MATHEMATICS HIGH SCHOOL

What is the solution of log3x − 12 729 = 6?x = −5
x = −3
x = 3
x = 5

*"3x- 12" is next to log, but it's in the bottom, like an exponent, but instead of it being on top, it's below.

Answers

Answer 1
Answer: Domain:\nD:3x-12 > 0\ and\ 3x-12\neq1\ \ \ |add\ 12\ to\ both\ sides\n3x > 12\ and\ 3x\neq13\ \ \ \ |divide\ both\sides\ by\ 3\nx > 4\ and\ x\neq(13)/(3)\n\boxed{x\in\left(4;\ (13)/(3)\right)\ \cup\ \left((13)/(3);\ \infty\right)}\n----------------------\n\n\log_(3x-12)729=6\n--------\n\log_ab=c\iff a^c=b\n----------\n\log_(3x-12)729=6\iff(3x-12)^6=729\n\n(3x-12)^6=3^6\iff3x-12=3\ \ \ |add\ 12\ to\ both\ sides\n3x=15\ \ \ \ |divide\ both\ sides\ by\ 3\n\boxed{\boxed{x=5\in D}}
Answer 2
Answer: log _(3x-12) ^(729) = 6
(3x-12)^(6) = 7293x - 12 = \sqrt[6]{729} = 33x= 15x=5

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A rectangular prism has a length of 11.8 meters, a width of 4 meters, and a height of 5 meters. What is the volume of the prism?

Answers

Answer:

the volume of the prism is 236 m^3

Step-by-step explanation:

The computation of the volume of the prism is shown below:

As we know that

The Volume of the prism is

= length × width × height

= 11.8 × 4 × 5

= 236 m^3

hence, the volume of the prism is 236 m^3

P = a + (n - 1)b, for b

Answers

P = a + (n - 1)b   Subtratc a from both sides
P - a = (n - 1)b   Divide both sides by (n - 1)
(P - a)/(n - 1) = b   Switch the sides to make it easier to read
b = (P - a)/(n - 1)
The answer is b=P-a-(n+1) all you had to do was the a and the parenthesis from the b and put it on the other side

Round the fraction to the nearest whole number.
5 2/7

Answers

5 since there are7/7 in 1 whole 2/7 is less than half way to the next number

travis has passed 11 tests and his classmate Jennifer has passed 2 tests. Going forward Travis plans to pass 2 tests per week. Meanwhile Jennifer plans to pass 5 tests per week. Eventually she will catch up to Travis. How many tests will each student have passed and how many weeks will it take?

Answers

If Travis already has passed 11, and Jennifer has already passed 2, then we just add 2 to Travis and 5 to Jennifer x amount of times until they have passed the same amount of tests. So:

Travis:         11      Jennifer:     2
Week1      +  2                      + 5
Week2          2                         5
Week3          2                         5
                  -------                  --------
                    17                       17

So= it will take 3 weeks for them to have both passed a total of 17 tests each.

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

Answers

expand
y=3(x^2-4x+4)-(x^2-10x+25)
y=3x^2-12x+12-x^2+10x-25
y=3x^2-x^2-12x+10x+12-25
y=2x^2-2x-13
complete the square

y=2(x^2-x)-13
y=2(x^2-x+1/4-1/4)-13
y=2((x-1/2)^2-1/4)-13
y=2(x-1/2)^2-1/2-13
y=2(y-0.5)^2-13.5

Answer: D

y=2(x-1/2)^2 - 27/2

Maria is comparing the prices of two window cleaning companies. Company A charges $6 per window and an additional $12 as service charges. Company B charges $5 per window and an additional $15 as service charges. Part A: Write equations to represent Company A's and Company B's total charges for cleaning a certain number of windows. Define the variable used in the equations. (4 points) Part B: Which company would charge less for cleaning 8 windows? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company B instead of Company A to clean 6 windows? (3 points) (10 points)

Answers

Answer:

Part A:

Let 'x' be the number of windows cleaned.

Let 'y' be the total cost of cleaning 'x' windows.

Company A charges $6 per window and an additional $12 as service charges. So equation becomes y=6x+12

Company B charges $5 per window and an additional $15 as service charges. So equation becomes y=5x+15

Part B :

Cost for cleaning 8 windows.

Company A = y=6(8)+12 =$60

Company B = y=5(8)+15 =$55

Company B charges less for 8 windows.

Part C:

Cost for cleaning 6 windows.

Company A = y=6(6)+12 =$48

Company B = y=5(6)+15 =$45

Money saved by using company B is 48-45=3 dollars.
Part A Answer: Company A: (Wx6)+12 Company B: (Wx5)+15The varible used was W because windows start with a W i chose this as the variable because it is for the certain NUMBER of windows.Part B:Company A: 8x6=48+12=$70 for 8 windows and service charges.Company B:8x5=40+15=$55 for 8 windows and service charges.Company B would charge less for 8 windows.Part C:My work for Company A: 6x6=36+12=$48 for 6 windows and service chargesMy work for Company B: 6x5=30+15=$45 for 6 windows + service charges$48-$45=$3Answer for Part C: $3 would be saved by using the services of Company B instead if Company A to clean 6 windows.
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