charles had a sheet cake for his birthday when 9/12 remained charles took 1/3 of the remaining cake to wrap and save for later what fraction of the original cake did he wrap

Answer:

[tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]

Step-by-step explanation:

Because x=1 and x=4 are the solutions to x-1=0 and x-4=0, then we have (x-1)(x-4) in the denominator.

Because (-1,0) and (-6,0) are the solutions to x+1=0 and x+6=0, then we have (x+1)(x+6) in the numerator.

Now we have [tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex] where we plug in (0,8) to solve for a:

[tex]y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}[/tex]

[tex]8=\frac{a(0+1)(0+6)}{(0-1)(0-4)}[/tex]

[tex]8=\frac{6a}{4}[/tex]

[tex]32=6a[/tex]

[tex]\frac{32}{6}=a[/tex]

[tex]\frac{16}{3}=a[/tex]

Therefore, the equation for the rational function is [tex]y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}[/tex]

[tex]\text{Given that,}\\\\\\f(x) = \ln(x^4 +e^{2x})\\\\\\f'(x) = \dfrac{1}{x^4 + e^{2x}} \left(4x^3+2e^{2x}\right) = \dfrac{2(2x^3+e^{2x})}{x^4 + e^{2x}}~~~~;[\text{Chain rule}]\\\\\\\text{Note:}\\\\\dfrac{d}{dx} \ln x = \dfrac 1x\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} e^{mx} = m e^{mx}[/tex]

After solving the given equation, the value obtained is equal to [tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex].

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given data in the question,

f(x) = ln (x⁴ + e²ˣ)

[tex]f'(x)=\frac{1}{x^4+e^2^x}(4x^3+2e^2^x)[/tex]

Now, use the chain rule,

[tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex]

Also, note some points,

d/dx ln (x) = 1/x

[tex]\frac{d}{dx}x^n=nx^n^-^1[/tex]

To know more about Expression:

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Answer:

6:4:3

Step-by-step explanation:

each can be divided by 7

Answer:

6 4 3

Step-by-step explanation:

[tex]x+x(2x)=x+2x^2\\\\\text{when x =2}\\\\2+ 2(2)^2 = 2+ 2(4) = 2+ 8 = 10[/tex]

[tex]\text{So, the answer is (a).}[/tex]

Answer:

if i correct pls comment I think it is 33

Δ PQR has: PM is a median

so: MR = QM = 3 cm

ANSWER: MR = 3 cm

Ok done. Thank to me :>

It would take 70 years for the deer population to reach 800.

An exponential function is in the form:

y = abˣ

where b is the multiplier, y, x are variables and a is the initial value.

Let y represent the population and x represent the time in years.

a = 200, b = 100% + 2% = 102% = 1.02

y = 200(1.02)ˣ

For a population of 800:

800 = 200(1.02)ˣ

ln(4) = xln(1.02)

x = 70 years

It would take 70 years for the deer population to reach 800.

Find out more on exponential function at: brainly.com/question/2456547

Answer: 200, 0.02, and 800

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

all angles add up to 180*, 180-90=90, 90=3x, 30=x

Answer:

x = 30

Step-by-step explanation:

One side is 90 so the other two sides have to add up to 90 too because a triangles' angles have to add up to 180.

So, we can write that 2x + x = 90

Then we can solve for x:

2x + x = 90

3x = 90

x = 30

Answer:

36n + 18

Step-by-step explanation:

6 * 6n = 36n

6 * 3 = 18

36n + 18 = 36n + 18

Answer:

36n+18

Step-by-step explanation:

6(6n+3)

(6×6n)+(6×3)

36n+18

But if you want it simplifed, you can divide both 36n and 18 by 18 and you will be left with 2n+1

Answer:

-1.5

Step-by-step explanation:

Answer:

1. 1[tex]\frac{1}{2}[/tex]

2. 1[tex]\frac{3}{10}[/tex]

3. [tex]\frac{1}{3}[/tex]

4. 1[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

I hope this helps!!

Answer:

It does not matter, since, from your second case, [tex]5\sqrt5 +11 = 11+5\sqrt5[/tex].

In general is a matter of personal preference but in general I like to start with a positive number (I like [tex]\sqrt2 -1[/tex] more than [tex]-1+\sqrt2[/tex] since if there's an equal sign before I'm guaranteed to have the two signs mesh together in a few steps).

If everything you are adding together is positive, I just go first come first served and pick a new term in order it appears in the previous passage.

Answer:ITS THE SECOND ONE

Step-by-step

Answer: yes they are

Step-by-step explanation:

Step-by-step explanation:

1 _21:00_ , _22:10_, 1:10

2. 1:20

3. 18:00

4. 21:35

1. 21:00, 22:10, 1 hr and 10 minutes

2. 20 minutes

3. 18:40

4. 21:35

Answer:

linear

Step-by-step explanation:

Answer:

350

Step-by-step explanation:

Write out the equation

d + d + 70 + d + 154 = 1274

Simplify

3d + 224 = 1274

Solve

3d = 1050

d = 1050 / 3

d = 350

Answer:

350

No probelm

Answer: The answer is Iπ + √17|.

Answer:

D

Step-by-step explanation:

Cosine is adjacent / hypotenuse, so 12/13

Answer:

see the attachment

a) The highest common factor and the least common multiple are 12 and 48, respectively.

b) The highest common factor and the least common multiple are 12 and 72, respectively.

c) The highest common factor and the least common multiple are 8 and 160, respectively.

d) The highest common factor and the least common multiple are 12 and 48, respectively.

e) The highest common factor and the least common multiple are 14 and 840, respectively.

In this question we must determine the highest common factor and the least common multiple of two integers.

The highest common factor consists in the maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.

Now, we proceed to determine the numbers for each case:

First, we factorize each integer:

[tex]12 = 2^{2}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex]

Then the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{4}\times 3 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]

First, we factorize each integer:

[tex]24 = 2^{3}\times 3[/tex], [tex]36 = 2^{2}\times 3^{2}[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{3}\times 3^{2} = 72[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 72, respectively. [tex]\blacksquare[/tex]

First, we factorize each integer:

[tex]32 = 2^{5}[/tex], [tex]40 = 2^{3}\times 5[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{5}\times 5 = 160[/tex], [tex]HCF = 2^{3} = 8[/tex]

The highest common factor and the least common multiple are 8 and 160, respectively. [tex]\blacksquare[/tex]

First, we factorize each integer:

[tex]24 = 2^{3}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex], [tex]60 = 2^{2}\times 3 \times 5[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{4}\times 3 \times 5 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]

First, we factorize each integer:

[tex]42 = 2\times 3 \times 7[/tex], [tex]56 = 2^{3}\times 7[/tex], [tex]70 = 2\times 5\times 7[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{3} \times 3 \times 5 \times 7 = 840[/tex], [tex]HCF = 2\times 7 = 14[/tex]

The highest common factor and the least common multiple are 14 and 840, respectively. [tex]\blacksquare[/tex]

To learn more on prime numbers, we kindly invite to check this verified question: https://brainly.com/question/4184435

Answer:

The number 9490 is called the numerator or dividend, and the number 5 is called the denominator or divisor.

The quotient of 9490 and 5, the ratio of 9490 and 5, as well as the fraction of 9490 and 5 all mean (almost) the same:

9490 divided by 5, often written as 9490/5.

Read on to find the result of 9490 divided by 5 in decimal notation, along with its properties.

Answer:

17

Step-by-step explanation:

Let the smaller number = x

Let the larger number = y

y = 2x + 8

y - x = 25                Add x to both sides

y = x + 25               Substitute this into the first equation

x + 25 = 2x + 8       Subtract 8 from both sides

x + 25 - 8 = 2x        Combine

x + 17 = 2x               Subtract x from both sides.

17 = 2x - x                Combine

17 = x

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(3-1)^2+(-4-1)^2}\implies d=\sqrt{2^2+(-5)^2}\implies d = \sqrt{29}[/tex]

Answer:

Solve for n

n=log5  (− 2 /y  −20x−5),y<−40x−10

Step-by-step explanation:

Answer:

yes this right cuz ye or nah?

Step-by-step explanation:

yes cuz 0 1 2 3 4 5 6 7 8 9 are the numbers

Answer: [?] is 6

Step-by-step explanation:

x=5

so, 2x=10

10-4 is 6