Simplify the expression

Mathematics

1 answer:

bearhunter [10]4 years ago

7 0

First we want to simplify the denominator
$\frac{1}{4} - \frac{5}{2}$

to subtract, we convert 5/2 to have a denominator of 4
$\frac{1}{4} - \frac{10}{4}$
$- \frac{9}{4}$

now we can put this back into the original problem
$\frac{4}{ - \frac{9}{4} }$
this equation can also be read as
$4 \div - \frac{9}{4}$

when dividing, we flip the right side and switch to multiplication
$\frac{4}{1} \times - \frac{4}{9} = - \frac{16}{9}$

$answer = - \frac{16}{9}$

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I would like you to help me with that since I do not understand very well please

JulijaS [17]

When you see the symbol "△", this denotes a triangle. Now combine the symbol with the letters FGH, this becomes △FGH, meaning a triangle FGH, with F, G, and H as the three points.

Now, the symbol "∠" means angle and "m∠" means the measure of an angle. So m∠F means the angle at the point F, m∠G means the angle at the point G, and m∠H means the angle at the point H. (I'll attach a diagram of this triangle).

Now we have to determine m∠H, which is the angle at point H. To do that, we have to find the value of $x$ . To do that, we have to use one of the laws of a triangle, which is:

The sum of angles in a triangle = 180°. This means when we add all the angles in a triangle, it sums up to 180°. Let's do that.

$\angle F + \angle G + \angle H = 180\textdegree \\\angle F = (5x - 6)\textdegree, \angle G = (3x + 16)\textdegree, \angle H = (x + 8)\textdegree \\(5x - 6) + (3x + 16) + (x + 8) = 180\\5x + 3x + x - 6 + 16 + 8 = 180\\9x + 18 = 180\\9x = 180 - 18\\9x = 162\\x = 18\textdegree$