Apply the distributive property to simplify the expression


8(12x – 20)

The natural logarithms of the given questions are f(e⁴) = 4, f(e ㏑ 5) = 5, and f(e³ ㏑ 5) = -0.5108.

What is the natural logarithm?

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Given,

f(x) = ln x,

a) f(e⁴)

f(e⁴) = In(e⁴)

= 4In(e)

= 4 * 1

f(e⁴) = 4

b) f(e ㏑ 5)

= f(e⁻⁵)

= [tex]f(e^{\frac{1}{5} })[/tex]

= In(1) - In(e⁵)

= 0 - 5In(e)

= 5*1

f(e ㏑ 5) = 5

c) f(e³ ㏑ 5)

[tex]= f(e^{\frac{3}{5} })[/tex]

=  In(3) - In(e⁵)

= ln(3) - ln(5)

f(e³ ㏑ 5) = -0.5108

Hence, The natural logarithms of the given questions are f(e⁴) = 4, f(e ㏑ 5) = 5, and f(e³ ㏑ 5) = -0.5108.

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11) (Level 2):

I believe if you just multiply the shaded area (10x6), then maybe subtract the non-shaded area (20cm and 10 cm). After doing this process, I believe you will get: 200-60 = 140! (But then again I could be wrong, I’ll admit it I’m not a pro but at least I gave effort!)

Fraction: 14/10

Decimal: 1.4

Percent: 140%

12) (Level 3):

I have absolutely no idea about this question and I don’t want to guess! Sorry!

Answer:

A peace sign has one line of symmetry.

The one line is up and down in the center.

Hope this helps! :D

Step-by-step explanation:

Answer:

B. y > 4x + 2

Step-by-step explanation:

The area of the graph above the dotted line is shaded; therefore, this inequality is greater than. The dotted line's slope is 4, hence x is multiplied by 4, and its y-intercept is at 2, hence + 2 on the right side.

Step-by-step explanation:

Firstly we determine how many people clara will reach in 40 phone calls.

6 people=12 calls

X people=40 calls.

make X the subject of the formula.

X=(6×40)÷12=20

So clara will reach 20 people in 40 phone calls.

Now lets determine how many people Toby will reach in 40 phone calls.

7 people=13 calls

Y people=40 calls.

Therefore making Y the subject of the formula we have,

Y=(7×40)÷13=21 people.

So toby will reach more people in 40 calls

Answer:

t = 60

t/4+5=20

Step 1:

multiply both sides of equation by 4 to separate t from the fraction t/4.

t + 20 = 80

Step 2:

Subtract 20 from both sides of the equation ( you have to put constant values on the same side)

t= 80 - 20

Step 3:

Do the math

80-20=60 so t=60

Step-by-step explanation:

hope this helps! please give brainiest ^^^

Answer:

He saved $121

Step-by-step explanation:

All you have to do is divide $726/6 which gives you $121.

Answer:

P= 8

Step-by-step explanation:

-1 (-2p = -3p + 8)

2p = 3p - 8

-p = -8

p = 8

to check this...

-2(8) = -3(8) + 8

-16 = -24 + 8

-16 = -16

The answer you are looking for would be 44.

Here,

The number lies between 41 and 46 are 42, 43, 44, and 45

From the straightforward observation and according to the condition that must be divisible by 2 and 11 there is only one number that is divisible by both 2 and 11 is 44.

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I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer: f^-1(x)=(3x-2)/4

Step-by-step explanation:

1. Change the x and y

y=(4x+2)/3 → x=(4y+2)/3

2. Swap sides (optional)

x=(4y+2)/3 → (4y+2)/3=x

3. Multiply the equation by 3 on both sides

(4y+2)/3=x → (3)*(4y+2)/3=x*(3)

4. Subtract 2 from both sides

(3)*(4y+2)/3=x*(3) → 4y=3x-2

5. Divide 4 from both sides

4y=3x-2 → y=(3x-2)/4

6 Substitute f^-1(x) for y

y=(3x-2)/4 → f^-1(3x-2)/4

Answer:

11

Step-by-step explanation:

If it is correct, could you please give me brainliest? I would really appreciate it! Thank you!

Answer:

8.35

A company orders 25 boxed lunches from a deli for $208.75

Given:

[tex]25\\208.75[/tex]

We need to find the cost.

Therefore, we need to work on the numbers we are given:

Therefore, the unit cost is 8.35

The Maclaurin series of sin(3x²) up to n = 3 is

[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]

The function is given in the question as

g(x) = sin(3x²)

Taylor (Maclaurin) series of sin(3x²) up to n = 3

A Maclaurin series is given by f(x),

[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]

[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]

We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.

f⁽⁰⁾(x) = f(x) =sin(3x²)

Evaluate the function at the point: f(0)=0

1st derivative: f(1)(x)=(sin(3x²))′ = 6xcos(3x²)

1st derivative at the given point: (f(0))′=1

2nd derivative: f(2)(x)=(f(1)(x))′=(6xcos(3x²))′=−36x2sin(3x2)+6cos(3x²)  

Evaluate the 2nd derivative at the given point: (f(0))′′=6

3rd derivative: f(3)(x)=(f(2)(x))′=(6xcos(3x²))′=−36x2sin(3x²)+6cos(3x²)  

Evaluate the 3rd derivative at the given point: (f(0))′′′=0

Now, use the calculated values to get a polynomial:

[tex]g(x)=0+\frac{0}{1!}x+\frac{6}{2!}x^2+\frac{0}{3!}x^3+\frac{0}{4!}x^4+\frac{0}{5!}x^5[/tex]

Thus, the Maclaurin series of sin(3x²) up to n = 3 is

[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]

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As per the question, the solution to the equation f(x) = a(x-h)2+k is y = 3(x+5)2 -1.

Equations are mathematical expressions with two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be similar to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a simple fundamental equation.

As per the given values mentioned in the question,

a=3, b=30, c=74.

To fix this issue, employ the Vertex Formula,

(-b/(2a)) , f(-b/(2a))

-b/(2a)

= -(30)/(2 × 3)

h = -5.

f(-b/(2a))

= 3(-5)² + 30(-5) + 74

k = 75 +-150 +74

k = -1.

Vertex, V = (h,k)

V = (-5,-1).

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The table of values that could be used to graph g(x), a reflection of f(x) across the x-axis is table (c)

From the question, we have the following equation that can be used in our computation:

f(x) = One-third(6)x

When this statement is represented as an equation, we have the following representation

f(x)= 1/3(6)ˣ

The transformation is given as

A reflection of f(x) across the x-axis

This means that

g(x) = -f(x)

So, we have

g(x) = -1/3(6)ˣ

What this means is that the values of f(x) are negated to get g(x)

The table that represents this is table (c)

Hence, the table of values is table (c)

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Answer: C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

I think the Answer choice = C

Step-by-step explanation:

The extra amount that the store would have to pay for buying 2 hardcover and 4 paperback books instead of her original plan is $1.51

The paper back books have a discount of 25%

hence we what would be paid for in such category would be 1 - 25% charge = 75 %

price of hardcover = 17.95

price of paperback = 9.95 dollars

Isa bought 2 hardcover and 4 paper back

we are to find the cost of these items

2 x 17.95 + (4 x 9.95 x 75%)

= 35.9 + 29.85

= 65.75

We have to find the cost of the initial plan of  2 hardcover and 3 paperback books.

2 x 17.95 + 3 x 9.95 x 0.75

35.9 + 22.3875

= 58.29

This is less than 59 dollars, she would have to pay the shipping fee.

58.29 +  $5.95

= 64.23

The extra amount that she has had to pay for going with  2 hardcover and 4 paperback books is:

65.75 - 64.23

= 1.51 dollars

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Using the given function, the income for day 31 is

the total Income for working 31 days is

Using the given function an = a1 (r)^n-1

where

a1 = first day = 1

r = common ratio = 2

The income on day 31, n = 31

= 1 * 2^(31 - 1)

= 2^30

= 1,073,741,824 cents

= $10,737,418.24

Total Income for working 31 days n = 31

Using Sn= a1 (1-r^n) / 1 - r

Sn = (1 * (1 - 2^31)) / (1 - 2)

Sn = (1 - 2^31)) / - 1

Sn = (1 - 2147483648) /-1

Sn = 2147483647

Sn = 2,147,483,647 cents

Sn = $21 474 836.47

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The predicted number of coffee sales, in hundreds of dollars, for an average daily temperature of 32 degrees is of:

63.34.

The definition of the line of best fit in this problem is given as follows:

y = -0.68x + 85.1.

The variables in the context of this problem are defined as follows:

Hence, for an average daily temperature of 32 degrees, the estimate of the number of coffee sales is given as follows:

y = -0.68(32) + 85.1 = 63.34 thousand dollars.

The problem is incomplete and is given by the image at the end of the answer.

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The largest possible area will be 14400 meters², the pen's length should be 120 meters, and the width should be 120 meters.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

Let's assume that the length of the pen would be x.

We have been given the perimeter as 480 meters.

Let w be the width of the rectangle  and l be the length of the rectangle

The perimeter of a rectangle = 2(l+w)

So, 480= 2(x + w)

240 = x + w

w = 240 - x

Length = x and width = (240 – x)

Area = x(240 - x) = 240x - x²

To get the maximum area, we equate the first derivative of the area to zero.

A = 240x - x²dA/dx = 240 - 2x = 0

2x = 240

x = 120

So, width = 240 – x = 240 – 120 = 120.

Maximum area = length × width

Maximum area = 120 × 120 = 14400 meters²

Thus, the pen should be 120 meters long and 120 meters wide, with a maximum possible area of 14400 meters².

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Answer:

Step-by-step explanation:

10 = 2(x - 2)

How would I solve for X?

10 = 2(x - 2)

10 = 2x - 4

14 = 2x

x = 7

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

check

10 = 2(7 - 2)

10 = 2 x 5

10 = 10

the answer is good

Answer:

x=7

Step-by-step explanation:

Given:

A linear equation is given as:

[tex]10=2(x-2)[/tex]

To Find:

The objective is to solve the equation and find the value of x.

Explanation:

[tex]10=2(x-2)\\[/tex]

⇒ [tex]\frac{10}{2}=x-2[/tex]

⇒[tex]5=x-2[/tex]

⇒ [tex]x=7[/tex]

Final Answer :

The value of x is 7.

Answer:

D x = 3 y = 4

(3.4)

Step-by-step explanation:

See below

Answer:

$4.84 per pound

Step-by-step explanation:

divide 12.10 by 2.5 and you get 4.84, which is the price per pound

Answer:

12.1 × 2.5 = 30.25

Step-by-step explanation:

12.1 × 2.5

12.1 has 1 decimal place

2.5 has 1 decimal place

Therefore, the answer has 2 decimal places

= 30.25

Answer:

Step-by-step explanation:

30,248.35

The amount you have after 18 months is $ 1143.96 .

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

[tex]A=P {(1 +\frac{r}{n})^{nt} }[/tex]

Given:

P = 1000 , r in decimal  = 0.09 ,

n = 12 ,  t = 1.5 ( 18 months = one and a half years).

Substituting the values into the formula:

A = 1000 ( 1 + 0.09/ 12 ) ^[12 ( 1.5 )]          

  ≈ 1000 ( 1.143960 )          

  = 1143.960

Rounding to the nearest cent, we get $ 1143.96 .

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Answer: 47

Step-by-step explanation: Let's call the number of chairs Liam has x. We can set up the following equations to represent the problem:

7r = x - 5

5r = x - 17

Where r is the length of each row.

To solve for x, we can set the two equations equal to each other:

7r = x - 5

5r = x - 17

Then we can solve for x by combining like terms and solving for the value of x:

7r - 5r = x - 5 - x + 17

2r = 12

r = 6

We can substitute the value of r back into either of the original equations to solve for x:

7r = x - 5

7 * 6 = x - 5

x = 47

Therefore, Liam has 47 chairs.

well, the decrease is really 30000 - 24500 = 5500.

now, if we take the 30000 to be the 100%, what is 5500 off of it in percentage?

[tex]\begin{array}{ccll} a&b\\ \cline{1-2} 30000 & 100\\ 5500& x \end{array} \implies \cfrac{30000}{5500}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 60 }{ 11 } ~~=~~ \cfrac{ 100 }{ x }\implies 60x=1100\implies x=\cfrac{1100}{60}\implies x=\cfrac{55}{3}\implies x=18\frac{1}{3}[/tex]