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

A) HL
B) Not enough information
C) AAS
D) SAS

Answers

A) HL

The 90° angle is vertical angles with the other unidentified angle

Given: 5n - 42 = 12n; Prove: n= -6
What are the Statements
What are the Reasons

Answers

Answer:

-72=-72

Step-by-step explanation:

5n-42=12n

n=-6

5*(-6)-42 = 12*(-6)

-30-42=-72

-72=-72

So, n= -6 is the right number for this equation

5x -4(x - 3) - 8 = Ax + B

Answers

Answer:

12= ax - x + b

Step-by-step explanation:

5x -4(x - 3) - 8 = ax + b

5x -4x + 12 - 8 = ax + b

x + 12 = ax + b

12= ax - x + b

Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference? A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units. Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. The distance is exactly the difference. The distance is the absolute value of the difference. The distance is not related to difference.

Answers

Answer:

The distance is the absolute value of the difference. aka c

Step-by-step explanation:

Alani has a summer job as a lifeguard. She makes $8/h for up to 40 h each week. If she works more than 40 h, she makes 1.5 times her hourly pay, or $12/h, for each hour over 40 h. 1. How much will Alani earn if she works: a. 37 hours?

Please i need this now

Answers

Answer:

356

Step-by-step explanation:

She will earn a total of $296.

We have - Alani who has a summer job as a lifeguard. She makes $8/h for up to 40 h each week. If she works more than 40 h, she makes 1.5 times her hourly pay, or $12/h for each hour over 40 h. How much will Alani earn if she works: a. 37 hours.

We have to determine - How much will Alani earn if she works for 37 hours.

If you earn $x per hour and you work for 30 hours, them calculate the amount of money you will earn.

The amount of money you will earn will be = $30[tex]x[/tex].

According to question, we have -

Pay per hour = $8

Number of hours she work in a week = 40 hours

For working 37 hours, which is less than 40, she will receive an hourly wage of $8 only. Therefore -

$8 x 37 = $296

Hence, she will earn a total of $296.

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Helpp the topic is about limits

Answers

Since we want to find the value of k where the limit exists, set both equations equal to each other. Then substitute x = -1 in for each equation to find k.

[tex]kx - 3 = {x}^{2} + k[/tex]

1. Set both equations equal.

[tex] - k - 3 = 1 + k[/tex]

2. Substitute x = -1.

[tex] - 3 = 1 + 2k[/tex]

3. Solve for k by adding k to both sides. Continue the process of solving the equation.

[tex] - 4 = 2k[/tex]

[tex]k = - 2[/tex]

Thus, k = -2. Check by graphing the function.

: $800 invested at a 9% interest rate for 8 years.

Answers

Answer:

576$

Step-by-step explanation:

$800×9/100×8=576$

You would make $576. 800 at a 9% rate is $72 per year. 72x8 years is $576

Help! Pls...........

Answers

Answer:

I don't know sorry sorryy

4
-3+x=17
5
11= -9 - x
6
14- X = 4
7
x - 30 = -44
8
16 = 27+ x
9
-75 = x - 50
10
15+ x = -15
11
-9 + x = -34
12
-27=-5-x
13
6+ x = 20
14
-8=x+7
15
13=3- X
ton nations

Answers

4. -17/3

5. -20

6. 10

7. -14

8. -11

9. -25

10. -30

11. -25

12. 22

13. 14

14. -15

15. -10

Richard wants to purchase a new Havaianas. The cost of the havaianas he wants to buy is Php299. Richard has saved Php42 for his new purchase. His parents are willing you give him three times what he has saved. On the weekends. Richard cut lawns for Php20 an hour. How many more hours will Richard have to work until he has enough money to purchase his Havaianas?

Answers

Using the required arithmetic operations, the number of mowing hours required to meet up with the cost of the Havannian ls 7 hours.

Cost of Havannian = Php 299

Amount saved = Php 42

The amount he'll be given by his parents = 3(42) = Php 126

Total amount = 42 + 126 = Php 168

Amount left to meet up cost of Havannian = (299 - 168) = Php 131

Lawn cutting rate per hour = Php 20

Number of cutting hours needed = (Php 131 ÷ Php 20) = 6.55 hours

Therefore, in other to meet up with the cost of the Havannian, hell have to mow for atleast 7 hours.

Learn more : https://brainly.com/question/18112348

The hours Richard would have to work more in order to purchase his Havaians is 7 hours.

The first step to take in order to determine the answer is to determine the total amount Richard has.

Amount saved = Php 42

Amount his parents would give him = php 42 x 3 = php 126

Total amount Richard has = 126 + 42 = Php 168

The total amount Richard has to get in order to purchase the item:

Php 299 - Php 168 = Php 131

The total hours Richard has to work in order to have enough money = Php 131 / 20 = 6.55 hours

This is approximately 7 hours.

A similar question was answered here: https://brainly.com/question/15580066?referrer=searchResults

Olivia typed 36-word paragraph in 2/3 minute. what is her typing speed, in words per minute?​

Answers

Answer:

Olivia typed speed per minutes is 54 words

Step-by-step explanation:

Given:

Olivia typed 36 word in 2/3

Solution:

By Unitary method, calculate the speed of typing by Olivia as-

2/3 Minutes → 36 Words

1 Minutes → 36 ÷(2/3) Words

1 Minutes → 36x3÷2 Words

1 Minutes → 54 Words

Therefore Olivia typed speed is 54 word.

in the given figure triangle abc is similar to triangle ADB write down the corresponding sides with their relation​

Answers

<B=<E

[tex]\\ \sf\longmapsto ∆AED=∆ABO[/tex]

[tex]\\ \sf\longmapsto \dfrac{AE}{AB}=\dfrac{AD}{AO}[/tex]

[tex]\\ \sf\longmapsto \dfrac{AD}{AE}=\dfrac{AB}{AO}[/tex]

Explanation:

Given that

In ∆ ABC, DE is a line drawn on AB and AC

In ∆ ADE and ∆ ABC

∠ AED = ∠ ABC = 70°

∠ AED = ∠ BAC (Common vertex angle )

By AA similarity criteria

∆ ADE and ∆ ABC are similar triangles

⇛ ∆ ADE ~ ∆ ABC

We Know that

If two polygons of same number of sides are said to be similar,

If the corresponding angles are equal.

If the corresponding sides are in the same ratio or in proportion.

So, The corresponding angles are mist be in proportion

⇛ AD / DB = AE/EC

Key Knowledge:-

If two polygons of same number of sides are said to be similar, If the corresponding angles are equal.If the corresponding sides are in the same ratio or in proportion.

Note :-

If DE || BC then by Basic Proportionality Theorem, AD / DB = AE/ECIf a line drawn parallel to one side of a triangle intersecting other two sides at two different points and the line divides the other sides in the same ratio.

Supposed the length of a rectangle is three times the width and the area is 300 ft.² then what is the width of the rectangle in feet

Answers

Step-by-step explanation:

the area is

A = length × width.

length = 3 × width

=>

A = 3 × width × width = 3 × width²

300 = 3 × width²

100 = width²

width = 10 ft

Here is a better picture​

Answers

Answer:all

Step-by-step explanation:so because u have done all

The increasing on the intervals
The decreasing on the intervals

Answers

do you need the technical term? or the normal term? there’s multiple answers for both

EASY WILL GIVE BRAINLIEST
Three postal workers can sort a stack of mail in 25 ​minutes, 45 ​minutes, and 225 ​minutes, respectively. Find how long it takes them to sort the mail if all three work together.

Answers

Answer:

I think the answer is 98?

Step-by-step explanation:

I added 225+45+25 and got 295. Next, I divided 295 by 3 and got 98. (sorry if I'm wrong.)

Three postal workers can sort a stack of mail in 25 ​minutes, 45 ​minutes, and 225 ​minutes, respectively. Time taken if all the three work together is 15min

What is Time?

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

The first worker can sort the stack in 25 minutes. So every minute that goes by,

he does 1/25 of the job.

The second employee completes 1/45 of the stack per minute,

While the third employee completes 1/225 of the task.

Minutes are represented by x, and I've set them all to 1 to indicate that a single stack was sorted.

x·1/25 + x·1/45 + x·1/225 = 1

To eliminate all fractions from the calculation, multiply each term by 225.

225x/25 + 225x/45 + 225x/225 = 225

9x + 5x + 1x = 225

15x = 225

x = 225 / 15

x = 15

Hence, It will take 15min to sort the mail if all three work together

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what is the present value of $6,000 to be received at the end of 6 years if the discount is 12%

Answers

Future value = FV = $6000

Time period = n = 8

interest rate = r = 12%

Present value (PV) is calculated using the formula:

PV = FV/(1+r)n

Present Value = PV = 6000/(1+12%)8 = 6000/1.128 = 2423.299368

Answer -> 2,423

Answer:

$3,039.79

Step-by-step explanation:

In a recipe, for every tablespoon of sugar there are four teaspoons of salt. If a batch uses twelve tablespoons of sugar, how many teaspoons of salt does it use?

Answers

4*12= 48
The answer is 48

solve pls brainliest

Tell me where to put the dot

Answers

Answer:

You will put one mark in front of 5 and the other in front of 10. For question a the answer is 11 is to the right of 6. For question B the correct answer is that 11 is greater then 6 or >

Step-by-step explanation:

Can someone please help me with this question

Answers

Answer:

40 degrees

Step-by-step explanation:

i'm use......

Whatia the slops of the lime through (-2,16) and (2,2)

Answers

The answer would be B) 2.

Justine has 4 1/2 pounds of red apples, 3 1/4 pounds of green apples, and 2 1/4 pounds of yellow apples. How many kilograms of apples does she have?

Answers

4 1/2 + 3 1/4 + 2 1/4 = 10 pounds of apples.

10 pounds is approximately 4.5 kilograms.

Evaluate -8x+5-2x-4+5x

Answers

Answer:

The value of the expression is - 9.

Evaluating the expression before simplifying is preferred because you only have to substitute once instead of substituting three times.

Step-by-step explanation:

x = 2

- 8x + 5 - 2x - 4 + 5x

= - 8x - 2x + 5x + 5 - 4

= - 10x + 5x + 1

= - 5x + 1

= - 5 ( 2 ) + 1

= - 10 + 1

= - 9

Can you guys help me out

Answers

Answer:

what grade are you in that requieres this type of math

Step-by-step explanation:

4. 4^6x4^3
4^9 4^18 12^9 64^9

Answers

4^6*4^3= 4^9= 262144
Final answer: 4^9
Please mark brainliest, thanks

one step equations. due in 30 minutes pls help quick!!

Mr. Rao's gas tank holds up to 17 gallons of gas. It took 12.65 gallons of gas to fill his tank. How many gallons of gas did Mr. Rao have in his tank before he filled it? Enter your answer as a decimal or as a mixed number in simplest form in the box.
only answer if you know it

Answers

Answer: Im 99.9% sure that its 4.48

Step-by-step explanation: 17 1/8 is 17.13 as a Decimal and that subtrcated by 12.65 is 4.48   :)

Anyone know this? ..........

Answers

Answer:

Yes, Each value in the domain goes to only one value in the range.

Step-by-step explanation:

Since each x goes to a different y value, the relation is a function

Each value in the domain goes to only one value in the range.

Find values of x and y.
(x +12)/yº
114

Answers

9514 1404 393

Answer:

  x = 54

  y = 114

Step-by-step explanation:

The angle marked y° corresponds to the one marked 114°. Corresponding angles in this geometry are congruent, so ...

  y = 114

__

The angle marked (x+12)° and the one marked y° form a linear pair, so are supplementary:

  (x +12)° +114° = 180°

  x +126 = 180 . . . . . . . . divide by °, collect terms

  x = 54 . . . . . . . . . . . . subtract 126

There are 120 apples, 1/16 have sprinkles. How many have sprinkles?

Answers

Answer:

7.5

Step-by-step explanation:

because 7.5 x 16 = 120

Please help me with the question

Answers

Answer:

Rate of Change: 2

Step-by-step explanation:

Rate of change is the same as slope:

( y1 - y2 ) / ( x1 - x2 )

( 2 - 4 ) / ( 0 - 1 )

( -2 ) / ( -1 )

2

Hopefully this helps!

Brainliest please?

rise/run up two over 1; the slope is 2/1 or just 2
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