How is the change of base formula used in solving logarithmic equations?

Answer:

See below.

Step-by-step explanation:

Each term increases by 3 for A and 4 for B.  Either do this calculation manually on a table, or use a spreadsheet to calculate all terms quickly.

The ten first terms for A and B are shown.  

A B Difference

1 1 1    0

2 4 5    1

3 7 9    2

4 10 13    3

5 13 17    4

6 16 21    5

7 19 25    6

8 22 29    7

9 25 33    8

10 28 37    9

We can see that the difference between the two patterns is that B increases more rapidly until there is a difference of 9 by the 10th term.

Answer:

Step-by-step explanation:

Given that a cylinderal can has base with a diameter of 6 cm and its height measures 5 cm.

So,

Radius = Diameter/2 = 6/2 = 3 cm

We know that,

Substituting required values:

➝ TSA = 2 × 22/7 × 3(5 + 3)

➝ TSA = 44/ 7 × 3 × 8

➝ TSA = 1056/7

➝ TSA = 150.8 cm²

Hence,

Answer:

Total surface area of cylindrical can :- 150.72 cm²

Step-by-step explanation:

Given:-

To find :-

Solution :-

Formula for Total surface area of cylinder :-

2πr(r + h)

putting the known values ,

= 2 × 3.14 × 3 ( 3+5) cm²

= 18.84 × 8 cm²

= 150.72 cm²

Answer:

Step-by-step explanation:

Use Pythagorean's theorem. The two shorter sides (6+x) and 20 are apart of a right triangles of a hypotenuse of (18+6). Therefore:

[tex](6+x)^2+20^2} =(18+6)^2[/tex]

[tex](6+x)^2+400 =576[/tex]

[tex](6+x)^2=176[/tex]

Take the square root of both sides:

[tex]6+x=\sqrt{176}[/tex]

[tex]x=\sqrt{176} -6[/tex]

Moving on to the smaller triangle, we can find the value of 'y' to be:

[tex]6^2+y^2=18^2[/tex]

[tex]y^2+36=324[/tex]

[tex]y^2=288[/tex]

[tex]y=\sqrt{288}[/tex]

Answer:

[tex]\boxed{{x} > -3}[/tex]

Step-by-step explanation:

Given inequality:

To solve this inequality, we need to isolate the variable on one side and the constant on the other. To do this, we can divide both sides by -5.

[tex]\rightarrowtail -5x < 15[/tex]

[tex]\rightarrowtail \dfrac{-5x}{-5} < \dfrac{15}{-5}[/tex]

[tex]\rightarrowtail x < \dfrac{15}{-5}[/tex]

Note: If we are dividing both sides by a negative integer, the sign changes.

[tex]\rightarrowtail {x} > \dfrac{15}{-5}[/tex]

To simplify 15/-5, we can multiply -1 to the numerators and the denominators. As a result, the negative sign should transfer to the numerator, as when two negative integers multiply each other, the result is a positive integer.

[tex]\rightarrowtail {x} > \dfrac{15}{-5} \times \dfrac{-1}{-1}[/tex]

[tex]\rightarrowtail {x} > \dfrac{-15}{5}[/tex]

[tex]\rightarrowtail \boxed{{x} > -3}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-5x < 15}\\\\\large\text{DIVIDE -5 to BOTH SIDES}\\\\\mathsf{\dfrac{-5x}{-5} < \dfrac{15}{-5}}\\\\\large\text{SIMPLIFY IT!}\\\\\mathsf{x > -3}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{x > -3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

median is 16 ducky quack

Answer:

16

Step-by-step explanation:

Median, also known as the "middle" value in a data set. To be able to find the median, your data needs to be in numerical order.

Quiz scores:

9, 13, 20, 15, 18, 17

Arrange in numerical order:

9, 13, 15, 17, 18, 20

Find the "middle" value:

9, 13, 15, 17, 18, 20

When there are two middle values, you add them up and divide it by 2.

15 + 17 = 32

32/2 = 16

Therefore, the median, "middle" value of this student's quizzes is 16.

Hope this helps!

Answer:

39.9

Step-by-step explanation:

Pls give brainlest if correct.

   *Answer*:39.9

Say you wanted to round the number 838.274. Depending on which place value you'll round to, the final result will vary. Rounding 838.274:   Rounding to the nearest hundred is 800 Rounding to the nearest ten is 840 Rounding to the nearest one is 838 Rounding to the nearest tenth is 838.3 Rounding to the nearest hundredth is 838.27  

When you "round to the nearest _____" regardless of what goes in the blank the steps are nearly always the same:   Identify which place value you are rounding to. The smaller the place value, the more accurate the final result will be. Look to the next smallest place value, the digit to the right of the place value you're rounding to.

Therefore, the answer is C. 39.9

~NatLikesAnime

#LearningWithBrainly

Please give brainliest, a thanks, and a 5 start rating if helpful :)

Answer:

A. Is the answer

I'm correct right?

Answer: 6

Step-by-step explanation:

The length of all sides of the square ceiling is 15 ft

Perimeter of the ceiling = 4 * length of each side = 15 * 4 = 60 ft

Distance from one corner to another corner i.e. BD and AC (in the figure below) forms the diagonals of the square ceiling

We know that,

Diagonal of a square = √(2) * a , where a is the length of the side of the square.

Therefore,

BD = AC = 15 √(2)

Thus,

Total crepe paper required = Perimeter of the ceiling + BD + AC = 60 + 15 √(2) + 12 √(2) = 102.43 ft

Crepe paper in each roll = 20 ft

Therefore,

Number of rolls required = 102.43 / 20 = 5.1215

Therefore, the minimum number of rolls she should buy is 6

Answer:

slope intercept for is y=MX+b and to find the slope it's y1-y2/x1-x2

The slope would be 10/3.

And the line should intersect at the origin (0,0) and the second dot should be at the point (3,10)

Answer:

5.7594087

Step-by-step explanation:

0.03x8888^14

Answer:(x+5)(x-2) I Dont know what a special product is sry

Step-by-step explanation:

If it didn't have that piece cut out on the bottom, it would be a rectangle that's 9cm wide and 5cm high.  Its area would be 9x5= 45 cm².

But that piece is cut out of the bottom.  The cut-out piece is 3cm wide and 3cm high, so its area is 3x3= 9 cm².

9 cm²  have been cut out of the 45 cm²  of the complete big rectangle.  So the remaining area of the figure is  45 - 9 = 36 cm² .

18.0% which is the same as 18%

==========================================================

Work Shown:

p = purchase price = $281,700

c = closing costs

c = 2.4% of purchase price

c = 0.024p

c = 0.024*(281,700)

c = 6,760.80

d = unknown down payment amount

m = total move in costs = $57,466.80

m = d + c

d = m - c

d = 57,466.80 - 6,760.80

d = 50,706

down payment percent = d/p = (50,706)/(281,700) = 0.18 = 18%

18% of the purchase price is the down payment.

Answer: awnser is m= 1/6

Step-by-step explanation: m = add the terms which is  -1 -5m-4+6 m= 1-5m

step 2 then rerange the terms  to m= 1-5m to m = 5m + 1

step 3  add 5m to both sides m= -5m+1 to m + 5m= -5m + 1  + 5m

step 4  simplify and combine like terms 6m= 1

step 5 divide both sides by the same factor 6m= 1  6m/6 =  1/6

step 6 simplify Cancel terms that are in both the numerator and denominator so it is m= 1/6 is the correct awnser mark me brainliest please

Answer:

3 is most likely

Step-by-step explanation:

Answer:

the shirt should be $20 and the pants $30

Answer:

<C=48 because 90-42=42 as in the other side of the triangle.

<B=42 because vertical angles are always congruent.

<B+<D=90 because <D is 48 because it is vertical to <C

Step-by-step explanation:

circumference = 2 pi r

2 × 3.14 × r = 527.52 yd

r = 527.52 × 1/2 × 1/3.14

r = 84 yd

Surface area = 4 pi r²

= 4 × 3.14 × 84²

= 88,623.36 yd²

The percentage of the children that have dog or cat is = 57%

The percentage of children that have a dog = 45%

The percentage of children that have a cat = 30%

The percentage of children that have dog and cat= 18%

Therefore the percentage of children that have dog or cat = (45 + 30) - 18

= 75 - 18

= 57%

Therefore, the percentage of the children that have dog or cat is = 57%

Learn more about percentage here:

https://brainly.com/question/24304697

Answer:

A:) Yes it is a right triangle

Step-by-step explanation:

[tex]~~~~\left(\sqrt{5} \right)^2= \left(\sqrt{2} \right)^2+\left(\sqrt{3} \right)^2\\\\\implies 5=2+3\\\\\implies 5=5[/tex]

Answer:

A

Step-by-step explanation:

using the converse of Pythagoras' identity

If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.

longest side = [tex]\sqrt{5}[/tex] , and ([tex]\sqrt{5}[/tex] )² = 5

([tex]\sqrt{2}[/tex] )² + ([tex]\sqrt{3}[/tex] )² = 2 + 3 = 5

Thus the 3 sides form a triangle

Answer:

11.80

Step-by-step explanation:

The $11.80 will be her July finance charge option (c) is correct.

It is given that Elizabeth’s credit card computes her finance charges using the previous balance method and a 30-day billing cycle.

It is required to find the July finance charge.

It is defined as the annual percentage rate that represents the yearly interest rate on the borrowing.

We have a principal amount = $969.26

APR = 14.61 %

Per month percent rate = [tex]\frac{14.61}{12}[/tex] ⇒ 1.2175 %

We can calculate the finance charge from the given formula:

Finance charge = Principal value×rate×Time

= 969.29×1.2175%×1

[tex]= 969.29\times\frac{1.2175}{100}\times1[/tex]

= $11.80

Thus, the $11.80 will be her July finance charge.

Learn more about the finance charge here:

https://brainly.com/question/2588555

Answer:

Answer:56.8

Step-by-step explanation:

First you get how much he earned

Then you get how much days he worked

Then you divide

£284/5

Answer: £57.20

Hope this helps you guys!

Answer:

pretty sure the answer is 8 1/2 cups

Step-by-step explanation:

Answer:

RS RT ST

Step-by-step explanation:

This is due to the facts that tangency means having contact at a single point or along a line without crossing. so the first 3 options are correct

the area of the triangle.

area of triangle= 1/2 × h × b

= 1/2 × 8 × 11

= 44cm^2

Answer:

44

Step-by-step explanation:

area of a triangle=½×base×height

hope that hepls

Answer:

14π inches

Step-by-step explanation:

Diameter of the clock = 7 × π = 7π

one day = 24 hours which means

2 clockwise turns around the clock

sooo 7π × 2 = 14π

Answer:

527.52 in

Step-by-step explanation:

To answer this question you have to find the circumference of the circle.

You have to use the formula below to find the circumference.

C = π d

Here,

d ⇒ diameter ⇒ 7 in

Let us solve it now.

C = π × d

C = 3.14 × 7

C =  21.98 in

Let us find it now.

Distance traveled in a day = 21.98 × 24

                                            = 527.52 in

Answer:

86% of original (with tax included)

Step-by-step explanation:

(16 000 x 1.075) / 20 000   x 100%  = 86 %