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

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.

Answer:

domain [-1, ∞)

range [ -3, ∞)

Step-by-step explanation:

Answer:

5.1

Step-by-step explanation:

ik i am in the future

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.

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

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

Answer:

Step-by-step explanation:

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

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

Answer:

cost price of book is Rs. 570

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.

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

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

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

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

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

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.

Answer:

This is trapezium.

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

1/2×5(14-8)

=30/2

=15cm^2

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.

Substitute the known values into the formula.

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

Solve the exponents.

[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.

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

Answer:

4

Step-by-step explanation:

(21 + 5) : 2 = 13

(7 + 9) : 2 = 8

(36 + 2) : 2 = 19

(1 + 7) : 2 = 4

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

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.

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

Answer:

C

Step-by-step explanation:

There isn’t one

Answer:

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

Step-by-step explanation:

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

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

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

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