Answer:
x = 1
Step-by-step explanation:
Well the first step is to apply the distributive property:
4(3x - 1) is equal to (12x - 4). You DISTRIBUTE a '4' to what is inside the parentheses.
And btw, to make it easier, you can make 9 - x so that x is first. For example, (-x + 9). They're both the same thing, just written differently.
Your new equation is 12x - 4 = -x + 9. You want to now solve the equation.
Add the (-x) to both sides. It cancels out on the right side and you add it to 12x on the left side.
[If there's no number in front of a variable, you can always just put 1 in order to make it easier]
12x + 1x = 13x. Your new equation is 13x - 4 = 9. This should look very familiar. You simply add 4 to both sides. 9 + 4 = 13
Finally, 13x = 13. Divide 13 ÷ 13 to get 1.
x = 1
(180(total angle measure of triangle)-50(EFG))/2(the other two angles have the same measure)=65
The angle CGE=180=CGF+EGF
180-65=CGF
115=CGF
Yes. Angle bisector means where after splitting the angle the 2 angles formed has the same size.
Therfore when you construct an angle bisector on a straight line, both new angles would be 90°, and the angle bisector is just right in the middle.
Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0
As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ<u /> = 9 + 72
Δ<u /> = 81
Δ<u />>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √<u />81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √<u />81)/2*2 = (3-9)/4 = -6/4 = -3/2
So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2
A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.
3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.
So 2k^2 = 9 + 3k have two rational solutions (Option B).
Hope this Helps! :)
Concave up is U-shaped.
There will be a inflection/critical point f'(x) =0 then a negative slope f'(x) = neg then another inflection/critical point f'(x) =0 at the bottom of the U-shape then a positive slope to last inflection/critical point. The interval for the Concave Up shape is the first and last inflection points.
