Which of the following expressions are equivalent to 256^x? Select all that apply.

a. 8^2x
b. 4^4x
c. (64^x)^2
d. (16^x)^2
e. 2^8x​

Answers

Answer 1

Answer:

d

Step-by-step explanation:

i did it on eduhguenity

Answer 2

The solutions which satisfy the equation A = 256ˣ are

Option B. 4⁴ˣ

Option D. 16²ˣ

Option E. 2⁸ˣ

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by A = 256ˣ

a)

The value of equation B = 8^2x

B = 8²ˣ

On simplifying the equation , we get

B = 8²⁽ˣ⁾

B = 64ˣ

And the value of B ≠ A

b)

The value of equation B = 4^4x

B = 4⁴ˣ

On simplifying the equation , we get

B = 4⁴⁽ˣ⁾

B = 256ˣ

And the value of B = A

c)

The value of equation B = (64^x)^2

B = (64ˣ)²

On simplifying the equation , we get

B = 64²⁽ˣ⁾

B = 4096ˣ

And the value of B ≠ A

d)

The value of equation B = (16^x)^2

B = (16ˣ)²

On simplifying the equation , we get

B = 16²⁽ˣ⁾

B = 256ˣ

And the value of B = A

e)

The value of equation B = 2^8x​

B = (2⁸)ˣ

On simplifying the equation , we get

B = 256⁽ˣ⁾

And the value of B = A

Hence , the equations which satisfy are

Option B. 4⁴ˣ

Option D. 16²ˣ

Option E. 2⁸ˣ

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Step-by-step explanation

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Question 7. Jose has scored 874 points on his math tests so far this semester. To get an A for the semester, he must score at least 959 points. Part 1 Enter an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. Let n represent the number of points Jose needs to score on the remaining tests. What is the inequality. What is the solution to the inequality​

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Step-by-step explanation:

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Find the least number which when divided by 12 and 16 leaves the reminder 3 and 7 respectively. Plzz help in this question ​

Answers

Answer:  39

==============================================

Explanation:

Let n be the number we want to find. We want n to be as small as possible, but also be a positive integer. Intuitively, we can see that n cannot be smaller than 16; otherwise, we don't meet the remainder requirements.

Divide n over 12 and we get some quotient x and remainder 3

So,

n/12 = (quotient) + (remainder)/12

n/12 = x + 3/12

Multiply both sides by 12 to end up with

n = 12x + 3

Similarly, if we divide over 16 we get some other quotient y and remainder 7

n/16 = y + 7/16

which turns into

n = 16y + 7

after multiplying both sides by 16

-----------

We have these two equations

n = 12x+3n = 16y+7

Apply substitution and do a bit of rearranging like so

12x+3 = 16y+7

12x-16y = 7-3

4(3x-4y) = 4

3x-4y = 4/4

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The goal from here is to find the smallest positive integers x and y that make that equation true. We have a few options here and they are

Guess and check: We have a small sample size to work with so it shouldn't take too long. Make a table of xy values where you have x along the top row and y along the left column. Then plug each x,y pair into the equation above to see if you get a true statement or not. Again, keep in mind that x and y are positive integers. Graphing: Graph the line 3x-4y = 1, which is the same as y = (3/4)x - 1/4 and note where the line lands on a lattice point. Focus on the upper right quadrant of the graph. This quadrant is above the x axis and to the right of the y axis.Extended Euclidean Algorithm: This method is the most efficient, but it's only useful if your teacher has gone over it.

Whichever method you use, you should find that (x,y) = (3,2) is the point we want.

Note how:

3x-4y = 1

3(3)-4(2) = 1

9-8 = 1

1 = 1

So that verifies (3,2) is on the line 3x-4y = 1.

Because x = 3 and y = 2, we know that

n = 12x + 3

n = 12*3 + 3

n = 39

and we can see that

n = 16y + 7

n = 16*2 + 7

n = 39

So 39 is the smallest such integer such that when we divide it over 12 and 16, we get remainders 3 and 7 respectively.

Here's a quick verification that we've fit the requirements.

39/12 = 3 remainder 3

39/16 = 2 remainder 7

We know we hit the smallest value of n because (x,y) was made to be the smallest positive integer solution to 3x-4y = 1. There are infinitely many positive integer (x,y) solutions to 3x-4y = 1, which in turn means there are infinitely many numbers n that satisfy the remainder conditions (but n is not the smallest possible in those cases).

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Answers

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not sure

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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6
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Answers

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Step-by-step explanation:

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Step-by-step explanation:

hope this helped!!

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Answers

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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