Notice the picture below
recall, a triangle has a total of 180° for the interior angles.
make sure your calculator is in Degree mode.
Try to get x by itself
so minus 8 from both sides
you end up with 5x^2=125
answer is 3rd option
You need to divide.
We are dividing the mixed numeral 33 1/21 by the mixed numeral 5 1/4.
(33 1/2 ) / (5 1/4) =
The first step is to change the two mixed numerals into improper fractions.
33 1/2 = 67/2, and 5 1/4 = 21/4
= (67/2) / (21/4)
Now we are dividing the fraction 67/2 by the fraction 21/4.
To divide a fraction by a fraction, rewrite the first fraction, change division intro multiplication, and flip the second fraction. To divide 67/2 by 21/4, we multiply 67/2 by 4/21.
= 67/2 * 4/21
To multiply fractions, multiply together the numerators, and multiply together the denominators. 67 * 4 = 268; 2 * 21 = 42
= 268/42
Using a calculator, 268/42 = 6.38095...
You can fill 6 full glasses.
Let, one leg be x units.
since the other leg is 9.0 units shorter than the other,
the measure of the other leg =x-9
hypotenuse =13.0 units
According to Pythagorean theorem, the square of the hypotenuse is equal to the sum of squares of the other two sides.
x^2 +(x-9)^2 =13^2
x^2 + x^2 -18x +81 = 169
2x^2-18x-88=0
Divide the whole equation by 2
x^2 - 9x -44 =0
Let's use the quadratic formula to find the roots.
formula: x= [-b ± sqrt(b^2-4*a*c)]/2*a
a=1 b=-9 c=-44
x= [9±sqrt(81+176)]/2
=[9±sqrt(257)]/2
=[9±16.03]/2
=25.03/2 or -7.03/2
length of a triangle cannot be negative,
Therefore, x=25.03/2 =12.52
one leg =12.5 units
other leg =12.52-9 =3.5 units
2(x+4)=18
2•x + 2•4 = 18
2x + 8 = 18
2x + 8 = 18
- 8 -8
_________
2x = 10
2x = 10
__ __
÷2 ÷2
x = 5
