Answer:
Step-by-step explanation:
The quadratic formula is -b +/-sqrt(b^2-4ac) all over 2a.
First we have to get all the variables on one side so... Subtract 4x: 0=-4x^(2)+13x-3
OR add 3 and subtract 13x: 4x^(2)-13x+3=0
Since I prefer a to be positive, I'm going to choose the second equation.
So... now we just plug and chug. a is the value of the variable squared. In this case a=4. b is the value with the variable, or b=-13. c is the last term. c=3
**Remember: Ax^(2)+By+C**
Now we just plug everything in.
-b= 13 (negative minus a negative is a positive)
+/-sqrt((-13)^(2)-4(4)(3))
all over 2(4)
So work with the radical first.
(-13)^2=169
4(4)(3)=48
+/-sqrt(169-48)
+-sqrt(121)
sqrt(121)=11
Now it's just: (13+/-11)/2(4)
(13+/-11)/8
Split this into two equations:
(13+11)/8
(13-11)/8
Solve both: 24/8=3
2/8=1/4
So x= 3, 1/4
Plug them back in and see if there's one solution or two:
4(3)^2=13(3)-3
36=36
So x=3.
How about 1/4?:
4(1/4)^2=13(1/4)-3
4(1/16)=13/4-3
4/16=13/4-3
1/4=13/4-3
1/4=13/4-(3x4)/(1x4) *Like denominators to add or subtract*
1/4=13/4-12/4
1/4=1/4.
So x=1/4.
In this case, both answers work. So the answer, using the quadratic formula is x=1/4, x=3
Answer:
12
Step-by-step explanation:
20²-16²=400-256=144
√144=12
10 times 3 minus 8 equals 22
9 times 2 plus 1 equals 19
Answer:
Step-by-step explanation:
Remeber that a right triangle with a 30 degree leg is a 30-60-90 traingle, and a 30-60-90 triangle has the following properties.(Check Picture Below)
So since the other leg will be times more than the other leg, the exact length of the other leg in the triangle will
The picture is from Study.com, you can check there for more info on special triangles.
Hope this helped.