Evaluate each logarithm.
log₁₂ 144

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)

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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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)

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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The missing value of direct variation is 56/3

The direct variation property states that , whenever the division of values of two quantities is a constant value then there is same variation between these two corresponding values. Or we can also say that if the divisible nature of two corresponding values is constant, then one quantity is directly varies with second quantity. That mean if one quantity increase other will also increase and vice versa.

Let say if x and y are two values and k is a constant value, then

According to direct variation

k = y/x or y = k x

In the given question,

Take the order pair (3,7)

As it is an direct variation, we can substitute it

y=k x  

7=k (3)

K=7 / 3

Now find the direct variation equation

y=k x

Also, k=7/3

Solve this equation for the second pair (8,y)

As, y=7/3 x

   y= 7/3 (8) = 56/3

Therefore, missing value is 56/3

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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

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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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:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, 2 ) and (x₂, y₂ ) = (10, 2 )

m = [tex]\frac{2-2}{10-8}[/tex] = [tex]\frac{0}{2}[/tex] = 0

Answer: D

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

Answer:

Diagram A

Step-by-step explanation:

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

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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Answer:

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

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.

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]

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]

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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Answer:d=-3743

Step-by-step explanation:

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

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: x=8

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

The distance of the earth from the star is mathematically given as

2.537 x 10¹⁵ miles

Generally, the Coefficients for the problem are mathematically given a

Coefficients =4.6 x 5.9

Coefficients =27.14

For Exponents

Exponents  10² x 10¹² = 10⁽²⁺¹²⁾

Exponents =10¹⁴

In conclusion, After that, we put them together once again to produce a scientific notation:

25.37 x 10¹⁴

2.537 x 10¹⁵ miles

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

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

Answer: Everything lol

Step-by-step explanation:

Step-by-step explanation:

f(x) = x² - 3x + 3

f(4) = 4² - 3.4 + 3

f(4) = 16 - 12 + 3

f(4) = 7

Answer:

The answer is 12.

Step-by-step explanation:

Let the smallest number = x and the largest number = x+2(since the three numbers are consecutive, we would have to use x+2. If we wanted the second largest number, it would be x+1)

We would write the statement "four times the smallest integer is equal to six more than more than three times the largest" as:

4x = 3(x+2) + 6

Now just solve.

4x = 3x+6+6     distributive property

4x = 3x+12        simplify

x  = 12               subtraction property

And since x is the smallest number, we have our answer.

Therefore, the answer is 12.

Answer:

Can I see a diagram?

Step-by-step explanation: