Mathematics Middle School

Solve for n.

25n−3=5n+8
the n-3 and n+8 are powers

Answers

Answer 1

Final answer:

The equation 25n⁻³ = 5n⁺⁸ suggests an incorrect use of exponents, as no solution exists if we assume the bases should be the same. However, if the bases are 25 and 5, after simplifying, we find that the solution is n = 14.

Explanation:

To solve the equation 25n⁻³ = 5n⁺⁸, we need to use properties of exponents and logarithms. Here are the steps:

Assuming the bases are the same and only the exponents are different, equate the exponents: n - 3 = n + 8.This implies that no solution exists because once the bases are the same, the exponents on both sides must be equal for the equation to hold true, but here they are not.

Alternatively, if 25 and 5 are the bases, we can rewrite the equation as (52)n-3 = 5n+8, then applying properties of exponents gives us 52n-6 = 5n+8. Equating the exponents yields 2n - 6 = n + 8, which we can solve for n.

Subtract n from both sides: n - 6 = 8.Add 6 to both sides to isolate n: n = 14.

Related Questions

3.25 meters to 2.95 meters

Answers

3.25 - 2.95 = 0.3

The difference between 3.25 and 2.95 metres is 0.3 metres.

A baker wants to put 3 3/4 pounds of apples in each pie she makes. She purchased 52 1/2 pounds of apples. How many pies can she make

Answers

3 3/4=3.75
52 1/2=52.5
52.5/3.75=14
She can make 14 pies.

Answer:

UCOSVGLJHBdfbhksd

Step-by-step explanation:

Solve the following word problems by writing an equation and then solving algebraically:

During the 2007 baseball season, Wade was up to bat 10 more times than his teammate Dwight. Dwight batted 17 fewer times than another teammate, Ellis. The three players were up to bat a total of 1650 times. How many times did Ellis come to bat?

I only really need help making an equation because the ones I tried making didn't work.

Answers

This problem requires more than one equation, at least for me to get it to work ~this is how I did it

Wade = w     Dwight = d    Ellis = e     Up to Bat = 1650
These are the equation to find each personw = d + 10e = d +17d = w - 10    or     d = e - 17
This is the basic equation you have to plug the other equations into1650 = w + d + e
I solved for Dwight so I plugged in for w and for e1650 = (d + 10) + d + (d + 17)     ~then I simplified1650 = 3d + 27     ~everything grouped together than matched1623 = 3d     ~I subtracted 27 from both sides541 = d     ~I divided both sides by 3Dwight batted 541 times

This is where I solved for Ellis since that is what the question waskede = d + 17     ~first equation
e = 541 + 17     ~plugged in 541 for d since that's how many times d battede = 558     ~finally simplified the equation

Ellis came up to bat 558 times in the 2007 baseball season

What is the slope of the line whose equation is –48 = 2x − 8y?



convert in to a fraction

I need it done now

Answers

We need to isolate y,, –48 = 2x − 8y,, –48-2x = -8y,, -8y = -2x - 48,, y = (-2x - 48)/(-8),, y = (-2x)/(-8) - 48/(-8),, y = (1/4)x + 6,, The last equation above is in the form y = mx+b where m = 1/4 is the slope

Thirty-one is three more than twice a number divided by three

Answers

The answer is 22.6666667, hope this helps. You do this problem but backwards.

what is the last step when solving the following equation for m? 4m-6=92

Answers

The last step is dividing both sides by 4: 4m=98 which would become: m=24.5

Hope this helps :)

Answer: 24.5

Step-by-step explanation:

4m-6 = 92

If we replace m with 24.5

4 x 24.5 = 92

therefore the answer is:

24.5

(sin2a+sin4a)²+(cos2a+cos4a)²=4cos²a

Answers

Expanding this out gives:
[tex](sin^2 (2a) + 2sin(2a) sin(4a) +sin^2 (4a)) \\ +(cos^2 (2a) + 2cos(2a) cos(4a) +cos^2 (4a)) \\ = 4cos^2 (a)[/tex]

Simplify by using pythagorean identity:
sin^2 + cos^2 = 1
[tex]2sin(2a)sin(4a) + 2cos(2a)cos(4a) + 2 = 4cos^2 (a)[/tex]

Next use cosine difference identity:
cos(x-y) = cos(x)cos(y) +sin(x)sin(y)
[tex]2 cos(4a-2a) +2 = 4cos^2 (a)[/tex]

Next use cosine double angle identity:
cos(2x) = 2cos^2 - 1
[tex]2(2cos^2 (a) -1) + 2 = 4cos^2 (a)[/tex]

Finally distribute and Right side  = Left side
[tex]4 cos^2 (a) = 4 cos^2 (a)[/tex]
Identity is proved

I am making an acrostic poem and I am using the word "slope". Anyone have any ideas?

Answers

does the poem have to be about anything specific??

how to turn 5x+10y=15 in to slope intercept form (y=mx+b)

Answers

5x+10y=15
5x-5x=0
15-5x
10y=-5x+15
-5x /10 and 15/10
y=-1/2x +1.5
Final answer:

To convert the equation 5x+10y=15 into the slope-intercept form y=mx+b, subtract 5x from both sides and then divide by 10. The final equation will be y = -0.5x + 1.5, where -0.5 is the slope (m) and 1.5 is the y-intercept (b).

Explanation:

Converting the equation 5x+10y=15 into slope-intercept form (y=mx+b) involves isolating y on one side of the equation. The slope-intercept form of an equation is defined such that m is the slope and b is the y-intercept.

Here are the steps to convert this:

Start with the original equation: 5x + 10y = 15.Subtract 5x from both sides to get: 10y = -5x + 15.Divide every term by 10 to isolate y: y = -0.5x + 1.5.

The equation is now in the form y = mx + b. Here, the slope, m, is -0.5 and the y intercept, b, is 1.5, which is the point at which the line intercepts the y axis.

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what are two linear expressions with a sum of -5x+4

Answers

(-3x+1)+(-2x+3) is one example

What is 126 divided by 2?

Answers

the answer is 63

126/2=63

The quotient of  126 divided by 2 is  63.

What are some alternative names for arithmetic operations?

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

Given, A statement that the number 126 is being divided by the number 2.

We know, 126 is an even number so it is definitely divisible by 2 without remainder.

Now, (126/2) = 63    (as 2×6 is 12 and 2×3 is 6).

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In an orchestra there are 42 with Woodwind players to 56 brass players what is the ratio of woodwinds to brass written as a fraction in simplest form

Answers

3/4 is the ratio of woodwinds to to brass players

Car A travels 180 miles in 7 hours. Car b travels 350 miles in 4 hours. Car c travels 584 miles in 15 hours. Which car has fastest average speed?

Answers

Car b has the fastest average speed

Answer:

Car B has the fastest average speed 87.5/ per hours

Step-by-step explanation:

Car A

180/7 = 25.714

Car B

350/4= 87.5

Car C

584/15= 38.93

Can I have halp with all and an explanation because I am terrible at properties.

Use properties of equality to simplify each of the following expressions so that you can simplify them in your head. Identify the properties used and describe how you used them.

1. 4 • (–3) • 5



2. (2.25 • 23) • 4





4. 5 • 12 • (–2)



5. 35(26)(0)

Answers

1.   4 • (–3) • 5
   so 4 x (-3) = -12  and then -12 x 5 = -60
2.   (2.25 x 23) x 4
so (2.25 x 23) 51.75  and then 51.75 x4 = 207
4.  5 x 12 x (-2)
 so 5 x 12 = 60  and then 60 x (-2) = -120
5.   35(26)(0) =
  so 35 x 26 = 910  and then  910 x 0 = 0

Explanation of simplifying expressions using properties of equality.

Properties of equality are used to simplify expressions. Let's go through each example:

4 • (–3) • 5 = -60 (Multiplicative property of equality) (2.25 • 23) • 4 = 207 (Associative property of multiplication) 5 • 12 • (–2) = -120 (Multiplicative property of equality) 35(26)(0) = 0 (Multiplicative property of equality)

HELP!!

What is the solution of the system?

Use the substitution method.

{y+7=3x
6x−2y=12

(a.) (14, 12)
(b.) (12, 14)
(c.) There is no solution.
(d.) There are an infinite number of solutions.

Answers

c. There is no solution
I just took the test and the correct answer is c.

Paula received a paycheck of $585. This amount reflects her weekly earnings less 10% of her earnings for deductions. How much was she paid before deductions were taken out?

Answers

In order to do this we must set up an equation
We are looking for the original amount she was paid, which we'll represent by the variable X
We know that $585 is X minus 10% of X
This means that $585 is 90% of X (or X times 0.90)
So, our equation is

X(0.90)=585

In order to solve this, we can divide both sides by 0.90

X=650

So, she was originally paid $650

What is the value of x?
x/48 = 12/32

Answers

To solve for the value of X, first reduce 12/32 into lowest terms = 6/16 = 3/8.

X/48 = 3/8
3 • 6/8 • 6 = 18/48
X = 18.
well the answer to your question is real easy you just have to simplify twelve over thirty two and see if you can find out what equals to that. I found out the x would equal 18. If you want proof look on solution.com

use the decimal model to find the product 3×0.33

Answers

I am pretty sure its 0.99
The answer is 0.99, btw I double checked my answer.

a factory can make 2,418 footballs in 1 week. How many can it make in 9 weeks

Answers

2418 * 9 = 21,762

hope it helps

Deirdre doubled her savings account balance of $100 . Then she withdrew $30 to buy some new clothes. Represent this situation with a numerical expression.

Answers

Your answer would be 100-30=70
(100*2)-30 
100 is multiplied by two to get 200 and then you subtract 30 to get 170 because they withdrew money so they took away money.

The seventh-grade band is going to sell baked goods at the craft show. The cost to rent a booth at the craft show is $60. The band plans to charge $1.50 per baked good. How many baked goods must they sell in order to profit at least $200?

Answers

200+60=260/1.50=173.3
selling 173 would be under 260 dollars and im assuming you cant sell half a baked good 
so the answer is 174

The number of baked goods to have at least a profit of $200 is

94 or more.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

Cost of renting a booth = $60

Charge per baked good = $1.50

The number of baked goods to have a profit of at least $200.

60 + 1.50x ≥200

Solve for x.

60 + 1.50x ≥ 200

Subtract 60 on both sides.

1.50x ≥ 200 - 60

1.50x ≥ 140

Divide both sides by 1.50

x ≥ 140/1.50

x ≥ 93.33

This means,

94 or more baked goods.

Thus,

94 or more baked goods need to be sold to have a profit of at least $200.

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Grey 2.4 times as many miles as Emory. If Emery ran 2.08 miles, how many miles did grey run.

Answers

the answer is 499.20 becasue you have to multply 2.4. to 2.08 and that's how you get the answer
The answer is 499.20

Answer the 2 pictures please and thank you (":

Answers

7/9 is 0.78 so .85 is greater so the day she sold the most boxes is Tuesday.

78% as a fraction and in simplest form

Answers

39/50 and thats in simplest form
So percent is 100 so the fraction would be 78/100 and then u can divide both numbers by 2 and get 39/50 in simplest form

Plz Help fast!!
25 points. Which equation correctly applies the distributive property?
A. 2.4⋅(−3.4)⋅(−1.25)=−3.4⋅2.4⋅(−1.25)
B. −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08)
C. (42⋅3.5)+(42⋅1.3)+(42⋅5.2)=42+(3.5+1.3+5.2)
or D. −2.5⋅(4⋅3.67)=(−2.5⋅4)⋅3.67 ​

Answers

A. Because as you see the -3.4 and the 2.4 get multiplied on the right side, showing the distributive property.   

Answer:

The answer is B

Step-by-step explanation:

I know I'm late to this answer, but I'm just answering it just in case anyone else needs it.

How many fluid ounces are in 3 pints?

Answers

there are 16 ounces in one pint. You multiply 16 by three, and you get 48 fluid ounces.
48 because there 16 fl oz in one so 16×3 is 48

In a power,what is a number used as a factor

Answers

the power (exponet) tell you how many times you need to multiply the same number its attatched to. example 5 squared is 5x5 (to the power of two)
5 cubed is 5×5×5 (to the power of three)

In a power, the number used as a factor is called the base.

A power is an expression that represents repeated multiplication of the base by itself. It consists of a base raised to an exponent.

The base is the number that is being multiplied, and the exponent represents the number of times the base is multiplied by itself.

For example, in the expression 2³, the base is 2. It indicates that 2 is being multiplied by itself 3 times.

So, in a power, the base is the number used as a factor.

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Lightning strikes Earth 1000 times in 10 seconds. How many times does it strike per second?

Answers

100 lightning strikes per second because 1000 / 10 = 100.

Lightning strikes the earth 100 times per second.

What is an equation?

Two or more expressions with an equal sign are defined as an equation.

Given that, lightning strikes earth 1000 times in 10 seconds.

So, mathematically,

10 seconds = 1000 times

1 second = (1000/10) times

1 second = 100 times

Hence, lightning strikes the earth 100 times per second.

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Two bands are marching in a parade there are 32 people in the first band 40 people in the second band the same number of people are marching in each row in each band what is the greatest number of people that could be marching in each row

Answers

Eight people in each row
Basically, this question is asking you to find what is the smallest number that both 40 and 32 are divisible by evenly?
The answer here is eight.
40/8 = 5
32/8 = 4
So the first band will have 4 rows of eight, and the second will have 5 rows.

Jim said led 3/4 gallon of lemonade. Dwight sold some lemonade, to.together they sold 1 5/12 gallons.who sold more lemonade, Jim or Dwight

Answers

1 5/12= 1.416 (in decimal form)
3/4=.75 (in decimal form)
1.416 (total amount of lemonade sold) - .75 (amount of lemonade Jim sold) = amount of lemonade Dwight sold
Amount of Lemonade Dwight Sold = .666
Jim sold more lemonade because .75 gallons is greater than .666 gallons

It's clear that [tex]\( \frac{9}{12} \)[/tex] is greater than [tex]\( \frac{20}{48} \).[/tex] So, Jim sold more lemonade than Dwight.

Jim sold [tex]\( \frac{3}{4} \)[/tex] gallon of lemonade.

Dwight sold [tex]\( \frac{5}{12} \)[/tex] gallons.

To compare them, we need to find a common denominator, which is 12.

For Jim:

[tex]\[ \frac{3}{4} \times \frac{3}{3} = \frac{9}{12} \][/tex] gallon.

For Dwight:

[tex]\[ \frac{5}{12} \times \frac{4}{4} = \frac{20}{48} \][/tex] gallon.

Now, it's clear that [tex]\( \frac{9}{12} \)[/tex] is greater than [tex]\( \frac{20}{48} \).[/tex] So, Jim sold more lemonade than Dwight.

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