four students are trying to determine what number must replace the question (x^2)^7=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? Explain why.

Answers

Answer 1

Let's solve ourselves instead of believing anyone

[tex]\\ \rm\Rrightarrow (x^2)^7=x^4x^8[/tex]

a^m+a^n=a^m+n

[tex]\\ \rm\Rrightarrow x^{14}=x^{4+8}[/tex]

[tex]\\ \rm\Rrightarrow x^{14}=x^{12}[/tex]

[tex]\\ \rm\Rrightarrow x^{14}-x^{12}=0[/tex]

[tex]\\ \rm\Rrightarrow x^{12}(x^2-1)=0[/tex]

[tex]\\ \rm\Rrightarrow x^2-1=0[/tex]

[tex]\\ \rm\Rrightarrow x^2=1[/tex]

[tex]\\ \rm\Rrightarrow x=\pm 1[/tex]

0 is also a solution
Answer 2

Answer:

Joe is correct

Step-by-step explanation:

Given equation:

[tex](x^2)^?=x^4 \cdot x^8[/tex]

The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.

For ease of answering, let y be the unknown number (question mark):

[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]

First, simplify the equation by applying exponent rules to either side of the equation:

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}\quad\textsf{to the left side}:[/tex]

[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]

[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:[/tex]

[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]

[tex]\implies x^{2y}=x^{4+8}[/tex]

[tex]\implies x^{2y}=x^{12}[/tex]

Now, apply the exponent rule:

[tex]x^{f(x)}=x^{g(x)} \implies f(x)=g(x)[/tex]

Therefore,

[tex]x^{2y}=x^{12}\implies 2y=12[/tex]

Finally, solve for y:

[tex]\implies 2y=12[/tex]

[tex]\implies 2y \div 2 = 12 \div 2[/tex]

[tex]\implies y=6[/tex]

Therefore, Joe is correct as the unknown number is 6.


Related Questions

What’s the difference in these two questions and why did we divide in one and multiple in one ( also why did we divide by8 in question 2)

Answers

Answer:

times and divide

they are both diffrent equations

The center circle on a playing field has a radius of 7.5m find its circumference

Answers

Given:r= 7.5 mNote that:r= radius To find:

The circumference of the circular playing field.

Solution:

[tex]\huge\boxed{Formula:C= 2\pi{r}}[/tex]

We'll have to multiply 2, π and radius.

Substitute the values according to the formula.

[tex]C= 2× \pi ×7.5[/tex]

[tex]C= 47.12389 [/tex]

[tex]\large\boxed{C= 47.12 \: m}[/tex]

Therefore, the circumference of the circular playing field is 47.12 feets.

can i have help with this

Answers

Answer:

x^32

Step-by-step explanation:

A fraction bar is a division symbol. When you are dividing, you can subtract the exponents.

x^56 / x^24

= x ^ (56-24)

= x^32

Answer:

x^32

Step-by-step explanation:

a^m/a^n = a^(m-n)

so, x^56/x^24 = x^(56-24) = x^32

Book on Language made From Pi or π

Answers

Answer:

Step-by-step explanation:

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.

Answers

Answer:

Step-by-step explanation:

what is the value of the digit 5in the number 734.95?​

Answers

Answer:

0.05

explanation

value means total value

so it's 5*0.01

=0.05

Dan has a list of the scores of all his
math tests and quizzes during the
year. What are the mode and median
of the data set?
88, 79, 71, 75, 53, 88
a. mode = 88, median = 88
b. mode = 88, median = 77
C. mode = 77, median = 77
d. mode = 77, median = 88

Answers

Answer:

b. mode = 88, median = 77

Step-by-step explanation:

First, arrange all the numbers least to greatest.

53, 71, 75, 79, 88, 88

The mode is the number that occurs the most.

mode = 88

The median is the middle number. Since there is an even number of numbers, look at the two middle numbers 75 and 79. Add them together and divide by two (finding the average or mean of the numbers).

75 + 79 = 154

154/2 = 77

median = 77

Find the period and amplitude of the function.
y=5cos2O

Answers

Answer:

period pi and amplitude 5


What is the force, in N, when a pressure of 22 N/m² is exerted on an area of 750 cm²?

Answers

Answer:

1.65 N

Step-by-step explanation:

Step 1: convert cm^2 to m^2

1 cm^2 = 0.0001 m^2

750 cm^2 = 0.075 m^2

Step 2: multiply pressure by area

F = P*A = 22 N/m^2 * 0.075 m^2 = 1.65 N

If a rectangle’s perimeter is 86 units and the width is 15 units, what is the length in units?

Answers

Answer:

I think the answer would be 28

Peter takes 7 minutes and 30 seconds to run 1 mile. How many miles can he run in 15 minutes?
miles

Answers

Answer:

2 miles

Step-by-step explanation:

Peter takes 7 minutes and 30 seconds per mile.

7 times 2 is 14 minutes.

30 seconds times 2 is 1 minute.

If you add these 2 values together you get 15 minutes.

So we need to times the miles by 2 to get 2 miles.

I hope this helps, have a lovely day.

help me, please i need your help

Answers

The answer to each question in the image is given below:

y - 0.32y  =  0.68yy + 0.32y  =  1.32yy +  [tex]\frac{2}{5}[/tex]y   =  [tex]\frac{7}{5}y[/tex]y - [tex]\frac{2}{5}y[/tex]  =  [tex]\frac{3}{5}y[/tex]  

Meaning of equivalent equations.

An equivalent equation can be defined as an equation that has the same meaning and also has the same answer with another equation or with an equation it is said to be equivalent with.

The above equation are equivalent to each other meaning they can be used to derive each other.

In conclusion, the list above is the right pairs of equivalent equations.

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help pls im being timed i cant do mathhh

Answers

I think the answer is 4.21

Please help Fast! Need answer by 1:00 pm

Answers

Answer is 30

Multiply top of bottom of each fraction to get 30 on the bottom

So 2m/5•6 and 2m/6•5

3^x+3^x =54 what's the value of x ?​

Answers

Answer:

x = 3

Step-by-step explanation:

if you need an explanation let me know

Answer:

x = 3

Step-by-step explanation:

Given:

[tex] \implies \rm 3 {}^{x} + {3}^{x} = 54[/tex]

To Find:

Value of x

Solution:

We could re-write 3^x+3^x as:

[We factored here]

[tex] \implies \: 2(3 {}^{x} ) = 54[/tex]

Divide both sides by 2

[tex] \implies \cfrac{2(3 {}^{x}) }{2} = \cfrac{54}{2} [/tex]

[tex] \implies \: 3 {}^{x} = 27[/tex]

Take logarithm on both sides

[tex] \implies \: \log(3 {}^{x} ) = \log(27)[/tex]

[tex] \implies \: x \times \log(3) = \rm \: log \: (27)[/tex]

[tex] \implies \: x = \cfrac{ \log(27)}{ \log \:(3)} [/tex]

[tex] \implies \boxed{x = 3}[/tex]

Hence, x = 3 .

simplify 4^(3)*4^(5)


A. 16^8

B. 4^8

C. 4^15

D. 16 * 15

Answers

Answer:

B. 4^8

Step-by-step explanation:

The indices of the base 4 can be added while multiplying i.e. 3+5=8 but the base remains the same.

Answer:

B

Step-by-step explanation:

Because in powers we just add so it will be 4^3+5

=4^8

how do i solve 8(2-6v) + 19 = -61

Answers

Answer:

v=2

Step-by-step explanation:

Solve for x.
x/12 = -4​

Answers

Answer:

[tex] \frac{x}{12} = - 4[/tex]

[tex] \frac{x}{12} = \frac { - 4}{1} [/tex]

[tex]x \times 1 = 12 \times - 4[/tex]

[tex]x = - 48[/tex]

value of x is -48

Answer:

x=-48.

Step-by-step explanation:

To find x we should multiply both sides, by 12:

[tex]\sf \cfrac{x}{12}\times12=\-4\times12[/tex]

                                       ↪

The 12s cancel on the left:

[tex]x=-4\times12[/tex]

After multiplying we obtain [tex]\sf x=-48[/tex]. Which is our answer.

Hope that this helped you! Have a good day ahead.

Best Wishes!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\text{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

◆◆-Greetings!-◈◈

--

A restaurant bill is £132
A 10% service charge is included in the bill.
How much is the service charge?

Answers

Answer:

1.1x= 132

Step-by-step explanation:

Which organisms reproduce through a...se...xu...al reproduction? (Select all that apply.)
starfish


yeast


fungi


bacteria

PICK MORE THAN ONE and no links please 1+1

Answers

Answer:

bacteria and fungi

Step-by-step explanation:

Single organism makes an exact copy of itself

Bacteria, some plants and fungi, few animals (sponges)

Offspring are identical to parent

Lindsay sketches a right triangle with lengths f, g, and h as shown. She uses the Pythagorean Theorem to write the equation f2 + g2 = h2 to represent the triangle. How can Lindsay correct her error? Explain your reasoning.

Answers

Answer:

hope you can understand

Combine the like terms to create an equivalent expression:−3z−z

Answers

Answer:

-4z

Step-by-step explanation:

Hi student! Let me help you out.

_____________________

Note that, -3z and -z are like terms. This means we can combine them right off the bat, which gives us [tex]\mathrm{-4z}[/tex].

[tex]\mathrm{-3z-z=-4z}[/tex]. -4z is our final answer.

Hope that this helped you! have a good day ahead.

Best Wishes!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. AIm high. Dream big.}}}}}\bigstar\star[/tex]

◈◈-Greetings!-◆◆

___________________

Answer:

-4z

Step-by-step explanation:

-3z-z

On combining like terms,

= -4z

Here,the terms are -3z and -z, where - and - combines and + is the result,so we need to add the expression.

A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water.

1. Solve for the y-variable.

y – 12 = –3(x – 1)

y – 12 = –3x + 3

y = –3x +15

2. Write the equation using function notation.

f(x) = –3x +15

The tub started with
gallons of water.

Answers

The initial amount of the water is 15 gallons

Linear functions

These are functions that has a leading degree of 1. Given the equation that represents the amount of water remaining after x minutes;

y - 12 = -3(x- 1)

y -12 = -3x + 3

y = -3x +3 + 12

y = -3x + 15

In order to determine the initial amount of water, we will substitute x =0 into the function

y = -3(0) + 15

y = 15

Hence the initial amount of the water is 15 gallons

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Answer:

15

Step-by-step explanation:

y=x^2+5x-8 to factored form

Answers

Answer:

Factor and set each factor equal to zero. Y=x2+5x−8

Step-by-step explanation:

Explain why cos(−3π4)=cos(5π4).

Answers

Answer:

See below

Step-by-step explanation:

Think about what happens when you rotate around a circle [tex]-\frac{3\pi}{4}[/tex] radians. This means that you are going clockwise [tex]-\frac{3\pi}{4}[/tex] radians.

Likewise, if you went [tex]\frac{5\pi}{4}[/tex] radians counterclockwise, you'd end up in the same place, so the cosine values must be the same.

The table below shows the value of Henry's car at the end for each of the first 3 years after it is purchased. The values form a geometric
sequence.
Year
Value
dollars)
18000
116200
14580
(in
What will be the approximate value of the car at the end of the 10th year?
O
A. $6,974
B. $8,610
C. $11,810
D. $7,748

Answers

Using a geometric sequence, it is found that the approximate value of the car at the end of the 10th year will be given by:

A. $6,974.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the first term and the common ratio are given, respectively, by:

[tex]a_1 = 18000, q = \frac{16200}{18000} = 0.9[/tex]

Hence the equation is:

[tex]a_n = 18000(0.9)^{n-1}[/tex]

At the end of the 10th year, the value will be of:

[tex]a_{10} = 18000(0.9)^{10-1} = 6974[/tex]

Hence option A is correct.

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To remain healthy, a person needs at least 8 hours of sleep. A company wants to know if their employees get enough sleep. A random sample of 24 employees revealed that the average number of hours of sleep an employee gets is 6.7 with standard deviation of 2.3. What should be the test statistic?

Answers

Answer:

how many hours a week the employees are working?

Step-by-step explanation:

I could be wrong but that's my fault if it's wrong sorry

some one please help me slove this I can't figure it out I will give Brainliest answer to who ever answer frist... ​

Answers

keeping in mind that twin sides stemming from a common vertex make twin angles at the "base", Check the picture below.

The first term of a geometric sequence is 2, and the 4th term is 250. Find the 2 terms between the first and the 4th term.

Answers

Answer:

second term: 10

third term: 50

Step-by-step explanation:

The equation for any geometric sequence is [tex]a_{n} = a_{1} *r^{n-1}[/tex] where n is the term number you want to find, [tex]a_{1}[/tex] is the first term in the sequence, and [tex]r[/tex] is the common ratio. The equation for this sequence specifically uses 5 as its common ratio, so the equation is [tex]a_{n} =2*5^{n-1}[/tex]

[tex]a_{1} = 2*5^{1-1}=2*5^{0} =2*1=2[/tex]

[tex]a_{2} = 2*5^{2-1}=2*5^{1} =2*5=10[/tex]

[tex]a_{3} = 2*5^{3-1}=2*5^{2} =2*25=50[/tex]

[tex]a_{4} = 2*5^{4-1}=2*5^{3} =2*125=250[/tex]

Andre took 6 kicks and made 4 goals: 4/6
Tom wants to take more than 20 kicks and make an equivalent fraction to Andre.
what are two possible fractions of goals Tom can make

Answers

I believe it’s 16/24 and 20/30
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