We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:

y = 10x

Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:

2(x + y) = xy and we know that y = 10x so

2(x + 10x) = x(10x) and

$2(11x)=10x^2$ and

$10x^2-22x=0$ and

x(10x - 22) = 0 so

x = 0 or 10x - 22 = 0 which makes

x equal to $\frac{22}{10}=2.2$

So x = 2.2 and y = 22.

7 0

2 years ago

If you rolled a fair number cube 1-6, 12 times, about how many times would you expect to roll a 5 or a 6?

Sav [38]

Well it is definately not c haha. I would say 3 because it is a pretty even chance of getting three.

4 0

2 years ago

The following triangles are similar. Find x.

AlladinOne [14]

Let's use the line on the right side. In the smaller triangle, the length is 4. The same side on the bigger triangle is 12. The ratio of the smaller triangle to the bigger triangle is:

$\frac{4}{12} \rightarrow 4:12$

$12 \div 4 = 3$

To find a side length for the bigger triangle, all you need to do is multiply by 3. The same side on the smaller triangle is 5. Multiply by 3

$5 \times 3 = 15$

That means x = 15

8 0

2 years ago