Find the difference quotient and simplify your answer. f(x) = 7x − x2, f(7 + h) − f(7) h , h ≠ 0

Answers

Answer 1
whatever is inside of the ( ), simply plug that digit into the x-values for f(x)
So: f(x) = 7x - x^2, and f(7+h) - f(7)
= [7(7+h) - (7+h)^2] - [7(7) - (7)^2]
= [49+7h - 49+14h+h^2] - [49-49]
= 49-49 + 7h+14h + h^2 = h^2 + 21h =
h (h+21), h (h+21) = 0
h=0... But it stated h cannot = 0
So h+21 = 0, h = -21
Answer 2
Final answer:

The difference quotient for the function f(x) = 7x - x² is (7h - h²) / h.

Explanation:

The difference quotient is used to find the rate at which a function changes over a small interval. To find the difference quotient for the given function f(x) = 7x − x², we substitute f(7 + h) and f(7) into the formula: [f(7 + h) - f(7)] / h. Simplifying the expression, we get [(7(7 + h) - (7 + h)²) - (7(7) - 7²)] / h. Expanding and simplifying further, we have [(49 + 7h - h²) - (49 - 49)] / h, which becomes (7h - h²) / h.

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Related Questions

What is the equation of a line with a slope of 2 that goes through the point (4,12)?

Answers

Formula for point-slope: [tex]y - y1 = m(x-x1)[/tex]
Plug in the values: [tex]y -12 = 2(x - 4) [/tex]

And there you have your answer in point-slope form

what did the candle say to the match

Answers

you light up my life

What is the surface area of a sphere with a diameter of 16 cm?

A. 1,024n cm²

B. 32n cm²

C. 256n cm²

D. 128n cm²

Answers

C is the correct answer

Answer:

The correct option is C. The surface area of a sphere is 256π cm².

Step-by-step explanation:

Given information: The diameter of the circle is 16 cm.

[tex]r=\frac{d}{2}=\frac{16}{2}=8[/tex]

Radius of the circle is 8 cm.

Surface area of a sphere is

[tex]A=4\pi r^2[/tex]

Where, r is radius.

[tex]A=4\pi (8)^2[/tex]

[tex]A=4\pi (64)[/tex]

[tex]A=256\pi[/tex]

The surface area of a sphere is 256π cm². Therefore the correct option is C.

There are 240 coins in a jar, all dimes and quarters. The value of the coins in the jar is $27.60. There are nine times as many dimes as there are quarters. How many dimes (d ) are in the jar?

Answers

I believe it is 28 dimes
.25 × 30 = 7.50
.10 × 190 = 19
19 + 7.50 = 26.50
Then, you add 4 more quarters which is 27.50 and the 28 dime makes it 27.60

What is the square root of 99 simplified?

Answers

Step-by-step explanation: To simplify the square root of 99, first create a factor tree that has 2 branches.

99 factors as 11 × 9 and 9 factors as 3 × 3.

Since we have a pair of 3's in our factor tree, a 3 can come out of the radical. Since we have a 11 that doesn't match up, it stays inside the radical and this gives us the answer of [tex]\sqrt[3]{11}[/tex].

I have also attached my work in the image provided.

The square root of 99, when simplified as much as possible, is approximately 9.94987437.

We have,

The square root of a number is a value that, when multiplied by itself, gives the original number.

In the case of the square root of 99, there is no whole number that can be multiplied by itself to result in 99.

Therefore, the square root of 99 is an irrational number.

To find an approximate value for the square root of 99, we can use a calculator or mathematical methods.

The square root of 99 is approximately 9.94987437.

This means that when we multiply 9.94987437 by itself, we get a value close to 99.

Since 9.94987437 cannot be simplified further as a whole number or a simplified radical, it is the most accurate representation of the square root of 99.

Thus,

The square root of 99, when simplified as much as possible, is approximately 9.94987437.

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Can someone explain 15-20? I really need help and it's due tomorrow. Thank you in advance!

Answers

15-20 is -5. If you put 15 on a number line and go back twenty spaces you land on -5 hope this helps.
ok so one of the halves will always be half of the other so 
15) NL = 5 because since JM = 14 Mk =7 because it is half of JM same goes for the other side since JN =10 NL =5
i hope this helped

What is the answer to p/3 -2=1

Answers

(p/3) - 2 = 1

p/3 = 1 + 2

p/3 = 3

3(p/3) = 3(3)

p = 9

If 5 is transformed into 11 and 12 is transformed into 25, then what does 15 become

Answers

5x2=10+1=11 12x2=24+5=24+1=25 15×2=30+1=31 so the awnser is 31

A new car has an msrp of $20,150, and it comes with a sport package priced at $1500, a stereo package priced at $500, and a destination charge of $700. what is the sticker price of this car?

Answers

22850 is the answer
Thanks (:

Write a compound inequality that represents the situation.

all real numbers at least –6 and at most 3

Answers

Answer:

[tex]\[-6 \leqslant x \leqslant 3\][/tex]

Step-by-step explanation:

The requirement is to represent a compound inequality with all real numbers at least –6 and at most 3.

This can be broken into two parts:

a) All real numbers at least -6

[tex]\[x\geqslant -6\][/tex]

b) All real numbers at most 3

[tex]\[x \leqslant 3\][/tex]

Combining the two inequalities to generate the compound inequality:

[tex]\[-6 \leqslant x \leqslant 3\][/tex]

Which inequality's solution is graphed here?
A) x + 9 < 5
B) x - 5 < 9
C) x + 5 < 9
D) x - 9 < 5

Answers

there is an open dot on 4.....an open dot means there is no equal sign in the problem....and it is shaded to the left...means it is less then. So ur looking for an inequality with the answer being x < 4.

x + 5 < 9 <== its gonna be this one
x < 9 - 5
x < 4 

Answer:

there is an open dot on 4.....an open dot means there is no equal sign in the problem....and it is shaded to the left...means it is less then. So ur looking for an inequality with the answer being x < 4.

x + 5 < 9 <== its gonna be this one

x < 9 - 5

x < 4 

What was the approximate number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003?

The display gives the result of performing an exponential regression on a data set where the inputs are years since 2000 and the outputs are the corresponding mobile cellular subscriptions per 100 on Zimbabwe.

ExpReg
y=a*b^x
a=1.067905095
b=1.501755837
r^2=.9525580427
r= .9759908005

A. 2
B. 4
C. 6
D. 8

Answers

The answer is 4 when you plug in the equation and solve it equals 4

Answer:

B. 4

Step-by-step explanation:

Given exponential model that shows the number of mobile cellular subscriptions per 100 people in Zimbabwe since 2000,

[tex]y=a b^x[/tex]

Where,

a=1.067905095

b=1.501755837,

[tex]\implies y=1.067905095(1.501755837)^x[/tex]

Since, the number of years from 2000 to 2003 = 3,

Thus, for finding the number of subscriptions in 2003,

x = 3,

Hence, the number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is

[tex]y=1.067905095(1.501755837)^3=3.61685122094\approx 4[/tex]

Option 'B' is correct.

(a) if cigarettes are priced at $6 a pack, how many packs will smokers buy flashcards

Answers

Given the table below which depicts the market demand for cigarettes.

[tex]\begin{tabular} {|p{3.9cm}|c|c|c|c|c|c|c|c|} Price per pack&\$10&\$9&\$8&\$7&\$6&\$5&\$4&\$3\\[1ex] Quantity demanded (millions of packs per year)&2&4&6&8&10&12&14&16 \end{tabular}[/tex]

Part a:

If cigarettes are priced at $6 a pack, how many packs will smokers buy?

From the table it can be seen that when the price per pack of cigarette is $6, the quantity demanded is 10 million packs per year.

Therefore, if cigarettes are priced at $6 a pack, smokers will buy 10 million packs per year.

Can someone help me really quickly please? I already have an answer, but im not sure if it's wrong or right :/

Answers

Substitute in the values into the inequality.

11(-6) - 14(-6) > 18
-66 - (-84) > 18
-66+84 > 18
18>18

Since 18 is not greater than 18, the answer is false.

Hope this helps!
No! (-6, -6) Is the solution to 11x-14y>18

Find the perimeter of the figure. 2 1/4 in, 4 1/12in, 3 2/3in

Answers

 it would = out to be  9 18/73

If f(x) = 5x, what is f–1(x)?
A. f–1(x) = –5x
B. f-1(x)=-1/5x
C. f-1(x)=1/5x
D. f–1(x) = 5x

Answers

To get the inverse of a function interchange
the x's with the y'x and solve for y, as follows:
y=5x-7


Interchange to get:
x=5y-7
Solve for y to get:
y=(1/5)x+(7/5)

so I think it might be c


Answer:

The answer is C.

Step-by-step explanation:

Step 1: Replace f(x) with y.

     f(x)=5x >>>>> y=5x

Step 2: Switch x and y.

     y=5x >>>>> x=5y

Step 3: Solve for y

     x=5y >>>> y= x/5

Then you have to do the inverse of dividing by 5. Which is multipilying by 1/5. This leaves you with,

      y= 1/5x

Step 4: Write in standard inverse notation (Replace y with f^-1(x))

      f^-1(x)=1/5x  

Note: These steps work with ANY problem where you have to find the inverse function. I hope this helps :)

     

What is the area of a rectangle with vertices at ​ (−6, 3) ​, ​ (−3, 6) ​ , (1, 2) , and (−2, −1) ? Enter your answer in the box. Do not round any side lengths.

Answers

You would have to find the magnitude of the sides to find out the area. 

A=(-6, 3) 
B= (-3,6) 
C= (1, 2) 
D= (-2, -1) 

A-B = √(x₁-x₂)²+(y₁-y₂)² 
=√(-6+3)²+(3-6)²
=√9+9
=√18 
=4.24

C-D=√(x₁-x₂)²+(y₁-y₂)² 
=√(1+2)²+(2+1)²
=√9+9 
=4.24 

Area= lxw 
A=√18x√18
a=18 

Hope I helped :) 

The area of the rectangle is 18 square units if the vertices at ​ (−6, 3) ​, ​ (−3, 6) ​ , (1, 2) , and (−2, −1).

What is the area of the rectangle?

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is given that:

A rectangle with vertices at a​ (−6, 3) ​, ​b (−3, 6) ​ , c(1, 2) , and d(−2, −1)"

As we know,

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

ab = √(x₁-x₂)²+(y₁-y₂)²

=√(-6+3)²+(3-6)²

= √18

cd =√(1+2)²+(2+1)²

= √18

Area= lxw

A=√18x√18

a=18

Thus, the area of the rectangle is 18 square units if the vertices at ​ (−6, 3) ​, (−3, 6) ​ , (1, 2) , and (−2, −1).

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What is the point slope form of the line with slope −1/4 that passes through the point (−2, 9) ?



y+9=−14(x−2)

y−2=−14(x+9)

y+2=−14(x−9)

y−9=−14(x+2)

Answers

y - 9 = -1/4 ( x + 2)

answer
y−9=−14(x+2) 
last one

Answer:

Step-by-step explanation:

Point slope form of the equation with point (a,b) and slope m is given by this equation

y-b=m(x-a)

Here we are given that the slope is -1/4 so m= -1/4

and the point is (-2,9) so a =-2 and b =9

Hence plugging the values in the equation we get

y-9 = -1/4 (x-(-2))

y -9 =-1/4 (x+2)

If x is an even number, the function f(x) = 2x − 1 gives an odd number. Identify the set of odd numbers corresponding to this set of even numbers: {0, 2, 4, 6, 8}.

Answers

x = {0, 2, 4, 6, 8}.

=> f(x) = 2x - 1


x                  f(x) = 2x - 1

0                   2*0 - 1 = - 1

2                   2*2 - 1 = 3

4                   2*4 - 1 = 7

6                   2*6 - 1 = 11

8                   2*8 - 1 = 15

Answer: {-1, 3, 7, 11, 15}

Jacks wild souvenirs shop is selling all shirts for $10 each and all flip flops for $5 per pair. At the end of one day jacks shirts and flip flops sales totaled $325 for $41 items. How many shirts and flip flops did jack sell?

Answers

Let x =  the number of shirts sold
Let y =  the number of pairs of flip flops sold

Because 41 items were sold, therefore
x + y = 41           (1)

Shirts sell for $10 each, and a pair of flip flops for $5 per pair (or $2.50 each). Total sales is $325.
Therefore.
10x + 5y = 325
or, divide by 5 to obtain
2x + y = 65      (2)

Subtract (1) from (2).
2x + y - (x + y) = 65 - 41
x = 24
From (1), obtain
y = 41 - x = 41 - 24 = 17

Answer:
Jack sold 24 shirts and 17 pairs (or 34) of flip flops.

When the measured number 0.0090 is multiplied by the measured number 87.10, the answer has two significant figures?

Answers

Correct.
The number 0.0090 has two significant figures in it, as we can represent the placeholder zeros (the ones between the decimal and the first 'significant' number - in this case, the 9) with a power of ten: 9.0x10^-3. Additionally, it is a measured number, meaning whatever instrument was used to measure displayed the zero in the ten thousandths place. 
The number 87.10 has four significant figures. There are no placeholder zeros between the decimal and a 'significant' number, and it is also a measurement made by an instrument which displayed a zero in the hundredths place.
When numbers are multiplied or divided, the answer should be rounded to the same number of significant figures as the value with the least number of sig figs in the calculation.
0.0090 x 87.10 = 0.7839
= 0.78  rounded to 2 sig figs
or
7.8 x 10^-1 in scientific notation

What is the exterior angle of triangle ABC

These are the points:
A=3, B=10, C=6

Answers

Based off of  what I can see in the  photo (its too blurry to know for sure) and what I think you're asking:

The angle of a triangle always adds up to 360degrees, so base it on that and the acute and obtuse  angles  and get the degrees from there, the angle would be those degrees you find or <10, 5, 4 (what I assume  is a 5)

Jake is comparing the prices of two laundry service companies . company a charges $20 per load and an additional $8 as service charges . company B charges $24 per load and an additional $4 as service charges .

part A: write equations to represent company a's and company b's total laundry charges for a certain number of loads. define the variable used in the equations

part B: which company would charge less for 5 seconds of laundry ?

part C: how much money is saved by using the services of company A instead of company B to clean 9 loads of laundry

Answers

If you meant loads instead of seconds then this is what you get:

Part A:
    A(x)= 20x+8
    B(x)= 24x+4

Part B:
    Company A. It cost $108 for 5 loads, while it cost $124 for 5 loads using company B

Part C:
   For 9 loads, you save $32 when using company A vs company B.

Which graph represents the solution set of the system of inequalities?

{3y≥x−9
3x+y>−3
WHICH ONE ?

Answers

the first graph

the solid line passes through (0,-3) and (0,9)

 dotted line passes through (0,-3) and (0,-1)

 see attached sketch

A diver descends to a location of −5014 meters relative to the surface of the water. He then descends another 1012 meters.

What is the diver’s final location relative to the surface of the water?

Enter your answer as a simplified mixed number in the box.

Answers

Its -60 3/4


Hope this helps!~

Answer: Using operations with fractions, the diver's final location is:

- 60 3/4 meters relative to the surface of the water (60 3/4 meters below the surface of the water).


Solution:

Initial location: -50 1/4 meters

He descends another 10 1/2 meters: -10 1/2 meters

Final location = Initial location - 10 1/2 meters

Final location = - 50 1/4 meters - 10 1/2 meters

Final location = - (50+10) (1/4+1/2) meters

Final location = - 60 [(1)(1)+2(1)]/4 meters

Final location = - 60 (1+2)/4 meters

Final location = - 60 3/4 meters

Θ is an acute angle and cosecant theta equals nine halves commacscθ= 9 2, find secant ((pi over 2) minus theta) .sec π 2−θ. do not use a calculator and express

Answers

?????????IM NOT SUREEEE

This writing prompts is hard

Answers

a.) Simplifying the equation would lead you to 15x^2-3x+9

b.) You know your answer is correct because you're adding the two polynomials together. 9x^2+6x^2 is 1tx^2. Now you have 2x-5x and since the negative is bigger, you get -3x. Then 5+4 is 9. You have no like terms therefore your answer is 15x^2-3x+9

Which equation can be used to find the value of b if side a measures 8.7 cm? 8.7 + b = 54.6 17.4 + b = 54.6 26.1 + b = 54.6 34.8 + b = 5

Answers

The correct equation is 8.7 + b = 54.6
because it is given that measure of side a is 8.7cm, in all other equations the values of a is different.
from the first equation we can find the value of b, that is
b = 54.6 - 8.7 = 45.9
so, value of b is 45.9cm

What is 7.4/2.5 = 16/y what is y

Answers

7.4/2.5=16/y
2.96=16/y
y·2.96=16/y·y
2.96y=16
2.96y/2.96=16/2.96
y=5.4

A local charity sponsors a 5K race to raise money. It receives $25 per race entry and $5,000 in donations, but it must spend $5 per race entry to cover the cost of the race. Write and solve an inequality to determine the number of race entries the charity needs to raise more than $25,000. Show your work!

Answers

The charity needs at least 1001 entries to raise more than $25000. Let n be the number of race entries, i be the income of the race, and c the cost of the race. The money that the 5K brings in is given by i = 25 * n + 5000 The cost is given by c = n * 5 Now if the charity needs to raise more than 25000 then the income minus the cost must be greater than 25000. 25000 < i - c subsituting for i and c 25000 < i - c = (25 * n + 5000 ) - (5 * n) simplifying results in 25000 < 25*n - 5*n + 5000 25000 < 20*n + 5000 20000 < 20*n 1000 < n The number of entries must be greater than 1000. Since entries must be an integer the charity needs at least 1001 entries.
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