of the tub and the time needed to fill the tub are directly proportional. However, when the volume of the tub stays the same, the number of faucets used and the time needed to fill the tub are inversely proportional, therefore, if I double the number of faucets used, it will half the time needed, so the answer is 1.5 / 2 = 0.75 minutes or 45 seconds.

Answer:

[tex]\large\boxed{45 seconds}[/tex]

Step-by-step explanation:

------------------------------------------------------------------------------------------------------------

Variable Key

Faucets = f

Minutes = m

Gallons = g

------------------------------------------------------------------------------------------------------------

Write an equation to display how long it takes for the 3 faucets to fill up a 100 gallon tub.

100g = 6m

Divide both sides of the equation by 6

m = 16.67g

This means that approximately 16.67 gallons are filled up per minute with 3 faucets. We found the measurement (gallons), which is based on the time (minutes). This is called the unit rate.

Now that we found the unit rate for 3 faucets, let's find the unit rate for 6 faucets by multiplying our unit rate by 2.

3f = 16.67g per minute

6f = (16.67g per minute)(2)

6f = 33.34 g per minute

We now know the unit rate for 6 faucets, so now all we have to do is divide that by 25 gallons, the second tub.

25g / 33.34 g = 0.75 minutes

Convert to seconds

0.75 minutes = 3/4 of a minute

1 minute = 60 seconds

Substitute

3/4(60)

[tex]\large\boxed{45 seconds}[/tex]

Hope this helps :)

Write as an inequality "The difference of a number squared and three is at least twelve"

Answers

Answer:

using the equilateral formula of solution

Answer:

[tex]x^2-3\geq 12[/tex]

Step-by-step explanation:

[tex]x^{2} -3[/tex] is the difference of a number squared and three

is at least 12, means that is greater but not less

[tex]x^2-3\geq 12[/tex]

what is the domain of the function shown in the graph below?
answer type: interval, all real numbers, all values except one, all values except two
interval:

Answers

Answer: interval from -8 to 5

In interval notation, we would write [-8, 5]

The domain is the set of allowed x inputs to a function. The left-most point is (-8,0) so x = -8 is the smallest x value allowed. The largest x value allowed is x = 5 due to the point (5,0) being the right-most point.

The use of square brackets in interval notation says "include this endpoint as part of the interval".

it is would be -5 to 8

help i want help i want help

Answers

Answer:

[tex] \boxed{127 \: {in}^{2} }[/tex]

Option A is the correct option.

Step-by-step explanation:

Surface area of the rectangle base = 9 × 5 = 45 in²

Surface area of lateral square = ( 5 )² = 25 in²

Surface area of lateral rectangle = 6.4 × 5 = 32 in²

Surface area of top square = ( 5 )² = 25 in²

Surface area of two parallel trapezoids:

[tex] (\frac{1}{2} (9 + 5) \times 5) \times 2[/tex]

= 7 × 5 × 2

= 70 in²

Total surface area:

= 45 + 25 + 32 + 25 + 70

= 197 in²

Hope I helped!

Best regards!

great work from them^ , the person above me answered this correctly it is 197in ^2

On the number line below, P represents a number. What is the value of the opposite of that number? A number line from negative 4 to positive 4 in increments of 1 over 4, with all whole numbers alone labeled is shown. Put point P at the fifth tick mark to the right of 0. negative 2 and 2 over 4 negative 1 and 1 over 4 1 and 1 over 4 2 and 2 over 4

Answers

Answer:

[tex]-1\frac{1}{4}[/tex]

option 2

Step-by-step explanation:

In this number line, each interval equals 1/4.

P represents 1 1/4

So, opposite of number P is   ( [tex]-1\frac{1}{4}[/tex] )

option 2 would be the best answer

PLEASE HELP ME WITH THIS QUESTION ANYTHING HELPS!

Answers

Answer:

x = 148

Step-by-step explanation:

CPD is a straight line so it equals 180

CPB + BCD = CPD

x + 32 = 180

Subtract 32 from each side

x+32-32 = 180-32

x =148

32 x 2= 64
since angles at a point add up to 360 degrees
360 -64= 296
296 divided by 2= 148

So angle x is 148 degrees

Hope dis helps ya

Can someone tell me if I got the answer right? For the first one I got 2 and for the second one I got -1.

Answers

Answer:

see explanation

Step-by-step explanation:

f(g(2)) = f(0) = -2

g(f(1)) = g(0) = 0

Answer:

The correct answers for both of them is -2 and 0.

Step-by-step explanation:

I)

[tex](f\circ g)(2)=f(g(2))[/tex]

From the red graph, we can see that g(2) is 0.

Therefore, f(g(2)) is equal to f(0).

And from the blue graph, we can see that f(0) is -2.

Therefore:

[tex](f\circ g)(2)=-2[/tex]

II)

[tex](g\circ f)(1)=g(f(1))[/tex]

From the blue graph, we can see that f(1) is 0.

Therefore, g(f(1)) is equal to g(0).

And from the red graph, g(0) is 0.

Therefore:

[tex](g\circ f)(1)=0[/tex]

So, you got one correct. Nicely done!

Compute the odds in favor of obtaining a number divisible by 5 in a single roll of a die.

Answers

Answer:

1/6 or 16.7% chance

Step-by-step explanation:

A die has 6 sides, and there is only one side with a number divisible by 5, which is the number 5.

So, the probability of rolling a number divisible by 5 is 1/6.

= 1/6 or 0.167

The odds in favor of obtaining a number divisible by 5 will be 1/6 or 0.1667.

What is probability?

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

The die is rolled for a single time. Then the total number of the events will be

Total event = 6 {1, 2, 3, 4, 5, 6}

The odds in favor of obtaining a number divisible by 5 will be

There is only one number that is divisible by 5 which is 5.

Then the number of favorable events will be

Favorable event = 1 {5}

Then the probability will be

P = 1 / 6

P = 0.1667

The odds in favor of obtaining a number divisible by 5 will be 1/6 or 0.1667.

More about the probability link is given below.

https://brainly.com/question/795909

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Help
Find the lateral area of this cone.
Round to the nearest tenth.

Answers

Answer:

233.5 in²

Step-by-step explanation:

First we have to find the slant height.

5²+14²=c²

25+196=c²

221=c²

c=14.866

Now we can find the lateral area.

[tex]\pi[/tex]rl

[tex]\pi[/tex](5)(14.866)

=233.51566

To the nearest tenth=

233.5 in²

233.5 I just guessed but I’m sure that’s is it

A lab technician is dividing a cell that has a diameter of 4.32×10−4 4 . 32 × 10 - 4 millimeters. Each of the new cells has a diameter measuring exactly one half of the diameter of the original cell. Which is the diameter of a new cel

Answers

Answer:

Bottom right option

Step-by-step explanation:

To find this, we can calculate:

1/2 * 4.32 * 10⁻⁴

= (1/2 * 4.32) * 10⁻⁴

= 2.16 * 10⁻⁴

The diameter of a new cell is 2.16×10−⁴millimeters

First step is to calculate 4.32×10−⁴ to the original numbers

4.32×10−⁴ =0.000432

Second step is to determine the diameter of a new cell

New cell diameter=0.000432×1/2

New cell diameter=0.000216

New cell diameter=2.16×10−⁴millimeters

Inconclusion The diameter of a new cell is 2.16×10−⁴millimeters

Learn more here:

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Clara has a lawn in front of her house as mapped on the coordinate plane. She wants to plant a bed of flowers between the points P and Q. Find the length of the bed of flowers. Question 2 options: A) 2 units B) 7 units C) 13 units D) 8 units

Answers

Answer:

Look Below In the Explanation

Step-by-step explanation:

Point P has coordinates of (4,4) and point Q has coordinates of (4,-4).

Since both points have the same x-coordinates we can subtract point Q's y-coordinate from point P's y-coordinate.

I will set the equation up and try and figure this part by yourself. I hope you learned what to do from previous questions that are very similar to this that I answered.

4 - ( -4) = length of the bed of flowers

Hope that helps and maybe earns a brainliest!

Have a splendid day! :^)

The length of the bed of flowers will be 8 units.

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

Clara wants to plant a bed of flowers between the points P and Q.

And, The value of P = (4, 4)

And, The value of Q = (4, - 4)

Now,

Since, Clara wants to plant a bed of flowers between the points P and Q.

And, The value of P = (4, 4)

And, The value of Q = (4, - 4)

Hence, The length of the bed of flowers will be;

PQ = √ (- 4 - 4)² + (4 - 4)²

PQ = √64

PQ = 8 units

Thus, The length of the bed of flowers will be 8 units.

Learn more about the coordinate visit:

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O E. $68.00
QUESTION 16
3.04 poi
You are a school photographer taking individual and class pictures for 2 classes of
21 students each. On average, each individual picture takes 3 minutes and a class
picture takes 10 minutes. About how long should it take you to get all of the
pictures?
O A. 1 hour 3 minutes
B. 1 hour 13 minutes
OC. 2 hours 6 minutes
OD. 2 hours 16 minutes
O E. 2 hours 26 minutes

Answers

The answer to your question is E
Answer is E 2 hours and 26 min

Select the correct answer from each drop-down menu.
35
30
25
Number of Roses
20
15
10
5
0
2
1
3
4
5
X
Number of Plants
According to the graph, the relationship between the number of rose plants and the number of roses is

Answers

Answer:

I think it is b

Step-by-step explanation:

I really feel like it’s B

How many numbers between 1 and 1000 do not contain the digits 8, and 9 ?

Answers

Answer:

998

Step-by-step explanation:

I haven't included the 1 or the 1000

Answer:

There are 200 numbers between 1 and 1000  that do not contain the digits 8, and 9.

Step-by-step explanation:

1-100

=(8,9,18,19,28,29,38,39,48,49,58,59,68,69,78,79,88,89,98,99)=20

101-200

=(108,109,118,119,128,129,138,139,148,149,158,159,168,169,178,179,188,189,198,199)=

201-300=20

.......

100*10=1000

20*10=200

If we transform the parabola y=(x+1)^2+2 by shifting 7 units to the right and 5 units down, what is the vertex of the resulting parabola? Vertex of resulting parabola: (__ a0,__ a1)

Answers

Hey there! I'm happy to help!

The vertex form of a parabola is y=a(x-h)²+k. The h represents the horizontal transformation, while the k represents the vertical. The vertex of a parabola in this form is (h,k). The a represents a vertical stretch or shrink.

Our parabola is y=(x+1)²+2. This is already in vertex form, so we do not need to change the equation. There is no a (basically a=1), which means that the parabola has not been stretched or shrunk from its parent form.

We see that the h is -1. This is because in the original equation it is (x-h)², so it has to be -1 because the two negatives make a positive which is the +1. (x--1)=(x+1).

We see that the k value is 2.

Since the vertex is (h,k), this vertex is (-1,2).

However, we have to shift the parabola 7 units to the right and 5 units down. So, we add 7 to the x-value and subtract 5 from the y-value of the vertex.

(x,y)⇒(x+7,y-5)

(-1,2)⇒(6,-3)

Therefore, the vertex of the resulting parabola is (6,-3).

Have a wonderful day! :D

I did the math and the other comment is correct

PLEASE NEED HELP ASAP!!!!!!! WILL GIVE BRAINLY!!!!!! what are the domain, range, and asymptote of h(x)=(0.5)^x-9

Answers

Answer:

[tex]\mathrm{Domain\:of\:}\:0.5^x-9\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Range\:of\:}0.5^x-9:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>-9\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-9,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Asymptotes\:of}\:0.5^x-9:\quad \mathrm{Horizontal}:\:y=-9[/tex]

Step-by-step explanation:

Domain:

The function has no undefined points nor domain constraints. Therefore, the domain is

[tex]...-\infty \:<x<\infty \:[/tex]

Definition: The domain of a function is the set of input or argument values for which the function is real and defined.

_________________________________________________

Range:

[tex]\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k\\k=-9[/tex]

[tex]f\left(x\right)>-9[/tex]

Definition: The set of values of the dependent variable for which a function is defined.

_________________________________________________

Asymptotes:

[tex]\mathrm{Vertical\:asymptotes\:of\:}0.5^x-9:\quad \mathrm{None}\\\mathrm{Horizontal\:Asymptotes\:of\:}0.5^x-9:\quad y=-9\\\mathrm{Horizontal}:\:y=-9x^{2}[/tex]

748489001.689 no clue if I did it or not

Laura has a step of 50cm She walks along by taking two steps forward and one step back. What is the least number of steps counting forward and backwards step, she takes to reach a step 20m away? ~Thanks - don't know how to solve :(

Answers

If she moves two steps forward and one step backward, she ends up traveling forward by the distance of one step: 50cm.

So, she took three steps to travel 50cm.

20m = 2000cm
2000cm/50cm = 40
She will have to do her three steps forty times to reach 20m. Thats a total of 120 steps.
The answer is Laura walked 20cm to 50cm

Can you help me learn how to solve problems like these? I need to know the answer, but I also need to know how to do it because this isn't all of them.
[tex]\frac{1}{p-2} / \frac{4p^2}{p^2+p-6}[/tex]
[tex]\frac{6n}{3n+2} - \frac{2}{2n-2}[/tex]
[tex]\frac{2x}{3x^2+18x} + \frac{3}{2}[/tex]

Answers

[tex]\dfrac{\dfrac{1}{p-2}}{\dfrac{4p^2}{p^2+p-6}}=\\\\\\\dfrac{1}{p-2}\cdot\dfrac{p^2+p-6}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{p^2+3p-2p-6}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{p(p+3)-2(p+3)}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{(p-2)(p+3)}{4p^2}=\\\\\dfrac{p+3}{4p^2}[/tex]

--------------------------------------------------------------------

[tex]\dfrac{6n}{3n+2}-\dfrac{2}{2n-2}=\\\\\dfrac{6n(2n-2)}{(3n+2)(2n-2)}-\dfrac{2(3n+2)}{(3n+2)(2n-2)}=\\\\\dfrac{12n^2-12n-(6n+4)}{6n^2-6n+4n-4}=\\\\\dfrac{12n^2-12n-6n-4}{6n^2-2n-4}=\\\\\dfrac{12n^2-18n-4}{6n^2-2n-4}=\\\\\dfrac{2(6n^2-9n-2)}{2(3n^2-n-2)}=\\\\\dfrac{6n^2-9n-2}{3n^2-n-2}[/tex]

----------------------------------------------------------------------

[tex]\dfrac{2x}{3x^2+18x}+\dfrac{3}{2}=\\\\\dfrac{2}{3x+18}+\dfrac{3}{2}=\\\\\dfrac{2\cdot2}{2(3x+18)}+\dfrac{3(3x+18)}{2(3x+18)}=\\\\\dfrac{4+9x+54}{6x+36}=\\\\\dfrac{9x+58}{6x+36}[/tex]

Answer:

p^3−10p^2+1

——————        We find roots of zeros  F(p) = p^3 - 10p^2 + 1 and see there

      p^2                                             are no rational roots

       

Step-by-step explanation:

                 p^2

Simplify   ——

                 p^2

1.1    Canceling out p^2 as it appears on both sides of the fraction line

   Equation at the end of step 1

:1

 ((————-(4•1))+p)-6

   (p^2)

STEP 2: working left to right

                  1

Simplify   ——

                 p^2

Equation at the end of step 2:    

1 /p^2 ((—— -  4) +  p) -  6

STEP 3:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  p^2  as the denominator :

          4         4 • p^2

   4 =  —  =  ——————

           1             p^2  

Equivalent fraction

: The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

             1 - (4 • p^2)                 1 - 4p^2

————————————  =  ———————

                    p^2                             p^2  

Equation at the end of step 3:

        (1 - 4p^2)          

 (————————— +  p) -  6

             p^2              

STEP 4:

Rewriting the whole as an Equivalent Fraction

4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  p2  as the denominator :

           p         p • p^2

   p =  —  =  ——————

           1             p^2  

Trying to factor as a Difference of Squares:

4.2      Factoring:  1 - 4p^2

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  1  is the square of  1

Check : 4 is the square of 2

Check :  p^2  is the square of  p^1

Factorization is :       (1 + 2p)  •  (1 - 2p)

Adding fractions that have a common denominator :

4.3       Adding up the two equivalent fractions

                (2p+1) • (1-2p) + p • p^2                                   p^3 - 4p^2 + 1

————————————————————————  =  ————————————

                               p^2                                                            p^2    

Equation at the end of step

4:

        (p^3 - 4p^2 + 1)    

 —————————————— -  6

                 p^2          

STEP 5:

Rewriting the whole as an Equivalent Fraction

5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  p^2  as the denominator :

           6         6 • p^2

   6 =  —  =  ——————

           1             p^2  

Polynomial Roots Calculator :

5.2    Find roots (zeroes) of :       F(p) = p^3 - 4p^2 + 1

Polynomial Roots Calculator is a set of methods aimed at finding values of  p  for which   F(p)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  p  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  1.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -4.00    

     1       1        1.00        -2.00    

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

5.3       Adding up the two equivalent fractions

(p3-4p2+1) - (6 • p2)     p3 - 10p2 + 1

—————————————————————  =  —————————————

         p2                    p2      

Polynomial Roots Calculator :

5.4    Find roots (zeroes) of :       F(p) = p3 - 10p2 + 1

    See theory in step 5.2

In this case, the Leading Coefficient is  1  and the Trailing Constant is  1.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1

Let us test ....

  P       Q    P/Q       F(P/Q)  Divisor

     -1      1        -1.00       -10.00    

       1      1    1.00       -8.00    

Polynomial Roots Calculator found no rational roots

Final result :

             p3 - 10p2 + 1

 —————————————

                 p2      

Solve the equation 14=7(2x-4) using two different methods. Show your work. Which method do you prefer? Explain. need help thanks

Answers

Answer:

x=3

Step-by-step explanation:

14=7(2x-4)

14/7=2x-4

2=2x-4

2x=2+4

2x=6

x=6/2

x=3

------------

14=7(2x-4)

14=14x-28

14x=14+28

14x=42

x=42/14

x=3

The equation 14 = 7(2x - 4) can be solved using two different methods: the distributive property method and the inverse operations method. Both methods yield the same solution, which is x = 3. The preference between the two methods depends on personal preference and the specific equation being solved.

Distributive Property Method:

We'll distribute the 7 to the terms inside the parentheses:

14 = 7(2x - 4)

14 = 14x - 28

Next, we'll isolate the variable term:

14x = 14 + 28

14x = 42

Finally, we'll solve for x by dividing both sides of the equation by 14:

x = 42/14

x = 3

So the solution to the equation is x = 3.

Inverse Operations Method:

We'll use inverse operations to solve the equation step by step:

14 = 7(2x - 4)

Divide both sides of the equation by 7 to isolate the term in parentheses:

14/7 = 7(2x - 4)/7

2 = 2x - 4

Add 4 to both sides of the equation to isolate the variable term:

2 + 4 = 2x - 4 + 4

6 = 2x

Divide both sides of the equation by 2 to solve for x:

6/2 = 2x/2

3 = x

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Wendy opened a savings account 15 years ago with a deposit of $2,340.73. The account has an interest rate of 4.7% compounded monthly. How much interest has
Wendy earned?

Answers

Answer:

$4661.77

Step-by-step explanation:

100 + 4.7 = 104.7%

104.7% = 1.047

$2340.73 x 1.047^15 = $4661.77

4661.77, that’s how much Wendy earned . Ah it’s no problem don’t mention it

What is the total surface area of the square pyramid below? A square pyramid. The square base has side lengths of 10 centimeters. The triangular sides have a height of 14 centimeters. 100 cm2 200 cm2 280 cm2 380 cm2

Answers

Answer:

380 cm^2

Step-by-step explanation:

10*10=100(base square)

Each triangle= (14*10) /2=70

4 sides, so therefore: 70*4=280

280+100=380

Since the square base has side 10 cm and triangular side has height 14 cm, the total surface area of square pyramid is 380 cm²

To answer the question, we need to find the total surface area of the square pyramid

Total surface area of a square pyramid.

Since a square pyramid has a square base and four triangular sides, its surface area, A = area of square base + 4 × Area of triangular side.

Area of square base

Area of square with side, L is A = L²

Area of triangular base

Area of triangle with height, h and base, L which is the length of the square base is A' = 1/2Lh

So, total surface area of square pyramid is A" = L² + 4 × 1/2Lh

= L² + 2Lh

Given that the length of the square base is 10 cm and the height of the triangular side is 14 cm.

We have that

L = 10 cm and h = 14 cm

So, substituting the values of the variables intot he equation, we have

A" = L² + 2Lh

A" = (10 cm)² + 2 × 10 cm × 14 cm

A" = 100 cm² + 280 cm²

A" = 380 cm²

So, the total surface area of square pyramid is 380 cm²

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PLEASE HELP I WILL GIVE BRAINLIEST!!!!! The box plots below show attendance at a local movie theater and high school basketball games: Two box plots are shown. The top one is labeled Movies. Minimum at 100, Q1 at 130, median at 165, Q3 at 185, maximum at 200. The bottom box plot is labeled Basketball games. Minimum at 135, Q1 at 225, median at 248, Q3 at 275, maximum at 300. Which of the following best describes how to measure the spread of the data? The IQR is a better measure of spread for movies than it is for basketball games. The standard deviation is a better measure of spread for movies than it is for basketball games. The IQR is the best measurement of spread for games and movies. The standard deviation is the best measurement of spread for games and movies.

Answers

I’ve also saw this question, the answer was b when I read it as well, you can also use Socratic for things like this

Correct option is Option B: The standard deviation is a better measure of spread for movies than it is for basketball games.

Visual analysis for movies:

Movies data is more centric to mean and not skewed on a particular side.

Visual analysis for Basketball games:

Basketball games data is not centric to mean but is skewed or say more dense in right then left.

Property of standard deviation and its limitation:

Standard deviation just measures the deviation or spread with respect to mean of collected data. It is non- sensible for skewness of the data and thus more information is needed in such case.

Property of IQR and its limitation:

IQR is interquartile range. IQR generally is less powerful than standard deviation, but more powerful if the data is skewed and its variability has to be measured. It measures the range or say difference between [tex]Q_3 \: and \: Q_1[/tex]

In the movies data, the data is more collected and barely visible to be skewed. Thus standard deviation is best suited for this dataset.

In the basketball data, the standard deviation will fail to give good information about the data. The IQR, is better here since we've to measure variability or dispersion of data which is skewed.

Thus, option B: The standard deviation is a better measure of spread for movies than it is for basketball games; is correct option.

Learn more here:

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