Suppose log7(10) = a and log7( 5) = b. Use the change-of-base formula along with properties of
logarithms to rewrite each expression in terms of a and b.

Answers

Answer 1

Step-by-step explanation:

log 10/log7=a

log10=alog7

log10=log7^a

10=7^a

log 5/log7=b

log5=blog7

log5=log7^b

5=7^b


Related Questions

My answer is 8, but I'm not completely sure, if I'm wrong could someone please explain how to find the length.

Answers

By knowing that S is bisected by the line shown, we will conclude that PD = 8

So here we know that PC = 8, we also can see that:

PCS is a right trianglePDS is a right triangle.

Notice that because the blue line bisects S, the angle at "S" on both of these right triangles is the same, and because both of these are right triangles, both must have a 90° angle.

Finally, if two angles are equal, then the 3 angles must be equal between these two triangles.

And notice that both of these triangles share one side, then:

Triangles we know for sure that triangles PCS and PDS have the same angles and one equal side.

This implies that the triangles are congruent, thus, the measures of the corresponding sides must be the same.

Then the length of the shorter side of both triangles must be the same, in triangle PCS the short leg measures 8 units, then in triangle PDS the short leg, PD, also must measure 8 units.

So you are correct.

If you want to learn more about congruent triangles, you can read:

https://brainly.com/question/12077512

Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400
could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone

Answers

Answer:

5 weeks

Step-by-step explanation:

The amount of money he has to earn in order to buy the phone is: 400-55 = 345( dollars)

He gets 345 dollars in: 345÷75= 4 weeks and remains 45 dollars

So he needs to work for 1 more week to have enough money to buy the phone

So he needs to work at least 5 weeks

You go to a restaurant and get a bill for $95. You need to tip the waitress. The service was good so you decide on tipping the waitress 20%. What is the tip that the waitress will receive

Answers

Answer:

19 dollars.

Step-by-step explanation:

0.20 x $95.00=$19.00.

19 dollars because 20% of 95 is 19. You can find this by doing 20% (or 0.2) times 95 :)

Two parallel lines are cut by a transversal, as shown below. Solve for b. Then explain your reasoning.

Answers

Answer:

b = 14

Step-by-step explanation:

Since both angles are diagonal each other, they are equal to each other.

5b = b + 56

-b      -b           (subtract b from both sides)

4b = 56

4       4            (divide both sides by 4 to solve for b)

 b = 14

How do you multiply a fraction and a whole number? Please explain step by step to get marked as brainliest!

Answers

Multiply the numerators then multiple the denominators

Answer: 1 1/2 x 4 4/7

= 3/2 x 32/7

= 96/14

Step-by-step explanation:

1. Write the whole number as a fraction with a denominator of 1.

2. Multiply the numerators.

3. Multiply the denominators

4. Simplify. If needed, if your answer is greater than 1, you may want to write your answer as a mixed number.

write an expression to represent admission to a zoo of $10.00 and the cost of special exhibits s at $4 each. Evaluate you expression when s=2

Answers

Answer:

10.00 +4s .

u wanted expression ,  not answer.?

Step-by-step explanation:

can anyone find out what this is?

Answers

Answer:

Expression D

Step-by-step explanation:

all other answers are above 15! hope this helps :D

PLEASE HELP IM BEING TIMED!
Ivan is making cookies for a party. He has 5 cups of flour. The recipe calls for 2 cups of flour. Ivan wants to double the recipe.
Which statement about the amount of flour for the doubled recipe is true?
O A. Ivan has 1 cups of flour more than he needs.
B. Ivan has
5
cup of flour more than he needs.
O c Ivan has exactly enough flour.
D. Ivan needs
cup more flour than he has.
OE. Ivan needs 1
cups more flour than he has.

Answers

The answer is He needs 1/3 more cups of flour than he has.

(2 2/3) x 2 = 16/3 = 5 1/3

The recipe calls for 2 cups of flour. The double of this amount is :

[tex]\mathfrak{2*2} [/tex]

[tex]\underline{\mathfrak{=4}} [/tex]

If Ivan has 5 cups, then :

[tex]\mathfrak{5-4} [/tex]

[tex]\underline{\mathfrak{=1}} [/tex]

So, O A. Ivan has 1 cup of flour more than he needs.

[tex]\mathbb{MIREU} [/tex]

Sue has 100 dimes and quarters. If the total value of the coins is &21.40, how many of each kind of coin does she have?

Answers

Answer:

Let x be the number of dimes and y the number of quarters

x +y = 100

a dime is $0.10 and a quarter is $0.25

0.1x + 0.25y = 21.40 multiply by 100 to remove the decimals

10x + 25y = 2140, From the first equation y = 100 - x and plug it in to the second equation.

10x + 25(100 -x) = 2140

10x + 2500 - 25x =2140

2500 - 15x = 2140

360 = 15x x = 24 and y = 76

There are 24 dimes and 76 quarters

Answer:

76 Quarters = $19.00

24 Dimes = $2.40

$19.00 + $2.40 = $21.40

Step-by-step explanation:

Yaga

What system the system that is made up of the heart,blood, and blood vessels is called the ____ this is for sceince but i cant find sceince

Answers

Answer:

Cardiovascular system

Step-by-step explanation:

can someone please help me with this I don’t wanna fail math

Answers

Answer: y = mx + b is the slope intercept form of writing the equation of a straight line

Step-by-step explanation:

Answer:

Step-by-step explanation:

, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.

Use the following table to answer the questions below. Give your probabilities as DECIMALS rounded to the hundredths place.
Fair Hair
Dark Hair
Blue Eyes
8
5
Other
7
10
Jamie investigated hair and eye color.
One of the people is chosen. Calculate the probability of choosing
a. Someone with Blue eyes
b. Someone with fair hair and blue eyes
A person with dark hair is chosen. Calculate the probability of
1. them having blue eyes.
2. them not having blue eyes

Answers

Answer: 1 =.43, 2=.26, 3=.16 4=.33

Step-by-step explanation: So to find all these answers we have to know the total number of people in the chart 30. Then we have to find what info we need from the chart and divide it by the total number of people. I hope this helped I tried to make it simple.

Please help me solve this math problem

Answers

Answer:

 (b)

Step-by-step explanation:

A suitable calculator or spreadsheet can find the matrix product for you. Here, the answer choices differ in their upper left term, so we can determine the correct choice by finding the value of that term. It is the dot product of the first row of B and the first column of A.

  (5)(3) +(7)(3) +(3)(2) = 15 +21 +6 = 42

This matches choice B.

Please help ASAP!!! Will give 10 pts!!​

Answers

A. Mixed
B. Proper
C. Mixed
D. Proper
E. Improper
F. Improper
G. Improper
H. Mixed
I. Improper
J. Improper
K. Mixed
L. Mixed
M. Proper
N. Proper
O. Mixed

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/ unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = .05. Use both p-Value and Critical-Value approaches. Type of Ride Roller Coaster Screaming DemonLog FlumeMethod 1 41 52 50 43 44 46 49 46 48Method 2 49 50 48 51 46 44 47 48 46
1. Set up the ANOVA table (to 1 decimal, if necessary).2. The p-value for Factor A is ___________.3. What is your conclusion with respect to Factor A?4. The p-value for Factor B is_________. 5. What is your conclusion with respect to Factor B?6. The p-value for the interaction of factors A and B is ____________.7. What is your conclusion with respect to the interaction of Factors A and B?8. What is your recommendation to the amusement park?

Answers

Answer:

An amusement park studied methods

Step-by-step explanation:

Write each expression in terms of sine and​ cosine, and then simplify so that no quotients appear in the final expression and all functions are of x only.
[tex]\frac{csc^2 (-x)-1}{1-cos^2 (-x)}[/tex]

Answers

[tex]\stackrel{\textit{reciprocal ident.}}{csc(\theta)=\cfrac{1}{sin(\theta)}} ~\hfill \stackrel{\textit{symmetry ident.}}{sin(-\theta )=-sin(\theta)}~\hfill \begin{array}{llll} \stackrel{\textit{pythagorean ident.}}{sin^2(\theta)+cos^2(\theta)=1}\\ sin^2(\theta)=1-cos^2(\theta)\\ cos^2(\theta)=1-sin^2(\theta) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\cfrac{csc^2(-x)-1}{1-cos^2(-x)}\implies \cfrac{~~\frac{1}{sin^2(-x)}-1~~}{sin^2(-x)}\implies \cfrac{~~ \frac{1-sin^2(-x)}{sin^2(-x)}~~}{\frac{sin^2(-x)}{1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{keeping in mind that}~\hfill }{sin^2(-x)\implies [sin(-x)]^2\implies [-sin(x)]^2\implies [sin(x)]^2\implies sin^2(x)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{~~ \frac{1-sin^2(x)}{sin^2(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{1-sin^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cot^2(x)csc^2(x)~\hfill[/tex]

pls help me anymore pls​

Answers

Answer:

thanks for the points again

Step-by-step explanation:

,(TT(TT)(TT)(TT)(TT)(TT)(TT

Mary has some chocolates. If she shares them equally among 4 friends or 5 friends, there are always 2 extra chocolates left. What is the possible number of chocolates Mary could have?

Answers

Answer:

22 chocolates

Step-by-step explanation:

First, let x represent the number of chocolates Mary has. Since she always has 2 extra chocolates, the number of chocolates distributed to her friends would be x - 2. And x - 2 is the least common multiple of 4 and 5 because x - 2 chocolates are evenly distributed among 4 and 5 friends. The LCM of 4 and 5 is 20, so x - 2 is 20.  Mary has 22 chocolates.

which holds the more capacity 0.75 litres or 350ml

Answers

Answer:

0.75 liters

Step-by-step explanation:

1000ml in 1 liter so 0.75*1000=750ml

750ml > 350ml

40x^-4 y^-6/(over)10x^-5 y^5

Answers

Answer:

4x/y¹¹

Step-by-step explanation:

1) take out constants

40/10 * x⁻⁴y⁻⁶/x⁻⁵y⁵

2) simplify 40/10 to 4

4 * x⁻⁴y⁻⁶/x⁻⁵y⁵

3) Use Quotient Rule: xᵃ/xᵇ=xᵃ⁻ᵇ

4x⁻⁴⁺⁵y⁻⁶⁻⁵

4) Simplify -4 + 5 to 1

4x¹y⁻⁶⁻⁵

5) simplify -6-5 to -11

4x¹y⁻¹¹

6) use rule of one: ₓ¹=ₓ

4xy⁻¹¹

7) use negative power rule: x⁻ᵃ=1/xᵃ

4x * 1/y¹¹

8) simplify

4x/y¹¹

need help solving this

Answers

Answer:

x ≈ 41.6°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{JK}{KL}[/tex] = [tex]\frac{80}{90}[/tex] = [tex]\frac{8}{9}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{9}[/tex] ) ≈ 41.6° ( to the nearest tenth )

If xy + xb + ya + ab = 32 and x + a = 4 , then x + b = ​
and i will give BRAINLIEST

Answers

Answer:

Step-by-step explanation:

If you're actually looking for y + b rather than x + b

Then

xy + xb + ya + ab = (x + a)(y + b) = 32

                                        4(y + b) = 32

                                           y + b = 8

otherwise we have a situation with only two equations and four unknowns. This cannot be resolved without further information.

Pure acid is to be added to a 10% acid solution to obtain 90L of 81% solution. What amounts of each should be used?
How many liters of 100% pure acid should be used to make the solution?

Answers

Answer:

Step-by-step explanation:

let X be the quantity of 100% acid

let Y be the quantity of  10% acid

X + Y = 90

Y = 90 - X

         X(100) + Y(10) = 90(81)

X(100) + (90 - X)(10) = 90(81)

   100X + 900 - 10X = 7290

                         90X = 6390

                              X = 71 L

The point (3, 3) is in what quadrant? 2,1,3,4

Answers

Answer:

1

Step-by-step explanation:

(3,3) has a positive x value and a positive y value which means it is in the first quadrant

Suppose a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year. Is this event unusual? Specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year? Know the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009.

Answers

Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.

Given that a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year, to determine if this event is unusual, and specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year knowing that the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009, the following calculation must be performed:

0.009 x 0.009 x 0.009 x 0.009 x 0.009 = X 0.000000000059049 = X 0.000000000059049 x 100 = X 0.0000000059049% = X

Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.

Learn more about maths in https://brainly.com/question/14696440

Molly went to play miniature golf on Monday, when it cost $7 to rent the club and ball, plus $1 per game. Sharon went Thursday, paying $2 per game, plus rental fees of $4. By coincidence, they played the same number of games for the same total cost. How much did each one spend?

Answers

Answer:

Molly played 4 games

which statement is true

Answers

Morgan earns more money per hour on Friday

you walk 3/4 miles to a grocery store. Then you walk another 1/5 miles to a shoe store. How many miles have you walked in all?

Answers

Answer:

19/20 miles

Step-by-step explanation:

3/4 + 1/5

3/4 = 0.75

1/5 = 0.2

3/4 + 1/5

= 0.75 + 0.2

= 0.95

= 95/100

= 19/20

Therefore,

the miles you have walked in all is 19/20.

Find the sum. 2/5(d-10)-2/3(d+6)

Answers

Answer:

-4d

Step-by-step explanation:

L.c.m=15

15×2/5(d-10)-2/3×15(d+6)

3×2(d-10)-2×5(d+6)

6(d-10)-10(d+6)

6d-60-10d-60

6d-10d-60-60

-4d-0

-4d

Solve for X
5x-8 Answer is not 4.5 or 9/2

Answers

Answer:

[tex]{ \rm{5x - 8 < x + 10}} \\ \\ { \rm{5x - x < 10 + 8}} \\ \\ { \rm{4x < 18}} \\ \\ { \rm{x < 4.5}}[/tex]

Solving for x in the inequality gives us;

x < 4.5

Inequality

We are given the inequality;

5x - 8 < x + 10

The first step is to use addition property of equality to add 8 to both sides;

5x - 8 + 8 < x + 10 + 8

5x < x + 18

Use subtraction property of equality to subtract x from both sides to get;

5x - x < x + 18 - x

4x < 18

Using division property of equality, we have;

x < 18/4

x < 4.5

Read more on inequalities at; https://brainly.com/question/25275758

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