Solve for the values of x for each of the following exponential equations and inequalities.
1. 82− = 2
3. 5 = 25−2
4. 3+2 ≥ 27
5. 43 = 8−1

Answers

Answer 1

Answer:

8

2−x

=2

8^{2-x}=8^{1/3}8

2−x

=8

1/3

2-x=\dfrac{1}{3}2−x=

3

1

x=\dfrac{5}{3}x=

3

5

2.

(\dfrac{1}{2})^{x}<\dfrac{1}{8}(

2

1

)

x

<

8

1

(\dfrac{1}{2})^{x}<(\dfrac{1}{2})^{3}(

2

1

)

x

<(

2

1

)

3

x>3x>3

3.

5^x=25^{x-2}5

x

=25

x−2

25^{x/2}=25^{x-2}25

x/2

=25

x−2

\dfrac{x}{2}=x-2

2

x

=x−2

\dfrac{x}{2}=2

2

x

=2

x=4x=4

4.

3^{x+2}\geq273

x+2

≥27

3^{x+2}\geq3^33

x+2

≥3

3

x+2\geq3x+2≥3

x\geq1x≥1

5.

4^{3x}=8^{x-1}4

3x

=8

x−1

2^{6x}=2^{3x-3}2

6x

=2

3x−3

6x=3x-36x=3x−3

3x=-33x=−3

x=-1x=−1

Step-by-step explanation:


Related Questions

Can somebody help me with number 5 and number 8

Answers

Answer:

8.b. 5.d

Step-by-step explanation:

I think. because of space is not to famielier on me and between of point i think

Can you please tell me the answer please

Answers

Answer:

34°

Step-by-step explanation:

21x - 1 + 11x +1 + 26x + 6 = 180

58x -1 +1 +6 = 180

58x +6 = 180

58x = 174

x = 3

11 × 3 + 1 = 34

heeelllllllllpppppppp meeeeee

Answers

Answer:

32

Step-by-step explanation:

36-4

Use Pythagorean theorem

Answer:

B=4

Step-by-step explanation:

I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!

Answers

Answer:

w= 8/7

Step-by-step explanation:

1. divide the numbers

[tex]12w-1*10=6-2w[/tex]

2. multiply the numbers

[tex]12-10=6-2w[/tex]

3. rearrange terms

[tex]12-10=-2w+6[/tex]

4. add 10 to both sides of the equation

[tex]12w-10+1-=-2w+6+10[/tex]

5. simplify

[tex]12w=-2w+16[/tex]

6. add 2w to both sides of the equation

[tex]12w+2w=-2w+16+2w[/tex]

7. simplify

[tex]14w=16[/tex]

8.divide both sides of the equation by the same term

14w/14 = 16/14

9. simplify

w = 8/7

Answer:

[tex]w = 2[/tex]

Step-by-step explanation:

[tex] \frac{(12w - 20)}{2} = 6 - 2w[/tex]

[tex]6w + \frac{ - 20}{2} = 6 - 2w[/tex]

[tex]6w + \frac{( - 10.2)}{(1.2)} = 6 - 2w[/tex]

[tex]6w + 10 = 6 - 2w[/tex]

[tex]6w - 10 + 2w = 6 - 2w + 2w[/tex]

[tex]6w + 2w - 10 = 6 - 2w + 2w[/tex]

[tex]8w - 10 = 6 - 2w + 2w[/tex]

[tex]8w - 10 = - 2w + 2w + 6[/tex]

[tex]8w - 10 = 6[/tex]

[tex]8w - 10 + 10 = 6 + 10[/tex]

[tex]8w = 6 + 10[/tex]

[tex]8w = 16[/tex]

[tex] \frac{8w}{8} = \frac{16}{8} [/tex]

[tex]w = \frac{16}{8} [/tex]

[tex]w = \frac{2.8}{1.8} [/tex]

[tex]w = 2[/tex]

[tex]Thank \: you!!![/tex]


3. Simplify the expression (x3 - 5x2 + 7x - 12) = (x – 4) using long division. Show your work.
Answer:

Answers

Answer:

x^2-x+3

Step-by-step explanation:

(x^3-5x^2+7x-12)÷(x-4)

x^3−5x^2+7x−12

Factors of 12,

1,2,3,4,6,12

Substitute 4 into x. Since the result is 0, x-4 is a factor..

4^3−5×4^2+7×4−12=0

x-4

           

        x^2      -x             3

x-4 |  x^3   -5x^2 7x    -12

        x^3   -4x

                -x^2   7x  -12

                -x^2   4x

                          3x  -12

                          3x  -12

                               

x^2−x+3

 

(x^2−x+3)(x−4)

        x−4

(x^2−x+3)

Answer = x^2-x+3

Hopes this helps

You deposit $200 in a savings
account that pays a simple
interest rate of 3.25% per year.
How much interest will you earn
after 5 years?

Answers

Answer:

$16.25

Step-by-step explanation:

First, you have to find 3.25*5 which is 16.25.

16.25 is the percent rate of your total interest over the course of 5 years.

In other words, you have to do 200*0.1625 which is 32.5.

So, your answer is $16.25.

Good luck!

$16.25 I took the test

1) Eight times the difference between a number and seven, is the same as when five times
the number is increased by four. Find the number.

Answers

Tip: Go step-by-step

Let the number = x

Eight times the difference between a number and seven.. = 8(x-7)

is the same as... =

the number increased by 4.. x+4

8(x-7)=x+4

Distribute

8x-56=x+4

Subtract x from both sides

7x-56=4

Add 56 to both sides

7x=60

x=60/7

Customer account “numbers” for a certain company consists of 2 letters followed by 2 single-digit numbers. How many different account numbers are possible if repetition of letters and digits are allowed?

Answers

Answer:

67600

Step-by-step explanation:

Let the format be:

LLDD- where L stands for letter and D- digit

For each L we have 26 (English alphabet) and for each D we have 10 options.

Number of possible accounts:

26*26*10*10 = 67600

The bearing of point Y from point X is 070°.
The bearing of point Z from point Y is 145°.
The bearing of point Z from point X is 100°.
Find the bearing of point X from point Z.

Answers

Answer:

i cant understand sorry

A principal of $2200 is invested at 6.25% interest, compounded annually. How much will the investment be worth after 13 years

Answers

Answer:

Let S = Sum after 13 years

So = amount invested

t = time in years

i = annual interest rate = .0325

The S = So(1+i)t = $2,200(1.0325)13 = $3,334.21

After 13 years, the investment will be worth approximately $4365.67. To calculate the future value of the investment after 13 years with annual compounding interest, we can use the formula for compound interest.

Future Value (FV) = Principal (P) * (1 + (Interest Rate (r) / 100))^Time (n)

Where:

P = Principal (initial investment)

r = Annual interest rate (as a decimal)

n = Number of years

Given:

Principal (P) = $2200

Annual interest rate (r) = 6.25% = 6.25/100 = 0.0625 (as a decimal)

Number of years (n) = 13

Now, let's calculate the future value:

FV = $2200 * (1 + 0.0625)^13

FV = $2200 * (1.0625)^13

FV ≈ $2200 * 1.984396861  (rounded to 9 decimal places)

FV ≈ $4365.672097  (rounded to 2 decimal places)

After 13 years, the investment will be worth approximately $4365.67.

To know more about investment:

https://brainly.com/question/29074561

#SPJ2

(20 Points) What is the value of x?

Answers

x would equal 41 cuz 3x-18=105

The degree of the polynomial function f(x) is 4.The roots of the equation f(x)=0 are −6, −2, 1, and 3.Which graph could be the graph of f(x)?

Answers

It’s a s 7.47 because of the five and six

six cocker spaniels have a total weight of 192 pounds. Five golden retreivers have a average weight of 71 pounds. what is the average weight of all 11 dogs.

Answers

Answer:

23.9lbs or 24lbs

Step-by-step explanation:

This may not be correct so don't bet your first born on it

The center of the circle whose equation is (x + 2)² + (y - 3)² = 25 is

Answers

Answer:

The center of the circle is at: C=(−2,3).

The radius of the circle is r=5.

Step-by-step explanation:

A circle with center at (h,k) and a radius of r has equation (x−h)2+(y−k)2=r2.

In this example our circle equation can be written as:

(x−(−2))2+(y−3)2=(5)2

So, we have: h=−2 , k=3 and r=5.

HELP ME!!!! MY HOMEWORK IS SOOO CONFUSING

Answers

i thing the answer is D the last chart

What did you learn in this lesson about the value of leaving the money invested for long periods of time? How can you apply this to retirement?

Answers

Answer:

65435675e

Step-by-step explanation:

12456764 br5654365

6) Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1,-1).
A) y = 2x + 1
B) y = 2x + 3
C) y = 4x + 3
D) y = 4x + 5

Answers

Answer:

A Y=2X + 1

Step-by-step explanation:

2x wouldn't the same because of the fact that is Is a parallel line and setting the slope to 1 caused it to pass through (-1,-1)

Given that lines a and b are parallel:
If m48 = (-x + 13), and
= +
m42 = (9x - 27),

Answers

Answer:

[tex]x= 9m+69​ ,m 48​ =− 9m​ + 316​[/tex]

 

 

 

Austin and his wife go out to dinner. Their bill is $59.36. They want to leave a 19%
tip, and there is a sales tax of 5.5%. What is the final amount they will pay?
$62.62
$73.90
$74.49
$70.64

Answers

Answer:

The final amount they will pay is $74.49

Step-by-step explanation:

59.36(Check)*0.19(19% tip rate)=11.27

59.36+11.27=70.62 Check+Tip

70.62(Check total)*0.055(5.5% tax)=3.87

70.62+3.87=74.49 Total check, tip & tax

help pls!!
#420hehsh

Answers

Answer:

It's gonna be probably A

PLEASE HELP ME WITH THIS!!!

Answers

Answer:

6. Bobby makes more money than John

Step-by-step explanation:

John's profits

(4.2 × [tex]10^{5}[/tex]) + (3.2 × [tex]10^{6}[/tex])

= 36.2 x 10^5

= 3.62 x 10^6

Bobby's profits:

323659000 = 3.23659 x 10^8

3.23659 x 10^8 > 3.62 x 10^6

Ajar contains 3 red and 5 green balls identical in all aspects except color. If two balls are drawn at random, then the probability that the two balls drawn are not green is​

Answers

Answer:

3/28.

Step-by-step explanation:

Total of 8 balls in the jar.

Prob (first one not green (= that its red) = 3/8

Prob ( Second one is also red) = 2/7.

So probability that both are not green = 3/8 * 2/7

= 6/56

= 3/28.

Paloma decided to divide 1,292 by 31 using partial quotients. She uses 30 as her first partial quotient. Which are the partial quotients Paloma should show in her work


A 20, 10

B 30, 10,1

C 10,10,10,1

D 10,10,10,10,1

Answers

I think it would be B-30,10,1

It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty"."Sleeping Beauty" Yan Limeng

Answers

Answer:

It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty".

Step-by-step explanation:

It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty".

what is the LCD of 5/7, 1/6, and 11/12

Answers

Answer:

celluar resperation

Step-by-step explanation:

John and Jill collect 280 stamps. Out of this John collected three time as many as
Jill. How many stamps did Jill collected?

Answers

Answer:

Jill collected 70 Stamps

John collected 210 Stamps

Step-by-step explanation:

280/4=70

Please allow me to know if my answer helped you with a thank you!

<3Miss Hawaii

Helpppp plzzzzzzzzzzzzz

Answers

Answer:

x=90 possibly

Step-by-step explanation:

3x all at 30 degrees. but not posative so please check elsewhere.

Z=8-i ^ w=12+3i, entonces ZxW, es:

a) 99-12i
b)93+12i
c)99+12i
d)93-12i


Necesito ayuda urgente!!

Answers

Answer:

21

Step-by-step explanation:

Slope of -3 passes through the point (2,1)

Answers

Answer:

Linked the work I did on a scientific calculator :)

( How to write it as an equation )

Step-by-step explanation:

kia worked 30 hours and 15 minutes this weekend . if she makes $15.60 per hours ,how much did she make?

Answers

$471.90

30 x 15.60 = 468 (total full hours x amount per hour)
60 / 15 = 1/4 (60 minutes per hour divided by the 15 minutes they worked = amount of the hour)
15.60 x 1/4 = 3.9 (amount for the 15 minutes worked)
468 + 3.9 = 471.9 (total full hours + 15 minutes total)

Answer:

$471.90 dollars

Step-by-step explanation:

First, we need to find out how many hours she's working.

There are 60 minutes in an hour so 15/60 is 0.25.

Thus, adding that to the 30 hours gives us 30.25.

If she makes $15.60 per hour we just multiply that by 30.25 hours and get the answer.

[tex]\frac{15.60}{hour}*30.25 hours = 471.9\\[/tex]

The [tex]\frac{}{hour}[/tex] comes from the wording of per hour, and since the unit is in the denominator, when we multiply it by the 30.25 hours, the units cancel out. Thus all we are left with is the amount of dollars made, which is $471.90.

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