What is the difference quotient for the function f(x) = 8/ 4x + 1

What Is The Difference Quotient For The Function F(x) = 8/ 4x + 1

Answers

Answer 1

Answer:

Last option (counting from the top)

Step-by-step explanation:

For a given function f(x), the difference quotient is:

[tex]\frac{f(x + h) - f(x)}{h} = \frac{1}{h}*(f(x + h) - f(x))[/tex]

In this case, we have:

[tex]f(x) = \frac{8}{4x + 1}[/tex]

Then the difference quotient will be:

[tex]\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1})[/tex]

Now we should get a common denominator.

We can do that by multiplying and dividing each fraction by the denominator of the other fraction, so we will get:

[tex]\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1}) = \frac{1}{h}*(\frac{8*(4x + 1)}{(4(x + h) +1 )*(4x + 1)} - \frac{8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)})[/tex]

Now we can simplify that to get:

[tex]\frac{1}{h}*\frac{8*(4x + 1) - 8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)}} = \frac{1}{h}*\frac{-32h}{(4(x + h) +1 )*(4x + 1)}} = \frac{-32}{(4(x + h) +1 )*(4x + 1)}}[/tex]

Then the correct option is the last one (counting from the top)


Related Questions

21,5=13
7,9=8
36,2=19
1,7=?
find the value of ?​

Answers

Answer:

4

Step-by-step explanation:

(21 + 5) : 2 = 13

(7 + 9) : 2 = 8

(36 + 2) : 2 = 19

(1 + 7) : 2 = 4

She/he is right tha answer is 4

A child is picking 3 days of the 7 days of the week to have Jello for lunch. What is the size of the sample space in this experiment?

Answers

4 feet of space to figure this out

Help anyone can help me do the question,I will mark brainlest.​

Answers

Answer:

a)11cm

b)49.5cm²

Step-by-step explanation:

to find the perimeter you use the formula

o/360×2piR

since 2pi R=18pi cm,to find the radius you cancel pi from both sides 2r/2=18/2...so the radius is 9cm

therefore the perimeter will be:

70/360×2×22/7×9

27720/2520

=11cm

then to find the area you say

o/360×pi R²

70/360×22/7×9²

124740/2520

=49.5cm²

I hope this helps

Simplify the expression.

StartFraction negative 44.288 minus 31.6 over negative 3.1 (6 minus 1.2) EndFraction
–5.1
–4.21
3.42
5.1

Answers

Answer:

5.1

Step-by-step explanation:

ik i am in the future

for what value of x does 4^x=(1/8)^x+5?

Answers

Use main properties of powers

(a^m)^n=a^{m\cdot n};(am)n=am⋅n;

\dfrac{1}{a^n}=a^{-n}an1=a−n

to simplify given equation.

1.

4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.

2.

\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.

3. Then the equation is

2^{2x}=2^{-3x-15}.22x=2−3x−15.

The bases are the same, so equate the powers:

2x=-3x-15,

2x+3x=-15,

5x=-15,

x=-3.

Answer: for x=-3.

State the domain and range of the graph below:

Answers

Answer:

domain [-1, ∞)

range [ -3, ∞)

Step-by-step explanation:

help me pleaseeeee!!!


Answers

Answer: A

Step-by-step explanation:

Using the distributive property, for the denominators, you get x^2+4x-5x-20. Combining like terms, 4x-5x is -1x. So x^2-x-20. -1x is the equivalent to -x because -1*x is -x. There is only one solution with this denominator, A. So there’s no need to figure out the numerator.

HELP ME PLS ITS PYTHAGOREAN THEOREM

Answers

Answer:

82

Step-by-step explanation:

You are looking for the hypotenuse.

c = ?

a = 80

b = 18

c^2 = a^2 + b^2

c^2 = 18^2 + 80^2

c^2 = 324 + 6400

c^2 = 6724

sqrt(c^2) = sqrt(6724)

c = 82 inches

Answer:

[tex]\boxed {\boxed {\sf 82 \ inches}}[/tex]

Step-by-step explanation:

We are asked to find the length of the rake.

We know it hits the wall 80 inches above the ground and the bottom of the rake is 18 inches away from the wall. The point where the top of the rake hits the wall and the distance away from the wall are the legs that form a right angle and the rake is the hypotenuse.

We want to find the hypotenuse or the length of the rake. We will use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

In this theorem, a and b are the legs and c is the hypotenuse.

The length of the legs are 80 inches (distance from ground to top of rake)  and 18 inches (distance from wall to bottom of rake). The hypotenuse is unknown.

a= 80 in b= 18 in

Substitute the known values into the formula.

[tex](80 \ in)^2+(18 \ in)^2= c^2[/tex]

Solve the exponents.

(80 in)²= 80 in*80 in= 6400 in²(18 in)²= 324 in²

[tex]6400 \ in^2+ 324 \ in^2= c^2[/tex]

Add.

[tex]6724 \ in^2=c^2[/tex]

We are solving for c, the hypotenuse, so we must isolate the variable. It is being squared. The inverse of a square is a square root, so we take the square root of both sides.

[tex]\sqrt {6724 \ in^2}= \sqrt{c^2}[/tex]

[tex]\sqrt{6724 \ in^2}=c[/tex]

[tex]82 \ in =c[/tex]

The length of the rake is 82 inches.

which algebraic expression represents this word description the quotient of six and the sum of a number and eight

Answers

6/x+8

Step by step explanation: Quotient means that you are dividing one term by another, so from this expression you would get that 6 is being divided by x (unknown variable) + 8

cos²x-√3sinxcosx = 0

Answers

Answer:

x= п/2+пn; nE Z    

x= п/6+пn; nEZ

Step-by-step explanation:

(cosx)^2- √3sinxcosx=0

Factorise it

cosx(cosx-√3sinx)=0

cosx=0                     or                      cosx=√3sinx

x= п/2+пn; nE Z                                 cosx/cosx= √3sinx/cosx

                                                          1/√3= tgx

                                                           x= arctg 1/√3+пn; nE Z

                                                            x= п/6+пn; nEZ

The answer is x= п/2+пn; nE Z    

x= п/6+пn; nEZ

If the lines 5x + 3my – 2 = 0 and 3x + 7y + 1 = 0 are parallel, then what is the value of m?

(a)9/35

(b)35/9

(c)9/5

(d)5/9

Please give full explanation!!!
ASAP!!​

Answers

Answer:

35/9

Step-by-step explanation:

7y=-3x-1

y=-3/7x-1/7

m=-3/7

Now,

3my=-5x+2

y=-5/3mx+2/3

So

-3/7=-5/3m

-9m=-35

m=35/9

Answer:

35/9

Step-by-step explanation:

What we need to know:

Parallel lines have the same slope

slope intercept form: y = mx + b

m = slope

The first thing we will want to do is put both equations in slope intercept form.

We must do this so we can identify the slope.

First equation:

3x + 7y + 1 = 0

Solve for y

Subtract 1 from both sides

3x + 7y + 1 - 1 = 0 - 1.

3x + 7y = -1

Subtract 3x from both sides

3x - 3x + 7y = -1 - 3x

7y = -3x - 1

Divide both sides by 7

7y/7 = (-3x - 1)/7

y = -3/7x - 1/7

So the equation of the first line is y = -3/7x - 1/7

Second equation:

5x + 3my – 2 = 0

Solve for y

Subtract 5x from both sides

5x - 5x + 3my - 2 = 0 - 5x

3my - 2 = -5x

Add 2 to both sides

3my - 2 + 2 = -5x + 2

3my = -5x + 2

Divide both sides by 3m

3my/3m = (-5x + 2)/3m

y = -5x/3m + 2/3m

So the equation of the second line is y = -5x/3m + 2/3m

So we have the two equations:

y = -3/7x - 1/7 and y = -5x/3m + 2/3m and we want to find the value of m if the two lines are parallel

Lines that are parallel have similar slopes

So the slope of the first equation should be the same as the slope of the second equation

The slope of y = -3/7x - 1/7 is -3/7 as it takes the spot of "m" in y = mx + b.

The slope of y = -5x/3m + 2/3m is -5/3m as it takes the spot of "m"

If the slopes of parallel lines must be similar than -3/7 = -5/3m

(Note that we've just created an equation that we can use to solve for m)

We now solve for m

-3/7 = -5/3m

Cross multiply

3*-3m = -9m

7*-5=-35

we acquire -35 = -9m

Divide both sides by -9

-35/-9 = 35/9

-9m/-9=

We're left with m = 35/9

So we can conclude that the value of m would be 35/9 if the two lines are parallel

the Marked price of a book is rupees 500 if 30% discount is all over there in a loss of rupees hundred is made what is the cost price of the book​

Answers

Answer:

cost price of book is Rs. 570

Find the value of b.

A. 57
B. 123
C. 50
D. 61.5

Answers

Answer:

please i need educere answers

Step-by-step explanation:

i have one day left and i cannot finish please reply with any way to contact you

HELPPP!!
Rate the following bank accounts from most to least liquid: CD, savings account, checking account, money market
account
a. CD, savings account, checking account, money market account
b. Savings account, checking account, CD, money market account
C. CD, money market account, savings account, checking account
d. Checking account, savings account, money market account, CD
Please select the best answer from the choices provided
OA
OB
О С
OD

Answers

Answer:

C

Step-by-step explanation:

There isn’t one

Use the diagram. Solve for p.

Answers

Answer:

A the first one.

Step-by-step explanation:

Wy = 28

WX = 12

XY = WY - WZ

XY = 28 - 12

XY = 16

4P = 16

P = 16/4

P = 4

Guided Practice


A recursive formula for a geometric sequence is given. What is an explicit formula for this sequence?

a1=100an=12 · an−1a subscript 1 baseline equals 100 line break a subscript n baseline equals one-half times a subscript n minus 1 baseline


A.
an=12 · 100n−1a subscript n baseline equals one half times 100 superscript n minus 1 baseline


B.
an=100 · (12)n−1a subscript n baseline equals 100 times left parenthesis one half right parenthesis superscript n minus 1 baseline


C.
an=100+(12)n−1a subscript n baseline equals 100 plus left parenthesis one half right parenthesis superscript n minus 1 baseline

Answers

Answer: The Answer IS Either Letter B Or Letter C

B.

an=100 · (12)n−1a subscript n baseline equals 100 times left parenthesis one half right parenthesis superscript n minus 1 baseline

Step-by-step explanation: I Think The Answer IS Letter B

Simplify the matrix.

a = 100 ,

a n = 12 a n − a ,

1 ,

100 ,

n , − h a l f ,

n ,

1

...............................................................................................................................................

whats the figures and how do I find the area?​

Answers

Answer:

This is trapezium.

Area of this figure =1/2h(d1-d2)

1/2×5(14-8)

=30/2

=15cm^2

using trig to solve for missing angle

Answers

Answer:

x = 14.0902 (After rounding to the nearest ten-thousandth)

Step-by-step explanation:

Using the bottom angle to solve x, the best option to use would be sine as we have the length for the opposite leg. Then we do the following:

Sin(69) = Opp/Hyp

Sin(69) = 14/x

0.9336 = 14/x

0.9336(x) = 14/x(x)

0.9336x = 14

0.9336x/0.9336 = 14/0.9936

x = 14.0902

Complete the equation: x2 + 10x +__= (__)^2

Answers

Answer:

x2 + 10x +25 = (x+5)^2

Step-by-step explanation:

x^2 + 10x

To complete the square

Take the coefficient of x

10

Divide by 2

10/2 =5

Square it

5^2 =25

Add it

x2 + 10x +25

The coefficient of x divided by 2 is the factor we add to x inside the square

(x+5)^2

Answer:

25 should go in the blank.

Step-by-step explanation:

You can factor and get (x + 5)^2, a perfect square trinomial when put into standard form.

Please help me anyone

Answers

Answer:

Quelles caractéristiques ces mots ont-ils en commun ? Cliquez sur tout ce qui s'applique.

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]

Step-by-step explanation:

What is the length of leg s of the triangle below?
90°
45
6
172
45
O
A. 72
B. 5
C. 3
O O O O a
D. 6
E. 3.2
F. 36

Answers

Answer:

6

Step-by-step explanation:

It's a 45-45-90 triangle, it has two similar sides, since it has two similar angles, which are both 45°

so, side = s = 6

Answered by GAUTHMATH

The length of the leg s of the triangle below is 6.

Option D is the correct answer.

What is the Pythagorean theorem?

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Applying the Pythagorean theorem in the triangle.

√72² = s² + 6²

72 = s² + 36

s² = 72 - 36

s² = 36

s = √36

s = 6

We can also say that,

Opposite angles of equal sides are equal

So,

s = 6.

Thus,

The length of the leg s of the triangle below is 6.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ7

Each side of a pentagon is 10 cm greater than the previous side. If the perimeter of this pentagon is 500 cm, find the lengths of the sides.

Answers

Answer:

(I'll leave cm out to save space and time in the answer)

the perimeter is 500, there are 5 sides. so on average a side will be 100.

that's already the important key idea.

it's indeed 100 for the third side, the second will be 10 less, the fourth 10 more (making the 2and and the 4th side 200 in sum, and therefore still 100 on average).

repeat this for the 1. and 5. side and we get:

80

90

100

110

120

Eldrick manages wildlife samples for Ducks Unlimited. Two samples of duck populations at a migratory site are shown
in the table below. Which statement about the samples is true?
Duck Pond Samples
Sample 1
Mallard
Wood Duck
Green Wing Teal
American Widgeon
21
4
9
6
Sample 2
Mallard
Wood Duck
Green Wing Teal
American Widgeon
8
17
15
0
Eldrick can use both of these samples to find the mean frequency of each duck.
Eldrick should take another sample because there is too much variability in the two samples.
Eldrick should use only the first sample to find the mean frequency of each duck.
Eldrick should use only the second sample to find the mean frequency of each duck.

Answers

Answer:

Eldrick can use both of these samples to find the mean frequency of each duck.

Step-by-step explanation:

Given

See attachment for samples

Required

Determine which is true

Reading through the options, we can see that Eldrick needs to evaluate the mean frequency of both samples.

To do this, both samples have to be put into consideration in order to arrive at the right value.

Considering the options, we can conclude that (a) is correct.

Answer:

B

Step-by-step explanation:

the answer is B cause I did A and it was wrong trust me, and have a good day

One-third of a number when subtracted from double of itself is equal to 10. Find the number.

2x−x3=10

X=?

Answers

Answer:

number is 6

Step-by-step explanation:

let the number be x , then double the number is 2x and

2x - [tex]\frac{1}{3}[/tex] x = 10 ( multiply through by 3 to clear the fraction )

6x - x = 30

5x = 30 ( divide both sides by 5 )

x = 6

That is the number is 6

A triangle, where the two angles are 30° and 90°, what are the remaining angles

Answers

Answer:

60⁰

Step-by-step explanation:

A triangle has three angles.

The sum of its angles = 180⁰

[ By angle sum property ]

Let the unknown angle be 'x'

Then,

30⁰ + 90⁰ + x = 180⁰

120⁰ + x = 180⁰

x = 180⁰ - 120⁰

x = 60⁰

Therefore, the unknown angle will be equal to 60⁰

60° because 90°+ 30°= 120°and 180°-120°=60°

juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x)=10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container.

Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?

0.8 units
1.3 units
8.2 units
9.8 units

Answers

Answer:

8.2 units

Step-by-step explanation:

For radioactive decay, the amount should decrease over time. Given the function:

f(x) = 10(0.98[tex])^{x}[/tex]

We substitute the time of x = 10 hours:

f(10) =  10(0.98[tex])^{10}[/tex]

f(10) = 8.17

Round 8.17 to 8.2.

Therefore 8.2 units will remain after 10 hours.

He’s correct ^^ its 8.2 units

Decide which kind of change(s) is/are illustrated in each equation
(meaning changed from "regular" y=sinx or y=cosx)
→ Note: more than once choice may be circled per question.

Answers

Phase shift and period change

Rewriting the equation:

y = cos ( 2 ( x - 2 ) )

Phase shift 2 units to the right

Period changed to 2pi/2 = pi

Need helppppp asappppppp

Answers

Answer:

Step-by-step explanation:

Select the correct answer.

Which inequality represents all the solutions of 10(3x + 2) > 7(2x − 4)?

A.
x > -4
B.
x < -4
C.
x > -3
D.
x < -3

Answers

Answer:

C

Step-by-step explanation:

Given

10(3x + 2) > 7(2x - 4) ← distribute parenthesis on both sides

30x + 20 > 14x - 28 ( subtract 14x from both sides )

16x + 20 > - 28 ( subtract 20 from both sides )

16x > - 48 ( divide both sides by 16 )

x > - 3 → C

Can someone please help me with these work rate questions!

Answers

Answer:

1/8 rooms per hour

Step-by-step explanation:

We are given that Beatrice can wallpaper 1 room in 8 hours. The work rate is how many rooms Beatrice can wallpaper in one unit of time (in this case, one hour).

Another way of saying 1 room in 8 hours is 1 room/8 hours. We want to find the rate over one hour, so we want to make the denominator ( in hours) equal to 0.

With fractions, we can divide/multiply both the numerator and denominator by the same amount, and still keep the fraction. Therefore, we want to make 8 hours 1 hour by multiplication or division. Since anything divided by itself is equal to 1, we can say that 8/8 is equal to 1. Therefore, we can divide both the numerator and denominator by 8 to get

(1 room/8) = (8 hours / 8)

= (1/8 rooms) / 1 hour

Therefore, the work rate is 1/8 rooms per hour

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