What is n? If 3 to the power of n equals 27

Answers

Answer 1

Answer: 3^n=27

Solve Exponent.

3^n=27

log(3n)=log(27)(Take log of both sides)

n*(log(3))=log(27)

n=log(27) / log(3)

n=3

Answer 2

Answer: 3 to the third power equals 3*3*3= 27

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What is the equation of the line that passes through (5;-2) and (-3;4

Answers

Step-by-step explanation:

Given points are: $(5, - 2) =(x_1,\:y_1) \:\&\: (-3, 4)=(x_2,\:y_2)$

Equation of line in two point form is given as:

$(y -y_1 )/(y_1 - y_2) = (x -x_1 )/(x_1 - x_2) \n \n \therefore \: (y -( -2 ) )/( - 2 - 4) = (x -5 )/(5 - ( - 3)) \n \n\therefore \: (y + 2 )/( - 6) = (x -5 )/(5 + 3) \n \n\therefore \: (y + 2 )/( - 6) = (x -5 )/(8) \n \n\therefore \: (y + 2 )/( - 3) = (x -5 )/(4) \n \n\therefore \: 4(y + 2 ) = - 3(x - 5) \n \n \therefore \: 4y + 8 = - 3x + 15 \n \n \therefore \: 3x + 4y + 8 - 15 = 0 \n \n \huge \: \orange{ \boxed{\therefore \: 3x + 4y - 7 = 0}} \n \: \: is \: the \: required \: equation \: of \: line$

For a Supplementary angle, what is THE VALUE OF X in this problem:
(4x + 40)degrees and 3x

Answers

if you add it all together it will be 180 so to work it out you would do this...
7x+40=180
7x=140
x=20

hope this helps :)

a supplementary angle means two angles that equal 180°

4x + 40 + 3x = 180

7x + 40 = 180
-40 -40
----------------
7x = 140 140 ÷ 7 = 20

Which of these numbers is in the solution set of x – 15 = 5? A. 10 B. 3 C. 20 D. –10

Answers

Answer:

C. 20

Step-by-step explanation:

Your main goal is to isolate X to find your answer. To do that, bring the -15 to the other side. Then it would be x =20

Answer:

Step-by-step explanation:

15 x 3 is 15

After earning interest,the balance of an account is $420. The new balance is 7/6 of the original balance. How much interest did It earn

Answers

420=7/6x

The 6, who was under / now goes across the equal sign with * value.
420*6 =7x
2520 = 7x
Now the 7, who is under * value, goes across the equal sign with / value, so
2520/7 = x
x= 360.

420-360 = 60
It earned $60 of interest.

Remi has two cone-shaped containers with the same diameter. He will place the smaller container inside the larger one. Before he does this, he wants to fill the larger container with water so that it will be completely full but won't spill when he places the smaller container inside. The diameter of both containers is 14 cm. The height of the smaller container is 3 cm, and the height of the larger container is 17 cm.What volume of water must Remi put in the large container? Round your answer to two decimal places and use 3.14 to approximate pi.

Answers

use the formula for the cone
1/3 times (area of base) times height

so first we want to find the volume of both cones then subtract the volume of the smaller container from the larger one

area of base for both are equal
area of base=area of circle=pi times r^2
radius=diameter/2
diameter=14
radius=14/2
radius=7

pi times 7^2
pi times 49
3.14 times 49=153.86

smaller so 1/3 times 153.86 times 3=smaller cone=153.86 cm^3

larger
so 1/3 times 153.86 times 17=871.873

subtract smaller from larger

871.873-153.86=718.013 cm^3
the volume of water needed is 718.01 cm^3

You are swimming each 25 yard length of a swimming pool 3 seconds faster than your personal best. What integer represents your change in time of your personal best after 200 yards?

Answers

Answer: He takes 24 seconds which represents change in time of his personal best after 200 yards .

Step-by-step explanation:

Since we have given that

Distance he covered by swimming = 25 yards

Time taken by him = 3 seconds

$\text{Speed of his swimming} =(Distance)/(Time)\n\n \text{Speed of his swimming} =(25)/(3)$

Now, if he covers 200 yards , the change of time will be

$\text{Time taken}=(Distance)/(Speed)\n\n\text{Time taken}=(200)/((25)/(3))\n\n\text{Time taken}=(200* 3)/(25)\n\n\text{Time taken}=8* 3\n\n\text{Time taken}=24 seconds$

Hence, he takes 24 seconds which represents change in time of his personal best after 200 yards .

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