I'll go by boxes (top statement box is #1, top reason box is #2, etc.)

If you don't have enough boxes, you can omit (remove) the first 2 I wrote, which is the given

1. 8y = 9x - 14; y = 5
2. Given

3. 8(5) = 9x - 14
4. Substitution

5. 40 = 9x - 14
6. Simplification (or multiplication)

7. 54 = 9x
8. Additive property of equality

9. 6 = x
10. Division property of equality

11. x = 6
12. Symmetrical property of equality

Hope this helps (:

7 0

4 years ago

What is the smallest and largest number that round to 170,000

Maksim231197 [3]

Assuming you're rounding to the nearest ten-thousand, Smallest is 165,000and largest is 174,000

8 0

3 years ago

How many elements does A contains if it has 64 subsets

Amanda [17]

<h3>Answer: 6</h3>

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

Explanation:

Rule: If a set has n elements in it, then it will have 2^n subsets.

For example, there are n = 3 elements in the set {a,b,c}. This means there are 2^n = 2^3 = 8 subsets. The eight subsets are listed below.

{a,b,c} .... any set is a subset of itself
{a,b}
{a,c}
{b,c}
{a}
{b}
{c}
{ } ..... the empty set

Subsets 2 through 4 are subsets with exactly 2 elements. Subsets 5 through 7 are singletons (aka sets with 1 element). The last subset is the empty set which is a subset of any set. You could use the special symbol $\varnothing$ to indicate the empty set.

For more information, check out concepts relating to the power set.

-------------------

The problem is asking what value of n will make 2^n = 64 true.

You could guess-and-check your way to see that 2^n = 64 has the solution n = 6.

Another approach is to follow these steps.

$2^n = 64\\\\2^n = 2^6\\\\n = 6$

Which is fairly trivial.

Or you can use logarithms to solve for the exponent.

$2^n = 64\\\\\text{Log}\left(2^n\right)=\text{Log}\left(64\right)\\\\n*\text{Log}\left(2\right)=\text{Log}\left(64\right)\\\\n=\frac{\text{Log}\left(64\right)}{\text{Log}\left(2\right)}\\\\n\approx\frac{1.80617997398389} {0.30102999566399} \ \text{ ... using base 10 logs}\\\\n\approx5.99999999999983\\\\$

Due to rounding error, we don't land exactly on 6 even though we should.

5 0

2 years ago