Solve:
"<span>twice the number minus three times the reciprocal of the number is equal to 1."
3(1)
Let the number be n. Then 2n - ------- = 1
n
Mult all 3 terms by n to elim. the fractions:
2n^2 - 3 = n. Rearranging this, we get 2n^2 - n - 3 = 0.
We need to find the roots (zeros or solutions) of this quadratic equation.
Here a=2, b= -1 and c= -3. Let's find the discriminant b^2-4ac first:
disc. = (-1)^2 - 4(2)(-3) = 1 + 24 = 25.
That's good, because 25 is a perfect square.
-(-1) plus or minus 5 1 plus or minus 5
Then x = ------------------------------ = --------------------------
2(2) 4
x could be 6/4 = 3/2, or -5/4.
You must check both answers in the original equation. If the equation is true for one or the other or for both, then you have found one or more solutions.</span>
3x-5=19-x
3x-5-19+x=0
4x-24=0
4x=24
x=6
Answer:
2
Step-by-step explanation:
First thing you gotta do is find the common denominator.
Do this by listing factors of the denominators:
5- 5, 10, 15, 20, 25, 30
6- 6, 12, 18, 24, 30, 36
5 and 6 both have 30 in common so that's the new denominator for all 3 of the terms.
What you do to the bottom you must do to the top.
Since you multiply 5 by 6 to get 30, you must multiply 2 and 4 by 6 as well.
Since you multiply 6 by 5 to get 30, then multiply 5 by 5 as well.
The new equation is:
+
+ 
=
Now add the numerators together
The solution is 
. Now simplify. 61 is prime, so you cannot change the fraction How many times does 30 go into 61? Two times. This gives us 2.
Answer:
4th option
Step-by-step explanation:
The chord- chord angle 67.5° is half the sum of the arcs intercepted by the angle and its vertical angle, that is
67.5 = 
(x + 90)
1) 10 3/10
3) 2 1/2
4) 10 2/3
6) 6 1/2
7) 4 3/4
9) 1 8/9
10) 1 5/6
