(3x+6)^2
Please show the work step-by-step, thank you! <3

The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z.

Logarithms are the reciprocal of exponential functions. In this question we must apply logarithms and its properties to obtain a linear-like expression in the following lines. The logarithm properties are summarized below:

㏒ₐ (b/c) = ㏒ₐ b - ㏒ₐ c     (1)

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c     (2)

㏒ₐ bⁿ = n · ㏒ₐ b     (3)

a) To obtain the corresponding logarithmic function we apply logarithms on both sides of the expression:

㏒ 12³ = ㏒ x⁴ · y³ · z⁶     (4)

The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. [tex]\blacksquare[/tex]

b) The expanded logaritmic form of (4) consists in the addition and subtraction of logarithms of non-power numbers, whose formed could be found, if possible, by logarithm properties:

㏒ 12³ = ㏒ x⁴ · y³ · z⁶

㏒ 12³ = ㏒ x⁴ + ㏒ y³ + ㏒ z⁶

3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z

The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z. [tex]\blacksquare[/tex]

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Answer:

300 - hope this helped :)

Step-by-step explanation:

340 to the nearest hundred

is 300 since thats the closest

Answer:

B, C, D, F

Step-by-step explanation:

if you know the length and width of the traffic jam is (F and C) you can start to calculate how many cars are stuck in it. then by using how long the vehicles are and how long the space between them is you can find out how many cars would fit in this area. (B and D)

A and F are irrelevant because the question is simply asking how many vehicles in the jam not how many people or what cuased it.

hope this helps :]

Answer:

a=0

Step-by-step explanation:

Step-by-step explanation:

For example ............

Answer:

4. y=3√2 and x=36

Step-by-step explanation:

Here,

interior angle of triangle = 180°

So, 90°+45°+45°=180°

Therefore, the triangle is isosceles triangle

So,

y=3√2 (the corresponding sides of corresponding angle of isosceles triangle are equal)

Again, x^2=(3√2)^2 + (3√2)^2

or, x= √(18 + 18)

or, x=√36

or, x=6

Using the given function, it is found that:

The profit when n students are enrolled in the class is given by:

f(n) = 70n - 400.

A profit is made when f(n) > 0, hence:

70n - 400 > 0

70n > 400

n > 5.71.

6 students need to be enrolled for the instructor to make a profit.

A profit of $1,000 is made when f(n) = 1000, hence:

70n - 400 = 1000

70n = 1400.

n = 20.

20 students must be enrolled for the instructor to make a profit of $1,000 a month.

More can be learned about functions at https://brainly.com/question/25537936

Atleast 6 students must be enrolled to make a profit and 20 student are needed to make $1,000.00 profit per month.

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the function:

f(n) = 70n - 400

To make a profit, f(n) > 0, hence:

70n - 400 > 0

n > 6

For a profit of $1000:

70n - 400 = 1000

n= 20

Atleast 6 students must be enrolled to make a profit and 20 student are needed to make $1,000.00 profit per month.

Find out more on equation at: https://brainly.com/question/2972832

Step-by-step explanation:

Your diameter is 15 and a diameter is a whole line, what your going to do it divide the 15 by 2, than mutiply the answer by 3.14 and than round ur answer :)

Answer:

Volume of larger box: 480

Length of small box: 5

Width of small box: 4

Height of small box: 3

Volume of small box: 60

Ratio of small box to large box: 1/8

Answer:

A

Step-by-step explanation:

[tex] - \frac{4}{3} \times \frac{4}{1} = - \frac{1}{3} [/tex]

Hope this helps

Answer:

871

Step-by-step explanation:

The State Board of Education can buy 871 calculators with the available budget.

Here, we have to find out how many calculators the State Board of Education can buy,

We have to divide the total amount they have ($1,742) by the cost of each calculator ($2):

So, we get,

Number of calculators = Total amount / Cost per calculator

Number of calculators = $1,742 / $2

Number of calculators = 871

So, the State Board of Education can buy 871 calculators with the available budget.

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#SPJ3

Answer:

4.1

Step-by-step explanation:

it was right sooo

Answer:

GCF = 12

for the values 60, 96, 156

Step-by-step explanation:

Solution by Factorization:

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

The factors of 156 are: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156

Then the greatest common factor is 12.

Answer: Right angled triangle

Step-by-step explanation: Find attached in the picture

Answer:

Joe is 16, Frank is 22

Step-by-step explanation:

To find the solution to this problem, we first divide 38 by two.

38 / 2 = 19.

Then, we subtract 6 from 19 and have 19 and 13.  Obviously, 19 is 6 more than 13 (19 - 13 = 6).  Now, we need to make sure our number on the left is always 6 more than the number on the right.  19 + 3 = 22, 13 + 3 = 16.  Since Frank is older than Joe by 6 years, we get 22 and 16 as their ages.

Answer:

5/6

Step-by-step explanation:

thats what it is

Answer:

a. 26%

b. It's a binomial distribution because the competition will only have two outcomes, win or lose.

c. 4/7 or 57%

Step-by-step explanation:

Hope this helps :)

check out brainly.com/question/7567074, same question, verified answer

Answer:

: L = r * θ = 15 * π/4 =

Step-by-step explanation:

Answer:

34.7791 [unit²].

Step-by-step explanation:

1) area of the circle is:

πr²;

2) area of the regular polygon is:

6*r²√3*0.25=1.5√3r²;

3) the required area:

πr²-1.5√3r²=r²(π-1.5*√3)=64*(3.1415-1.5*1.7321)=34.7791

Answer:

Hyperbola

Step-by-step explanation:

Sorry if incorect

Hope this helps

Answer:

Brother's age = 13 years

Step-by-step explanation:

Sister's age = 13 year

Brother's age = x

Brother's age will be equal to the Sister's age when x-14

According To The Question

[tex]x - 14 = 13 \\ x = 13 + 14 \\ x = 27[/tex]

Therefore, Brother's age will be 27 years

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Answer:

No.

Step-by-step explanation:

Two Angles are Supplementary when they add up to 180.

Let us consider the least obtuse angle, i.e., >90

Say 91 and add it to itself.

91+91 =182

This is >180

Hence, two obtuse angles can never be supplementary.

Answer:

C =113.04 ft

Step-by-step explanation:

[tex]C = 2\pi \: r \\ \\ \implies C =2(3.14)(18) \\ \\ \implies C =113.04 \: ft[/tex]

Answer:

9 1/6 laps

Step-by-step explanation:

1 5/6 * 5   = 11/6 *5  = 55/6 = 9 1/6

Answer:

[tex]y =\dfrac{1}{2}x+4[/tex]

Step-by-step explanation:

Slope-intercept form: y =mx +b

              7x - 14y = -56

Step1 : subtract 7x from both sides

                   [tex]-14y = -7x - 56[/tex]

Step2: now divide both sides by (-14)

                         [tex]y =\dfrac{-7}{-14}x -\dfrac{56}{-14}\\\\y = \dfrac{1}{2}x+ 4[/tex]

Answer:

y = [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

7x - 14y = - 56 ( subtract 7x from both sides )

- 14y = - 7x - 56 ( divide through by - 14 )

y = [tex]\frac{-7}{-14}[/tex] x - [tex]\frac{56}{-14}[/tex]

y = [tex]\frac{1}{2}[/tex] x + 4 ← in slope- intercept form

So here, ABCD is being inscribed in a circle, so ABCD is a cyclic quadrilateral (as inscribed in a circle) also, there exists a property of cyclic quadrilateral, i.e, the sum of opposite angles of a cyclic quadrilateral is 180°, so we can just write the following equation using this :

[tex]{:\implies \quad \sf y^{\circ}+83^{\circ}=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf y^{\circ}=180^{\circ}-83^{\circ}}[/tex]

[tex]{:\implies \quad \sf y^{\circ}=97^{\circ}}[/tex]

[tex]{:\implies \quad \boxed{\bf{y=97}}}[/tex]

The total amount of security deposit, deposited by three friends after paying the rent is $620.01. Option C is the correct option.

The monthly payment is the amount which is required to pay each month to pay off the borrowed principal amount or the rent of a service charged monthly.

The rent of the apartment is $650 per month. The rent for the two months (first and last) is,

[tex]\rm M = 2\times 650\\\\M =1300[/tex]

This rent is paid by three friends. Thus, the amount which is paid by an individual friend is,

[tex]\rm P=\dfrac{1300}{3}\\\\P=433.33[/tex]

They each paid $640 towards the total move-in cost of first and last month's rent and a security deposit. Therefore,

[tex]\rm P=640-433P=206.67\\\\[/tex]

Thus, $206.67 is paid by each of them towards security deposits. The total amount of security deposit, deposited by 3 of them, is,

[tex]\rm SD=206.67\times 3\\\\SD=620.01[/tex]

Hence, the total amount of security deposit, deposited by three friends after paying the rent is $620.01. Option C is the correct option.

Learn more about the monthly payment here;

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Answer:

Option C

Step-by-step explanation:

I got it right on the test

Answer:

B: 9 outcomes

Step-by-step explanation:

you have 3 possibilites in the left pocket, and 3 in the right. Multiply the number of possibilites in each pocket to find how many total possibilites there are.