Please explain to me how 3.2÷4=0.8 is done

2 answers:

4 0

To make it easier just assume there is no decimal point then just work out the 32÷4 where we know that 4 goes into 32 8 times so you get 8 remember the decimal point and since it was one decimal place you will push the decimal over to the left of 8 and that is how you get 0.8

trapecia [35]3 years ago

4 0

So the idea with literal equations is to get one variable in terms of all the rest. In this equation, we are trying to solve for x in terms of y (meaning that we are trying to get x all by itself with y on the other side of the equal sign). Whenever you have a single fraction by itself on one side of an equal sign, the first thing that I always do is cross multiply. This gets rid of the fraction completely and makes everything look a little nicer:

y * (5-4x) = 1 * (2x+3)

Distribute on the left side:

5y-4xy = 2x+3

Move the x's all to the same side. I'm doing this by subtracting 2x from both sides:

5y-4xy - 2x = 3

For simplicity's sake, move 5y to the right side of the equation by subtracting it from both sides:

-4xy - 2x = 3 - 5y

Factor out the x on the left side:

x (-4y-2) = 3 - 5y

Get the x term by itself on the left side by dividing both sides by -4y-2.

x = (3-5y)/(-4y-2)

And there you have it! I hope that this helped a little. Good luck!

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In right angle ABC, angle C is the right angle, AC = 3 and AB = 5. Point D is on hypotenuse AB, such that DB = 1. Find the area

Ivan

Look at the picture.

To find the area of triangle DBC we need to find its base, x, and its height, h.

Triangle ABC is a right triangle, so using the Pythagorean theorem we can find x.
$(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{the hypotenuse})^2 \\
3^2+x^2=5^2 \\
9+x^2=25 \\
x^2=25-9 \\
x^2=16 \\
x=\sqrt{16} \\
x=4$

Now look at triangles ABC and DBH. They both are right triangles and have the same angle α. That means they're similar and their corresponding sides are proportional. The ratio of the side opposite to angle α to the hypotenuse is the same in both triangles - so the ratio of h to 1 is the same as the ratio of 3 to 5.
$\frac{h}{1}=\frac{3}{5} \\
h=\frac{3}{5}$

The base x is 4, the height h is 3/5. Calculate the area:

$A=\frac{xh}{2}=\frac{4 \times \frac{3}{5}}{2}=2 \times \frac{3}{5}=\frac{6}{5}$

The area of triangle DBC is 6/5.