Mathematics College

1.)
a^2b^3
---------- <-----write in expanded form.
cd


2.)what is the exact solution to the equation 4^5x=3^x-2

Please show all work I've been struggling to understand these questions!!!! thank you so much <3

Answers

Answer 1

Answer:

1. Expanded form of [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)

2.Exact solution x = -0.376

Step-by-step explanation:

Solution:

First we have to write the Expanded Form of [tex]a^{2} . b^{3}[/tex], Let's do it.

1) [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)

Hence,

Expanded form of [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)

2) [tex]4^{5x} = 3^{x-2}[/tex]

Now, we have to find out the exact solution of the above equation:

In order to equate the exponents, we need to make sure the bases are same. Or we simply can use logarithm to solve the above equation.

So,

We are using logarithm to solve this equation.

Let's break this down:

[tex]4^{5x} = 3^{x-2}[/tex]

Taking log on both sides.

log[tex]4^{5x}[/tex] = log[tex]3^{x-2}[/tex]  

[tex]5xlog(4)[/tex] = [tex](x-2)log(3)[/tex]

Dividing both sides by log(4)

[tex]5x[/tex] = (x-2) [tex]\frac{log(3)}{log(4)}[/tex]

value of log(3) = 0.4771

value of log(4) = 0.6020

[tex]5x[/tex] = (x-2) [tex]\frac{log(0.4771)}{log(0.6020)}[/tex] =

5x = (x-2)0.792

5x = 0.792x - 1.584

by rearranging the equation, we get:

0.792x - 5x = 1.584

x(0.792 - 5) = 1.584

x(-4.208) = 1.584

x = -1.584/4.208

x = -0.376

Exact solution x = -0.376

Related Questions

a) This problem involves 8-digit binary strings such as 10011011 or

00001010.

i How many such strings are there?

ii. How many such strings end in 0?

iii. How many such strings have l's for their second and fourth digits?

iv. How many such strings have l's for their second or fourth digits?

b) Find how many 9-digit numbers can be made from the digits 1, 2, 3, 4, 5, 6,

7, 8, 9 if repetition is not allowed and all the odd digits occur first (on the

left) followed by all the even digits.

c) How many permutations of the letters A, B, C, D, E, F, G are there in which

the three letters ABC appear consecutively, in alphabetical order?

Answers

Answer:

a)

i) With an eight digit binary number, there are 2⁸, or 256 possible combinations.

ii) Each digit is set to 1 or 0 for exactly half of all combinations.  This means that half of all strings, or 256 / 2 = 128 strings end with a zero.

iii) 3/4, or 128 + 64 = 192 of the combinations have a 1 for either the second or fourth digit.  If you consider:

Half of all digits will have the second bit set to 1

Half of all digits will have the fourth bit set to 1

Half of those will overlap

Then that's half the digits, plus half the digits, minus half of half the digits. 1/2 + 1/2 - 1/4 = 3/4

iv) This is a duplicate of iii, so again, 192

b) If we're allowed to repeat the usage of the digits, then answer would be the number of values available to the power of the number of digits used.  We're allowed six distinct digits, so the total combination of 9 digit numbers would be 6⁹, or 10077696

c) In this case we can look at it simply as permutations of the set {"ABC", "D", "E", "F"}, which gives us 4! which equals 24

Anyone know the answer?

Answers

Answer:

5 feet = 152.4 centimeters      10 inches =25.4

Step-by-step explanation:

I learned from my classes of how to convert feet to centimeters and etc.

152.4,25.4 hope this works

Alex has 21 marbles. Zach has 19 times as many marbles as Alex. How many marbles does Zach have?

Answers

Answer:

399

Step-by-step explanation:

Zach has 21 * 19 marbles

Answer:

zach has 399 marbles

Step-by-step explanation:

according to the caluation

Define the domain and range of the relation. (MAFS.912.F-IF.2.4)
{(2,3), (0, 3), (4, 2), (5, 6)}
domain
range

Answers

Domain is the x value range is y
Domain is 2,0,4,5
Range is 3,2,6
uh... i’m not sure sorry .....

Paul withdrew $17.25 from his savings account every week for 3 weeks. Which equation is the best choice to help him determine the total amount of money he withdrew?

Answers

17.25 times by 3 I’m not sure if this is 100% correct

Answer: (3)(−17.25) = −51.75; he withdrew $51.75

Step-by-step explanation:

hope it helped xx

(-5b^3) (-3b^6)

Solve the equation

Answers

Answer: 15b^9

Explanation:

-5*-3=15

b^3*b^6=b^9

The total surface area of this cuboid is 76 cm.
Find the value of x.
x cm
4 cm
5 cm​

Answers

Answer:

76×5+4

380+4=384

Simplify.
3y - 4x + 6x - y
The simplified expression is???

Answers

Answer:

2y-4x+6x

=2y+2x

Step-by-step explanation:

Answer:

2x+2y

Step-by-step explanation:

Let's simplify step-by-step.

3y−4x+6x−y

=3y+−4x+6x+−y

Combine Like Terms:

=3y+−4x+6x+−y

=(−4x+6x)+(3y+−y)

=2x+2y

Write an algebraic expression for each verbal description. a number
!!please help me my assignment is due today at 9!!!

Thirty percent of the green house flowers are added to 25 ferns for the
school garden.

Answers

I believe it may be written like this:
.3g+25f

The algebraic expression is 0.3G+25F

What are algebraic expression?

An algebraic expression is a sentence with a minimum of two numbers or variables and at least one mathematical operation.  

First, we can use G to represent green house flowers and F to represent ferns.

Then thirty percent of the green house flower can be represented by 0.3G.

25 ferns can be written as 25F.

The algebraic expression for the given verbal description is 0.3G+25F.

To learn more about algebraic expressions, use the below link:

https://brainly.com/question/953809

#SPJ5

A company that makes​ hair-care products had 8,000 people try a new shampoo. Of the 8,000 ​people, 32 had a mild allergic reaction. What percent of the people had a mild allergic​ reaction?

Answers

Answer:

i think it 0.4%

Step-by-step explanation:

32/8000=0.004
0.004=0.4%

Suppose a friend tells you she paid a total of $20,500 for a car, and you’d like to know the car’s list price (the price before taxes) so that you can compare prices at various dealers. Find the list price of the car if your friend bought the car in:

Roswell, where the sales tax is 6.5%

Answers

Given :

Total amount paid for the car is, A = $20,500.

Sales tax is 6.5%.

To Find :

The list price i.e. price without tax.

Solution :

Let, list price is P.

P = A - 0.65A

P = A( 1 - 0.65 )

P = 20500×( 1 - 0.065 )

P = $19167.5

Therefore, the list price of car is $19167.5  .

Please help, I’m so close to passing math

Answers

Answer:

I believe it is the last choice

Step-by-step explanation:

square have equal sides      area= length x width

9x9=81

6x6=36

9 to power 2 is 81

6 to power 2 is 36

So the equation is 81-36

Answer: its the last choice i literally just took that test

Step-by-step explanation:

The perimeter of the triangle below is 10x - 3

Show how to solve

Answers

10x - 3 = x + 2 + 2x - 1
10x - 3 = 3x + 1
-3x on both sides
7x - 3 = 1
-1 on both sides
7x - 4

(Check 7x - 4 by adding them all up to equal 10x - 3)
x + 2 + 2x - 1 + 7x - 4 = 10x - 3
combine liked terms
10x - 3 = 10x - 3

Answer:
D) 7x - 4

Can someone help me with this question?
36x245

Answers

8,820 is the answer. 200x30=6000, 40x30= 1200, 30x5=150, 200x6=1200, 40x6=240, and 6x5=30. Lastly, you would want to add them together to get the total/sum which is 8820. (don’t ask me how I do it).

An architect is drawing a house with a living room measuring 18 feet in length. On the blueprint, the length of the living room is 9 inches. What is the correct scale on the architect’s blueprint?
Group of answer choices

1.5 inches = 2 feet

1.5 inches = 3 feet

1.5 inches = 3.5 feet

1.5 inches = 162 feet

Answers

Answer:

i think it is 3.5 and 3

Step-by-step explanation:

A customer wants to book a room with a seaview.
You show her 4 options but only 3 have sea views.
What fraction has a seaview?

Answers

3/4 is the fraction

lol

Hw help ASAPPP
+10PTS

Answers

Y=1/4x +5 is the answer

PLEASE ANSWER 16 17 18 CORRECTLY I WILL MARK BRAINLIST

Answers

Answer:

A   A  B

Step-by-step explanation:

Cost of shoes $29.95
Markup: 20%
What is the new cost?

Answers

New cost = original price x (1 + markup)

New cost = 29.95 x ( 1 + 0.20)

New cost = $35.94

I think the answer is 35.94

Five full creates of walnuts weigh 195 pounds, whereas an empty crate weighs 10 pounds. How much do the walnuts alone weigh?

Answers

I’m not sure if you want the weight of all the walnuts or the weight of the walnuts in each individual crate, so the answer is either 29 pounds or 145 pounds.
195/ 5= 39, so each crate weighs 39 pounds. Subtracting 10, the walnuts in each crate weigh 29. Since there are 5 crates, multiply 5 by 29 and you get 145 pounds.

Ok I’ll ask again cuz one of them said tomorrow and I should watch Jojo something lol so here’s the question shall I k^^* myself today or tomorrow

Answers

Answer:

never:)

Step-by-step explanation:

Answer:

Never! You are loved and have a purpose in life. Times may be hard at the moment but everything will get better.

Step-by-step explanation:

true or false need help asap 67%
33%
32% which one is true

Answers

Answer:

You need to attach something to this?

Step-by-step explanation:

I could help you but theres nothing here to see?

I don’t seeeeee a picture I only seeeeee percents

5cd.(-cd)
Monomials and polynomials

Answers


If you can reword this I might be able to help you but I don’t understand it in this wording 5cd

True or False: If an equation has different slopes, it has no solution. ​

Answers

Answer:

it's true. because it has more type of sums and head pain will come

Answer:

When two equations have the same slope but different y-axis, they are parallel. Since the two equations never intersect, the system has no solutions.

you can decide your answer from that explanation!

simplify pls

8(4x-12)

Answers

Answer:

32x-96

Step-by-step explanation:

8 · 4x = 32x

8 · 12 = 96

Subtract the number 6498 from the product of six doubles, four triples and one five. Which number did you get?​

Answers

Answer:

the answer will be 132

Step-by-step explanation:

''.''

Answer:

2142

Step-by-step explanation:

product of six doubles, four triples and one five: 2*2*2*2*2*2*3*3*3*3*5 =8640

8640 - 6498 = 2142

Wish this is right.

A home-improvement store sold blinds for $35. A customer signed up for a free membership card and received a 7% discount off the price. Sales tax of 7% was applied after the discount. What was the final price of the blinds?

Answers

Answer:35

Step-by-step explanation:

35x93/100=32.55

32.55x107/100=35

Desiree writes songs for her band. her first song is 3 1/2 minutes long. Her second song is 1 1/2 times as long as her first song. her third song is 2/3 times as long as her second song. How many minutes long are the second and third songs?

Answers

3 1/2 x 1 1/2= 7/2 x 4/2= 28/4. 28/4 x 2/3= 56/12. 56 divided by 12 is 4 8/12. The second song is 7 minutes is long and the third song is 4 8/12 minutes long.

Whoever answers first, I will give Brainliest! :)

Answers

Answer: b there are 12flasses

Step-by-step explanation:

Provide a radian measure of an angle that is 5/8 of a revolution counterclockwise from the x-axis.

Answers

I’m pretty sure but not so sure I think it is 180
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