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

[(1 1/5−2/5)⋅(−3/4)3]÷(−9)

Answers

Given that:

[{1(1/5)−(2/5)⋅(−3/4)3}]÷(−9)

= [{(5+1)/5 - (2/5).(-3/4)3}]÷(-9)

= [{(6/5) - (2/5).(-3/4)3}]÷(-9)

= [{(6/5) - (2/5).(-3/4)3}]÷(-9)

= [{(6/5) - (2/5).(-3*3)/4}]÷(-9)

= [{(6/5) - (2/5) . (-9/4)}]÷(-9)

= [{(6/5) - (2/5) × (-9/4)}]÷(-9)

= [{{6/5) - {{2*(-9)}/{5*4}]}]÷(-9)

= [{(6/5) - {-9/(5*2)}}]÷(-9)

= [{(6/5) - (-9/10)}]÷(-9)

Take the LCM of 5 & 10 is 10.

= [{(6*2 + 9*1)/10}]÷(-9)

= [{(12+9)/10}]÷(-9)

= [{-(21/10)}]÷(-9)

= -(21/10) ÷ (-9)/1

= -(21/10) × (1/9)

= {(-21*1)/(10*9)]

= {-21/90)

= {(-21÷3)/(90÷3)}

= -9/30

= {(-9÷3)/(30÷3)}

= (-3/10) = -3/10 Ans.

Explain how the ratios 5 tacos for every 2 guest and 2 tacos for every 5 guests are different. Include a model in your explanation.

Answers

Answer:

5 tacos for 2 guests would mean more for each person, while 2 tacos for 5 guests would mean less for each person

QUESTION 17 PLEASE HELP ME ASAPP

Answers

Answer: change over time
Explanation: it is decreasing in height therefore is decreasing in altitude

Hey there!

• If it CHANGES it means your temperature/time changes a bit overtime

• If it CONSTANT your temperature/time remains the same

So, basically to this question it was INCREASED then it was DECREASED

Therefore, your answer is: “Option A. “

Because it didn’t stay same

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Camden has a loyalty card good for a 17% discount at his local hardware store. What number should he multiply the prices on the tags by to find the price he would have to pay, before tax, in one step?

Answers

Answer:

0.83

Step-by-step explanation:

Let the price is x.

With 17% discount it becomes:

x - 17% of x =x - 0.17x = 0.83x

The number we need is 0.83

Solution,

Assume That The Price is x

When Will Put It in Equation,

[tex] \frak{ \bigstar}{ \rm{ {We \: Will \: Get,}}}[/tex]

[tex]{ \longmapsto{ \sf{x-17 \% \: of x =}}}[/tex][tex]{ \longmapsto { \sf{x-0.17x}}}[/tex]0.83

Hence, Required Price is 0.83

Simplify the expression

-4 + 3 + 5 =

Answers

Answer:

4

Step-by-step explanation:

-4+3=-1

-1+5=4

jorden claims that x^2+3=12 is exponential equation. is jorden correct

Answers

No.
Exponential functions take the form y = a^x

The function given is a quadratic function, as the highest exponent of x is 2

I want a way to solve such a problem​

Answers

Answer:

11.2

Step-by-step explanation:

The table below shows the deposits (+) and withdrawals ( - ) each week for a newly opened bank account with a starting balance of $100.
DEPOSITS AND
WITHDRAWALS
Week 1+120
Week 2 -100
Week 3 +50
Week 4 P
Week 5 +200
Week 6 -100
Week 7 -25
Week 8 +50
Part A: What is the value of p if the account shows a zero balance after 4 weeks?

Answers

From the given table, the positive sign connote deposit while the negative sign connotes withdrawal.

If the account shows a zero balance after 4 weeks, we will take the sum of all deposits and withdrawals for the first four weeks and equate to zero as shown:

[tex]+120+(-100)+50+p=0[/tex]

Open the parenthesis:

[tex]+120-100+50+p=0\\20+50+p=0\\70+p=0[/tex]

Subtract 70 from both sides

[tex]70+p-70=0-70\\p=-70[/tex]

Hence the value of p if the account shows a zero balance after 4 weeks is -70

Learn more on deposits and withdrawals here: https://brainly.com/question/11443019

please help me out on this one​

Answers

Answer:

6/6 or 1

Step-by-step explanation:

bow tie method

-8=-9 + √2x - 1
find a h and k​

Answers

Answer:

x=2?

Step-by-step explanation:

Please help!! I have less than an hour to turn this in!

Answers

Answer:

8 × 10¹

Step-by-step explanation:

don't panic. just breathe deeply and then think logically.

0.002 ... what is that ? 2 10ths ? 2 hundredths ? 2 thousandths ? 2 tenthousandths ?

the 3rd position after the decimal point is for 1/1000.

and that means 10^-3. in the same way as 1000 is 10³.

so, it is 2 × 10^-3.

the other rounded number is then 4 × 10⁴.

now, we are multiplying both numbers

2×10^-3 × 4×10⁴

what do we do ?

we combine the same types of factors, like the basic constants : 2×4 = 8

and 10^-3 × 10⁴.

what hairball when we multiply the same base number with exponents ? we add the exponents :

10^-3 × 10⁴ = 10¹ = 10

because -3 + 4 = 1

and so, the result is

8 × 10¹

6 divided by x squared​

Answers

Answer:

I think x should be equal to 0.

What number is being factored in this factor tree?





A. 34
B. 68
C. 136
D. 272

Answers

Answer:

C 136

Step-by-step explanation:

2×68= 136

...........

....

3
Johnny has been hired to draw a mural on the window of the pet store. The scale drawing he is using is shown below.
4.5 cm
6 cm
If 1 centimeter represents 10 inches on the mural, what is the actual height and width of the hamster that he will be drawing on the
mural?
OA.
66 in by 49.5 in
ОВ.
90 in by 120 in
Od
6 in by 4.5 in
OD. 60 in by 45 in

Answers

Answer:

OD 60 in by 45 in

Step-by-step explanation:

what is the y intercept of the graph

what is the slope ​

Answers

Answer:

y-intercept = 1

slope = 4

Step-by-step explanation:

The y-intercept is where the line intersects with the y.

And the slope is rise over run, so it rises 4 and walks over 1, therefore the slope is [tex]\frac{4}{1}[/tex] which simplifies to 4.

Hope this helped! :)

Answer:

y intercept (0,1)

slope 4

Step-by-step explanation:

The y intercept is where the graph crosses the y axis

The graph crosses at y =1

(0,1)

We can find the slope by taking rise over run

The graph rises 4 units ( goes up 4 units)

Then goes to the right 1 units

The slope is 4/1 = 4

find three solutions for 9x - 2y = 18​

Answers

Answer:

[tex](x,y) = \left(5,\dfrac{27}2 \right), \left(0,-9), \left(9, -\dfrac 92 \right)[/tex]

Step-by-step explanation:

Factor. 9(p-1)+(p-1)^2

Answers

Answer:

9(−1)+(−1)(−1)Step-by-step explanation:

[tex]9(p-1)+(p-1)^2[/tex]

[tex]p^2+7p-8[/tex]

[tex]=(p-1)(p+8)[/tex]

Answer:[tex](p-1)(p+8)[/tex]

Find the missing number of each unit rate.

20/4=?/1
10/15=?/1

Answers

Answer:

Step-by-step explanation:

divide 20 by four

20/4=5/1

now 10 and 15 can both be divided by 5 since 5 is the greatest common factor

10/15=2/3

Answer:

5 for the first 2/3 for the second

Step-by-step explanation:

just divide the numerator by what ever makes the denominator 1

4/4=1 so divide 20 by 4 which is 5

15/15 = 1 so 10/15 is 2/3

Mrs Ang bought k apples at 50% each from a supermarket. How much
change did she receive if she paid $10 to the cashier? Express your answer
in cents.

Answers

Answer:

The apples may have costed 0.50 cents each, and she may have bought 10, which would result in her paying 10 dollars, and receiving 5 dollars in change.

Step-by-step explanation:

Multiply 10 (the amount she gave to the cashier) by 0.50%, it equals 5, so that's how much she paid, and since she gave a 10 dollar bill, she should get 5 dollars in change.

T^T

Which statement is generally true about retirement?
A. Your income will increase, while your expense will stay the same.
B. Your income will decrease, while your expenses will increase.
C. Your income will increase, while your expenses will decrease.
D. Your income will decrease, while your expenses will stay the same.

Answers

The general statement that is true about retirement is B. your income will decrease, while your expenses will increase.

Retirement is the leaving of one's of occupation. This means you cease to be involved in active service in a job or occupation especially when one is considered old and of retirement age.

During retirement, retirement benefits and pension are usually made available to retirees. However, one's income will come to a decline which makes most people scared of retirement. Keeping up with the standard of living they are used to becomes difficult as income to sustain such may not be available.

Therefore, the general statement that is true about retirement is B. your income will decrease, while your expenses will increase.

Learn more about retirement on:

https://brainly.com/question/3063811

Answer:

It's B

Step-by-step explanation:

Just took it

the perimeter of a regular Pentagon is 100m how long is each side​

Answers

Answer:

20 cm is the answer.

20

Step-by-step explanation:

the parameter of any shape is the sum of all sides and since the pentagon has 5 sides we just have to divide the parameter by 5

100÷5=20

Q.


A circle has a radius of 21 cm. Then determine the area!


EASY​

Answers

Hello there! :-)

The formula for finding the area of a circle is

[tex]A=\pi r^{2}[/tex]

Notice that only the radius is squared.

We are given the radius of the circle: 21 cm.

We plug the value of r into the formula:

A=π(21)²A=π(441)A=1,385 cm

Hope this helps. Use the comment section to clarify your doubts.

Answered by

~A teen whose hobby is helping people with their homework

#LetItSnow

Good luck.

Answer:

A=1.386 cm²

Step-by-step explanation:

[tex]\sf\bf A = \pi \times r \times r[/tex]

[tex]\sf\bf = \frac{22}{7} \times 21 \times 21[/tex]

[tex]\sf\bf = \frac{22}{\cancel{7}} \times \cancel{21} \times 21[/tex]

[tex]\sf\bf = 22 \times 3 \times 21[/tex]

[tex]\sf\bf = 66 \times 21[/tex]

[tex]\sf\bf = 1.386 \: {cm}^{2}[/tex]

Sierra left $4.50 as a tip for a waiter. This was 18% of the bill before the tip. How much was her bill before adding the tip?

Answers

Answer:

25

Step-by-step explanation:

what is 4.5 18% of

100 / 18 = 5.56

4.5 x 5.55... = 25

$25

4.50 = 18%
0.25 = 1%
25 = 100%

According to his running log, Baldwin averaged 4 miles per week last month and 25% more this month. How much did he average this month?

Answers

4(1.25) = if it’s only one month then it’s 5 miles

Answer:

4(1.25) = if it’s only one month then it’s 5 miles

Step-by-step explanation:

Please mark brainliest

The average price of an item is $42 with a standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation!

Answers

Step-by-step explanation:

standard deviation of $3

Find a 98% confidence interval about the mean (one decimal place).

Is a value of X=48 unusually high or is it normal? Choose correct explanation

2x-y=3
X+y=3
Slove equations algebraially

Answers

These are simultaneous equations

Add the two equations together and get

3x = 6

x = 2

2 + y = 3

y = 1

2m>30
what is the answer to this

Answers

Answer:

m>15

Step-by-step explanation:

Divide both sides by 2

Hello there! :-)

This is a one-step inequality, which means we can solve it in one step.

The goal is to find m.

To isolate m, we divide both sides by 2:

m>15

Remember to divide both sides by 2.

Therefore, m>15 (this means m is greater than 15)

Hope it helps. Use the comment section to clarify your doubts.

Answered by

~A felicitous teen who helps others :-)

Good luck with your studies. :)

click on the measure of the triangle.

Answers

Answer:

a

Step-by-step explanation:

because a

There is no image!
Try reposting with the image of the question.
:)

A right triangle has legs of lengths 7.5 ft and 8.0 ft. Find the length of the hypotenuse.

Answers

Answer:

multiply

Step-by-step explanation:

3.-Las 80 habitaciones de un motel se podrían alquilar todas las noches si el director cobrará
40 € o menos por habitación. Si se cobra (40+x) € por habitación, entonces 2x habitaciones
permanecerán vacantes. Si cada habitación alquilada le cuesta al director 10 € al día y cada
habitación no alquilada 2 € al día, ¿qué precio debería cobrar el director por habitación para
maximizar su beneficio diario?
4.- Un fabricante de automóviles vende 2000 coches al mes, con un beneficio medio de 1000 €
por coche. Las prospectivas de mercado indican que por cada 50 € de descuento que el
fabricante ofrezca a los compradores podría vender 200 coches más al mes.
¿Cuánto descuento debería ofrecer para maximizar el beneficio mensual?

Answers

3) Para maximizar su beneficio diario el director debería cobrar cada habitación a €56.

4) El fabricante debería ofrecer un descuento de 150€ para maximizar su beneficio mensual.

3- Dado que las 80 habitaciones de un motel se podrían alquilar todas las noches si el director cobrara 40€ o menos por habitación, y si se cobra (40+x) € por habitación, entonces 2x habitaciones permanecerán vacantes, para determinar, si cada habitación alquilada le cuesta al director 10 € al día y cada habitación no alquilada 2 € al día, qué precio debería cobrar el director por habitación para maximizar su beneficio diario, se deben realizar los siguientes cálculos:

80 x 40 - 80 x 2 = 304070 x 50 - 10 x 10 - 70 x 2 = 326060 x 60 - 20 x 10 - 60 x 2 = 328065 x 55 - 15 x 10 - 65 x 2 = 329566 x 54 - 14 x 10 - 66 x 2 = 329264 x 56 - 16 x 10 - 64 x 2 = 329663 x 57 - 17 x 10 - 63 x 2 = 3295

Por lo tanto, para maximizar su beneficio diario el director debería cobrar cada habitación a €56.

3) Dado que un fabricante de automóviles vende 2000 coches al mes, con un beneficio medio de 1000 € por coche, y las prospectivas de mercado indican que por cada 50 € de descuento que el fabricante ofrezca a los compradores podría vender 200 coches más al mes, para determinar cuánto descuento debería ofrecer para maximizar el beneficio mensual se debe realizar el siguiente cálculo:

1000 x 2000 = 2.000.000900 x 2400 = 2.160.000800 x 2800 = 2.240.000700 x 3200 = 2.240.000600 x 3600 = 2.160.000850 x 3000 = 2.550.000

Por lo tanto, el fabricante debería ofrecer un descuento de 150€ para maximizar su beneficio mensual.

Aprende más sobre matemática en https://brainly.com/question/25809832

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