Question

For what value of a will 8×10^3 be 40 times larger than a×10^2 ?(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the problem, we can set up an equation using the given information.

We are told that 8×10^3 is 40 times larger than a×10^2.

Mathematically, we can write this as:

8×10^3 = 40(a×10^2)

Simplifying this equation, we can divide both sides by 40:

(8×10^3) ÷ 40 = a×10^2

Simplifying further, we can divide both sides by 10^2:

(8×10^3) ÷ 40 ÷ (10^2) = a

Note that (10^2) is equivalent to 100.

Simplifying the left side, we have:

(8×10^3) ÷ 40 ÷ 100 = a

Finally, simplifying the expression on the left side, we have:

20000 ÷ 4000 = a

Dividing these values gives us:

5 = a

Therefore, the value of a that will make 8×10^3 40 times larger than a×10^2 is 5.

Answer 2

[AI-generated answer — Explain Bot]

To find the value of `a` that makes `8×10^3` forty times larger than `a×10^2`, we can set up an equation and solve for `a`.

Let's start by expressing `8×10^3` and `a×10^2` in numerical form:

`8×10^3 = 8000`

`a×10^2 = a×100`

Now, according to the problem, `8×10^3` is forty times larger than `a×10^2`. Mathematically, this can be written as:

`8×10^3 = 40(a×10^2)`

To solve for `a`, we can simplify the equation:

`8000 = 40a×10^2`

Next, we can divide both sides of the equation by `40×10^2` to isolate `a`:

`8000 / (40×10^2) = a`

Now, let's simplify the expression on the left side:

`8000 / (40×10^2) = 8000 / 4000`

`8000 / 4000 = 2`

So, the value of `a` that makes `8×10^3` forty times larger than `a×10^2` is `a = 2`.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To find the value of "a" that makes 8×10^3 forty times larger than "a×10^2", we can set up the equation:

8×10^3 = 40(a×10^2)

First, let's simplify the right side by multiplying 40 with "a":

8×10^3 = 40a×10^2

Now, let's simplify further by multiplying the coefficients:

8×10^3 = 400a×10^2

Next, let's simplify the powers of 10 by adding the exponents:

8×10^3 = 400a×10^(2+2)

Simplifying further:

8×10^3 = 400a×10^4

Now, divide both sides by 400 to isolate "a":

8×10^3 / 400 = a×10^4

Simplifying the left side:

20 = a×10^4

Lastly, divide both side by 10^4 to solve for "a":

a = 20 / 10^4

Since 10^4 is equal to 10,000, we can rewrite this as:

a = 20 / 10,000

Simplifying the fraction:

a = 0.002

Therefore, the value of "a" that makes 8×10^3 forty times larger than "a×10^2" is 0.002.

Answer 4

we want x such that 8 = 40x

So, x = 0.2
0.1x10^3 = 2x10^2
so a = 2

or, since 8x10^3 = 80x10^2, we want a such that 80 = 40a
so a=2

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion in my previous responses. You are correct. The value of "a" that makes 8×10^3 forty times larger than "a×10^2" is 2.