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Solving proportions

Genrish500 [490]

Answer:

$2x - 12 = 9x - 63 \\ \\ 63 - 12 = 9x - 2x \\ 51 = 7x \\ x = 7.2$

4 0

3 years ago

HEEEEEEEELLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp

Debora [2.8K]

Answer:

6

Step-by-step explanation:

This problem centers on recognizing the relationship between fractions and repeating decimals.

Note the following:

$\frac{1}{3}=0.33333333333333333333333333333333333333333333333...$

or more simply $\frac{1}{3}=0.\bar{3}$

This means that $2\frac{1}{3}=2.\bar{3}$

Going back to the original expression, $3\frac{2}{3}+2.\bar{3}$ simplifies to $3\frac{2}{3}+2\frac{1}{3}$

Next, adding mixed numbers. For adding mixed numbers, whole number parts and fractional parts can be added separately (this is because of the associative and commutative properties of addition)... because

$3\frac{2}{3}+2\frac{1}{3}$ means the same thing as

$(3+\frac{2}{3})+(2+\frac{1}{3})$

Changing the order, we can write it as

$3+2+\frac{2}{3}+\frac{1}{3}$

Adding the whole number parts, 3+2 is 5.

Next, adding the fraction parts:

For adding fractions, one must have a common denominator (the bottom part of the fraction must be the same). Once they are the same, the denominator just sort of "hangs out" until the end without changing, and the numerators (the tops) are added together.

Fortunately, the denominators are already the same. So, add the numerators, and the denominator will stay as a 3.

$\frac{2}{3}+\frac{1}{3}$

$\frac{1+2}{3}$

$\frac{3}{3}$

It is important to recognize that any fraction* where the number on the top matches the number on the bottom, the fraction is equivalent to 1.

*(except if the number we're talking about is zero)

So, the fraction parts added together, are equivalent to 1, and the whole number parts added were equal to 5. Returning to our expression...

$3+2+\frac{2}{3}+\frac{1}{3}$

$5+\frac{3}{3}$

$5+1$

$6$

7 0

2 years ago

What's the vertex and is it a max or min

MrRa [10]

A vertex can be the max or min. The vertex is the highest point or lowest point of a function.

5 0

3 years ago

Read 2 more answers

Are the two lines parallel? Please show your work and explain how you know whether or not they are parallel: x + y = 1 and 3x +

Anna007 [38]

The easiest way would be to graph both of them on a coordinate plane. You can either use one online or on your own. When you do graph them, it shows the two lines ARE parallel. I hoped i could help you. Plz mark as brainlies im almost at 5 brainliest so plz mark as brainliest. Thank you very much!

5 0

4 years ago

A product has five factors. Three factors are negative integers and two factors are positiv

Tamiku [17]

Answer:

Make it as simple as possible, and use 1 and −1 .

1×1×1×1×1×−1×−1×−1×−1×−1=

15×(−1)2×(−1)2×−1=

1×1×1×−1=

−1.

So, the sign will be negative.

Another way of thinking about this is to not even think about the positive integers, as they won’t affect the sign. A positive integer times a positive integer is still a positive integer; a negative integer times a positive integer is still a negative integer.

So, you have five negative integers. Think of it like two negative integers, two more negative integers, and a single negative integer. Since two negative integers form a positive integer, you now have a positive, positive, and negative integer. This forms a negative sign.

3 0

3 years ago