100 divided by 16.4 as a fraction

[tex]\ln(5-x) = \ln 5 - \ln x\\\\\implies \ln(5-x) + \ln x = \ln 5\\\\\implies \ln[(5-x)x] =\ln 5\\\\\implies \ln(5x -x^2) = \ln 5\\\\\implies 5x -x^2 = 5\\\\\implies x^2 -5x +5 =0\\\\\implies x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 5}}{2(1)}\\\\\implies x = \dfrac{5 \pm \sqrt{5}}{2}\\\\\text{Hence} ~x = \dfrac 12\left(5 + \sqrt 5\right)=3.62~~ \text{and}~~ x =\dfrac 12 \left(5-\sqrt 5\right) =1.38[/tex]

Answer:

x1 = 3.618, x2 = 1.382

Step-by-step explanation:

ln(5-x) = ln5 - lnx

ln(5-x) + ln(x) = ln5

ln(5x-x^2) = ln5

5x-x^2=5

0=x^2-5x+5

x = -(-5)±√((-5)²-4(1)(5)) / 2(1)

x = 5±√(25-20) / 2

x = 5±√5 / 2

x1 = 3.618, x2 = 1.382

13in will be the longest like before .

Refer to the attachment for more observation.

The length of the longest side of the triangle after the rotation is 13 inches.

It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

Ancient geometry defined a right angle as the intersection of two straight, or right, lines in relation to dimensional axes.

Given:

A right triangle has side lengths of 5 inches, 12 inches, and 13 inches.

As, we know that the longest side is the Hypotenuse which is 13 inches and the base is 12 inches and perpendicular is 5 inches.

After 180° rotation only the base and perpendicular change the longest side still remain the same.

Learn more about Right Angle here:

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#SPJ2

Answer:

y=1/2x-8

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-4))/(6-8)

m=(-5+4)/-2

m=-1/-2

m=1/2

y-y1=m(x-x1)

y-(-4)=1/2(x-8)

y+4=1/2(x-8)

y=1/2x-8/2-4

y=1/2x-4-4

y=1/2x-8

Answer:

7.2q + 14.64

Step-by-step explanation:

Distribute 2.4 to what is inside of the parentheses and you will find this answer.

I hope this helps!!

Answer:

7.2q + 14.64

Step-by-step explanation:

The type of savings is the saving of uniform amount with interest applied to the sum of the amount in the account.

Reasons:

The amount saved per month = $150

Amount saved per year, A = 12 × $150 = $1,800

The interest rate on the account, i = 5%

The amount, F, in the account after 15 years is given as follows;

The uniform series compound amount factor formula is presented as follows;

[tex]\displaystyle F = \mathbf{\frac{A \cdot \left[ \left(1 + i \right)^n - 1 \right]}{i}}[/tex]

Therefore;

[tex]\displaystyle F = \frac{1,800 \times \left[ \left(1 + 0.05 \right)^{15} - 1 \right]}{0.05} \approx \mathbf{38,841.4}[/tex]

The amount the account is worth after 15 years to the nearest cent is approximately $38,841.4.

Learn more about compound interest here:

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Answer:

Associative Property of Addition

Step-by-step explanation:

Associative Property of Addition - if the grouping changes, the answer will be the same - Correct (2 + 3) + 5 = 2 + (3 + 5)

Identity Property of Addition - anything added by 0 will equal itself (5 + 0 = 0, 2.3 + 0 = 2.3, etc.)

Commutative Property of Addition - if the order changes, the answer will be the same (2 + 3 = 5 and 3 + 2 = 5 also)

Distributive Property of Addition - allows you to "distribute" a number (2(3 + 5) = 2 * 3 + 2 * 5 = 6 + 10 = 16)

Answer

Step-by-step explanation:

Answer:

$112.50

Step-by-step explanation:

1.5% = 0.015

$2500 × 0.015 × 3 = $112.50

Answer:

The equation of this line is y = -3x + 7

Step-by-step explanation:

Remember that when writing an equation for a graphed linear line, we must write it in slope intercept form (y=mx+b). The m represents the slope, and the b represents the y-intercept.

(The slope determines the direction in which the line goes, and is written as rise/run.)

In this case the slope is going to be negative, since the line is going downwards to the right. Additionally the slope of this line is -3/1 or just -3.

(The y-intercept is the point in which the line crosses the y-axis.)

In this case, since the line crosses the y-axis at positive 7, the y-intercept will be 7.

So all together we have y = -3x + 7.

Hope this helps you :)

Answer:

Step-by-step explanation:

a) The current term number is added to the previous term to get the current term.

__

b) Using n = 2, 3, 4 in the given formula, we have ...

  a2 = a1 +2 = 1 +2 = 3

  a3 = a2 +3 = 3 +3 = 6

  a4 = a3 +4 = 6 +4 = 10

The value of the current term is the sum of all positive integers up to the term number, that is, term n is the n-th "triangle number."

Answer: 12

Step-by-step explanation: there are 60 minutes in an hour. 60/5=12

Answer: the naswer is 0.154

Step-by-step explanation:

Applying the given probabilities, it is found that there is a 0.42 = 42% probability of watching a movie today.

These following probabilities involve a movie being watched today:

Hence, adding them:

[tex]p = 0.5(0.6) + 0.3(0.4) = 0.3 + 0.12 = 0.42[/tex]

0.42 = 42% probability of watching a movie today.

A similar problem is given at https://brainly.com/question/14398287

Answer: (a) discount is $55.20 (b) Emmett paid $82.80

Step-by-step explanation:

10% = $13.8

13.8*4 = 55.2

40% = $55.2

————————

138 - 55.2 = $82.8

Bye

Answer:

y = m x + b    equation for a straight line

m m' = -1    for perpendicular lines

Thus m' = -1/2    is required

Check:

-1/2 * -6 + 2 = = 3 + 2 = 5 = y    for the last equation give

Answer:

DE, EW, WD

Step-by-step explanation:

From shortest line to longest line this would be the correct order.

Answer:

Ellie's age is 41, Edna's age is 40, Elsa's age is 42

Step-by-step explanation:

Let Ellie's age be x. Because they're consecutive integers, Edna's age is x-1 and Elsa's age is x+1. Therefore, 3x=123, x=41, so Ellie's age is 41, Edna's age is 40, Elsa's age is 42

Answer:

Edna is 40, Ellie is 41 and Elsa is 42.

Step-by-step explanation:

let Edna be m years old

m - Edna

m+1 - Ellie

m+2 - Elsa

m+m+1+m+2=123

Collect like terms

3m+3=123

3m=123-3

3m=120

Divide through by 3

m=40

Therefore, Edna is m=40 years old

Ellie=m+1=41 years old

Elsa=m+2=42 years old.

[tex]\huge \rm༆ Answer ༄[/tex]

The value of x is ~

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve for x ~

I hope it helped ~

[tex]꧁  \:  \large \frak{Eternal \:  Being } \: ꧂[/tex]

The value of x in the given equation is [tex]-\frac{4}{5}[/tex]

From the question,

We are to solve the given equation

The given equation is

[tex]log_{6}(36) = 5x +6[/tex]

This becomes

[tex]log_{6}(6^{2} ) = 5x +6[/tex]

From one of the laws of logarithms, we have that

[tex]log_{x}(x^{2} ) = 2log_{x}(x)[/tex]

and

[tex]log_{x}(x) = 1[/tex]

∴ [tex]log_{6}(6^{2} ) = 5x +6[/tex] becomes

[tex]2log_{6}(6) = 5x +6[/tex]

and

[tex]2(1)= 5x +6[/tex]

[tex]2 = 5x +6[/tex]

Now, subtract 6 from both sides

[tex]2-6 = 5x +6-6[/tex]

[tex]-4 = 5x[/tex]

∴ [tex]x = -\frac{4}{5}[/tex]

Hence, the value of x in the given equation is [tex]-\frac{4}{5}[/tex]

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The cook needs to add 21.3 ounces of water to obtain the concentration

The cook has 32 ounces of 5% apple cider vinegar.

The total apple cider vinegar the cook has is:

[tex]Total = 32 \times 5\%[/tex]

[tex]Total = 1.6[/tex]

Let the quantity of water be x.

To dilute 3% apple cider vinegar, the cook would make use of the following equation

[tex]Total = 3\%\times (Apple\ Cider\ Vinegar + Water)[/tex]

So, we have:

[tex]Total = 3\%\times (32 + x)[/tex]

Substitute 1.6 for total

[tex]1.6= 3\%\times (32 + x)[/tex]

Divide both sides by 3%

[tex]53.3=32 + x[/tex]

Subtract 32 from both sides

[tex]53.3-32= x[/tex]

[tex]21.3= x[/tex]

Rewrite as:

[tex]x = 21.3[/tex]

Hence, the cook needs to add 21.3 ounces of water

Read more about concentration at:

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Step-by-step explanation:

the distance between 2 points can be seen as the Hypotenuse of a right-angled triangle with the legs being the x and y coordinate differences.

and so, we use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90 degree angle).

distance² = (5 - 0)² + (2 - -2)² = 5² + 4² = 25 + 16 = 41

so, the distance is sqrt(41) = 6.403124237...

Answer:

[tex]993,\!600[/tex].

Step-by-step explanation:

There is one way to choose the first character (has to be an [tex]\verb!A![/tex].)

There is one way to choose the last character (has to be a [tex]\verb!1![/tex].)

Since repetition among the letters is not allowed and the letter [tex]\verb!A![/tex] was already reserved for the first character, there would be [tex](26 - 1) = 25[/tex] English alphabet letters available for the second character.

Likewise, with the first and second characters chosen, the third character could be chosen from [tex](26 - 2) = 24[/tex] letters. There would be [tex](26 - 3) = 23[/tex] choices for the fourth letter.

Repetition of the digits is not allowed, either. With the digit [tex]\verb!1![/tex] already reserved for the last character, there would be [tex](10 - 1) = 9[/tex] ways to choose the fifth character (a digit.) There would then be [tex](10 - 2) = 8[/tex] ways to choose the sixth character (also a digit.)

Overall, the number of unique combinations would be:

[tex]\begin{aligned}& 1 \times 1 \times (25 \times 24 \times 23) \times (9 \times 8) \\ =& \; 993,\!600 \end{aligned}[/tex].

Answer:

54

Step-by-step explanation:

Answer:

It is, 6

Step-by-step explanation:

Good luck! Have a good day!! <33

Act like you have 2 fingers up and then add 4 more.

Answer:

1200

0.0012

56000

0.00056

120

0.012

560

0.0056

Step-by-step explanation:

Answer:

A=√26

-

2

Step-by-step explanation:

thank me later bye

Answer:

the slope of the line is 2

Step-by-step explanation:

3-1

1-0  

=

2

1

=

2

Answer:

Step-by-step explanation:

x² - 2x + y² - 4y - 4 = 0

x² - 2x + y² - 4y = 4

complete the squares

(x² - 2x + x₀) + (y² - 4y + y₀) = 4

the unknown number will be the square of half of the x¹ coefficient

(x² - 2x + 1) + (y² - 4y + 4) = 4 + 1 + 4

(x - 1)² + (y - 2)² = 9

This tells us that the circle is centered on (1, 2)

Which is also a point on the diameter

2x - y + a = 0

a = y - 2x

a = 2 - 2(1)

a = 0

Answer:

80-t

Step-by-step explanation:

8(10)=80

80-t

Not sure if this is what you mean... please attach a picture to your question.

Answer:

3.408 × 10 ^6

Step-by-step explanation:

The answer to this problem is going to be -2.3625

Is there more to the question that we are missing cause i need a little more for it to make sense