14,040-50x = 12,500+20x

After solving the equation ln x = -2, x is the value of equal to  [tex]e^{-2}[/tex]

We have been asked to find x in ln x = -2

⇒ ln x = -2

⇒ x = [tex]e^{-2}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

12'

Step-by-step explanation:

Pythagoras theorem = a² = b²+c²

*a² is always the hypothenuse (the longest side if the triangle)

you could use b² as the base and c² as the height

to find the height i.e., c² you transpose and substitute what we know so that'll be

13'² = 5'² + c²

you expand which will then give you

169 = 25 + c²

you then take over the 25+ which when addition goes over the equal sign becomes subtraction so that'll now give you

169 - 25 = c²

144 = c²

we want to find for c not c² so to do that we find the square root of 144 which is equal to 12.

so the height is equal to 12'

hope this helps

Answer:d=-3743

Step-by-step explanation:

let's firstly convert the mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}} ~\hfill \stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}~~ - ~~\cfrac{14}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~ - ~~(2)14}{6}}\implies \cfrac{51~~ - ~~28}{6}\implies \cfrac{23}{6}\implies {\LARGE \begin{array}{llll} 3\frac{5}{6} \end{array}}[/tex]

Answer:

Diagram A

Step-by-step explanation:

a line of best fit can only be drawn if thier is strong negative or positive correlation

The value of the given equation is x = ln(4) / 3 ≈ 0.4621

The features of log are employed to expand (or compress) a single logarithm into numerous logarithms. A logarithm is simply another way to express exponents. Thus, logarithmic features are derived from exponentiation qualities.

e³x=12

Can be written as:

[e^x] [e^(2x)] = 4

Using the property of power multiplication utilizing the same base

e ^ (x + 2x) = 4

e ^ (3x) = 4

Applying logarithm  properties both side:

3x = ln(4)

ln(4) / 3 ≈ 1.38629 / 3 ≈ 0.4621

The value of the given equation is x = ln(4) / 3 ≈ 0.4621

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Answer:

Step-by-step explanation:

try number 1

From the value found for the x, the angle ABD is 37° and the angle DBC is 58°.

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.

The question gives that the angle ABC is 95°. The angle ABC is composed of the angles ABD and DBC. Thus, you should sum the angles ABD and DBC, for finding x.

2x+23+9x-5=95

11x+18=95

11x=95-18

11x=77

x=7

Like x=7, you can find the angles ABD and DBC

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Answer:

100

Step-by-step explanation:

a quadrilateral has a total of 4 angles

so the sum of all four angles is 360degre

so let the two equal angles be 2x

so 110+50+2x=360

    2x=360-160

    2x=200

     x=200/2

therefore x = 100

Answer: The answer is B. a||b and l||m

Step-by-step explanation: I hope this helps.

150cm² is the area of matting visible.

So, the area of matting is 100 × 2.5:

Now, the area of the matting is visible:

Rounding to nearest tens: 150cm²

Therefore, the area of matting visible is 150cm².

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Tonya's total earnings for a month where her total sales were $80,000 is $5,450

What made up Tonya's total earnings?

Tonya's total earnings in any month comprises the basic salary of  $650 , 3% of sales as sales commission on sales revenue of up to $32,000 and 8% as commission on sales in excess of $32,000

total earnings=basic salary+(3%*sales of up to $32,000)+(8%*sales of above $80,000)

basic salary=$650

3%*sales of up to $32,000=3%*$32,000

3%*sales of up to $32,000=$960

8%*sales of above $80,000=8%*($80,000-$32,000)

8%*sales of above $80,000=8%*$48,000

8%*sales of above $80,000=$3,840

Tonya's total earnings for a month=$650+$960+$3,840

Tonya's total earnings for a month=$5,450

Note that the total earnings based on the basic salary of $650 and sales revenue of $80,000 is $5,450

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well, double of 10000 is 20000, so hmmm happens in 12 years, ok

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20000\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]20000=10000\left(1+\frac{~~ \frac{r }{100 } ~~}{1}\right)^{1\cdot 12} \implies \cfrac{20000}{10000}=\left( 1+\cfrac{r}{100} \right)^{12} \\\\\\ 2=\left( \cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{2}=\cfrac{100+r}{100}\implies 100\sqrt[12]{2}=100+r \\\\\\ 100\sqrt[12]{2}-100=r\implies {\LARGE \begin{array}{llll} \stackrel{\%}{5.95}\approx r \end{array}}[/tex]

now, what will it be after 10 years assuming we use 5.95%?  mind you that's a rounded figure, but close enough.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 5.95\%\to \frac{5.95}{100}\dotfill &0.0595\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=10000\left(1+\frac{0.0595}{1}\right)^{1\cdot 10} \implies {\LARGE \begin{array}{llll} A \approx 17824.18 \end{array}}[/tex]

Answer:

Step-by-step explanation: 37 times 1000 equals 37000 if you times anything by 1000 just add 2 zeros to the end

Answer: D

Explained: you find the solutions to x and the y axis to graph

The required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).

What is an expression?

An expression is any statement in mathematics written using numbers, variables and at least one operation present.

Simplification of the expression: 2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16

Given an expression,

2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16

On simplifying, we get,

(2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)

For the numerator, (2x - 8).(x² + 5x + 4), we have,

= 2(x + 1)(x - 4)(x + 4)

For the denominator,  (x² - 16).(x² + 8x + 16)

= (x + 4)(x - 4)(x + 4)(x + 4)

Now, (2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)

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

= 2(x + 1) / (x + 4)(x + 4)

The restriction to the given expression is that the denominator,  x + 4 should not be 0.

Hence, the required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).

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A) 54,912 B) 2,598,960 C)  15

A) The number of ways to produce three of a kind (Num3) is equal to the product of the number of ways to make each independent choice. Therefore,

Num3 = 13C1 * 12C2 * 4C3 * 4C1 * 4C1

Num3 = 13 * 66 * 4 * 4 * 4 = 54,912

B) First, we count the number of five-card hands that can be dealt from a standard deck of 52 cards. This is a combination problem. The number of combinations is n! / r!(n - r)!. We have 52 cards in the deck so n = 52. And we want to arrange them in unordered groups of 5, so r = 5. Thus, the number of combinations is:

52C5 = 52! / 5!(52 - 5)! = 52! / 5!47! = 2,598,960

Hence, there are 2,598,960 distinct poker hands.

C) 6 C 4 = 6! / 4! (6-4)!

= 6*5*4! / 4!*2!

= 30 / 2

= 15

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The name of each midpoint and the segment it bisects include the following:

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

In this scenario, the name of each midpoint and the segment it bisects include the following:

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Complete Question:

Name each midpoint and the segment it bisects.

In mathematics, an inverse function is one that "reverses" another function. The inverse of each function y = 3x + 1 is y = x−13.

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

Let the function be y = 3x+1

Replacing f(x) with y, we get

y = 3x+1

simplifying the above equation, we get

x = 3y + 1

Subtracting 1 from both sides to get

3y = x − 1

Dividing both sides by 3, we get

y = x−13

Replace y with f⁻¹(x), we get

f⁻¹(x) = x−13

The inverse of each function y = 3x+1 is f⁻¹(x) = x−13.

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Answer: Everything lol

Step-by-step explanation:

Answer: x=8

Step-by-step explanation: i did this exact question on OW

Answer:

31 minutes in total

Step-by-step explanation:

Going step by step, where m = minutes after the first 3:

0.58 + 0.15m = 4.78

We want to solve for m, so we need to isolate it. The first step is to get rid of 0.58 to simplify our equation.

0.15m = 4.78 - 0.58

Now we have:

0.15m = 4.20

To isolate further, we need to remove 0.15.

m = 4.20 / 0.15

m = 28

Now, we add the first 3 minutes to m to get our total time.

28 + 3 = 31

Step-by-step explanation:

f(x) = x² - 3x + 3

f(4) = 4² - 3.4 + 3

f(4) = 16 - 12 + 3

f(4) = 7

The domain of the function C(t) is R - { -5. -2}.

The domain of a function is the set of all values for which the range of the function is defined.

To achieve an immediate response to a particular drug's effects the concentration, C, in mg/L, of a particular medication after being injected into a patient is given by the function

C(t) = [tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex] where t represents time in hours.

We know that a function is undefined when its denominator becomes zero.

∴ We have to factor the quadratic equation t² + 7t + 10 which is,

t² + 5t + 2t + 10 = 0.

t(t+5)+2(t+5) = 0.

(t+5)(t+2) = 0.

So, t = -5 or t = -2 are the two values of this equation which makes the function c(t) undefined.

∴ The domain of the function [tex]\frac{-18t^2 + 54t}{(t+5)(t+2)}[/tex] is all real numbers except -2 and - 5 which can be written as

Domain of C(t) is R - { -5, -2}, where R represents all real numbers.

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The minutes when the scenes have the same amounts rendered is 14 minutes.

The expression for the kitchen is illustrated as 540 + 90t.

The expression for the garden is illustrated add 960 + 60t.

Therefore, for the same amount, this will be:

540 + 90t = 960 + 60t.

Collect like terms

90t - 60t = 960 - 540

30t = 420

Divide

t = 420 / 30

t = 14 minutes

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The solution to the given inequality in inequality and interval notation form are x < 5 and ( -∞,5 ) respectively.

Given the inequality in the question;

4 + 6.5x < 36.5

First, move all terms not containing x to the right side of the inequality.

4 + 6.5x < 36.5

6.5x < 36.5 - 4

Subtract 4 from 36.5

6.5x < 36.5 - 4

6.5x < 32.5

Divide both sides by the coefficient of x

6.5x < 32.5

6.5x/6.5 < 32.5/6.5

x < 32.5/6.5

x < 5

The solution in inequality form is x < 5

The solution in interval notation is ( -∞,5 ).

Therefore, the solution to the given inequality in inequality and interval notation form are x < 5 and ( -∞,5 ) respectively.

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Answer:

X < 5

Step-by-step explanation:

The solution is so subtract the 4 with the 4 and 36.5 you cross out the 4 and subtract 4 form 36.5 which leaves you with 32.5. Then to get the variable by itself you divide 6.5 on both sides, then cross out the 6.5 and divide 6.5 on 32.5 which gives you 5. (I solved it by myself)

Answer:

32081.

Step-by-step explanation:

-9x-9+5^3x4^4

Using PEMDAS, the exponents are calculated first:

= -9 x -9 + 125 x 256

Next the multiplications:

= 81 + 32000

= 32081.

When thinking about the small group as a system, the key component that connects all of the system's relevant parts is D. Communication.

It should be noted that the system framework is important as it reminds us that the piece of puzzle interacts with each other.

Therefore, when thinking about the small group as a system, the key component that connects all of the system's relevant parts is communication.

The sender, also known as the communicator or source, is where communication starts. The sender wishes to share some kind of information with the recipient(s), such as a request, query, or idea.

Understanding comes through good communication. Four essential elements make up the communication process. These elements consist of encoding, transmission medium, decoding, and feedback.

It should be noted that communication links the parts together.

Therefore when thinking about the small group as a system, the key component that connects all of the system's relevant parts is Communication.

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Answer:

U: (-7, 0)

S: (-7, -2)

T: (3, -2)

Step-by-step explanation:

Moving a point 6 to the left is the same as subtracting 6 from its x value. Moving a point up 1 is the same as adding 1 to its y value.

Point=(x-6, y+1) where x is the point's original x value and y is the point's original y value.

U: (-1-6, -1+1)=(-7, 0)

S: (-1-6, -3+1)=(-7, -2)

T: (9-6, -3+1)=(3, -2)