Y = 3x^2 - 3x - 6 {the x^2 (x squared) makes it a quadratic formula, and I'm assuming this is what you meant...}
This is derived from:
y = ax^2 + bx + c
So, by using the 'sum and product' rule:
a × c = 3 × (-6) = -18
b = -3
Now, we find the 'sum' and the 'product' of these two numbers, where b is the 'sum' and a × c is the 'product':
The two numbers are: -6 and 3
Proof:
-6 × 3 = -18 {product}
-6 + 3 = -3 {sum}
Now, since a > 1, we divide a from the results
-6/a = -6/3 = -2
3/a = 3/3 = 1
We then implement these numbers into our equation:
(x - 2) × (x + 1) = 0 {derived from 3x^2 - 3x - 6 = 0}
To find x, we make x the subject of 0:
x - 2 = 0
OR
x + 1 = 0
Therefore:
x = 2
OR
x = -1
So the x-intercepts of the quadratic formula (or solutions to equation 3x^2 - 3x -6 = 0, to put it into your words) are 2 and -1.
We can check this by substituting the values for x:
Let's start with x = 2:
y = 3(2)^2 - 3(2) - 6
= 3(4) - 6 - 6
= 12 - 6 - 6
= 0 {so when x = 2, y = 0, which is correct}
For when x = -1:
y = 3(-1)^2 - 3(-1) - 6
= 3(1) + 3 - 6
= 3 + 3 - 6
= 0 {so when x = -1, y = 0, which is correct}
Answer:
b= (0,3)
m= 2/3
inequality= y < 2/3x+3
Step-by-step explanation:
b is the y-intercept. the way to find the y-intercept is looking where the line ends up on the y line. m is the slope. the trick to finding the slope is to choose two points and go up then go to the side where the point is. it forms a triangle. count how much it went up and how much you went to the side. then make it rise over run. the inequality works that way since y is 2/3 of x.
Step-by-step explanation:
The vertices and foci are on the x-axis. Thus, the equation for the hyperbola will have the form x2a2−y2b2=1 x 2 a 2 − y 2 b 2 = 1 . The vertices are (±6,0) ( ± 6 , 0 ) , so a=6 a = 6 and a2=36 a 2 = 36 . The foci are (±2√10,0) ( ± 2 10 , 0 ) , so c=2√10 c = 2 10 and c2=40 c 2 = 40 .
(5/8) * (4/7) + 45 * .05 = 2.60714285714
Complete question :
A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.
What are the measures of the angles in triangle ABC?
a) m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90°
b) m∠A ≈ 73.0°, m∠B ≈ 17.0°, m∠C ≈ 90°
c) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
d) m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°
Answer:
c) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
Step-by-step explanation:
Given:
Length AC = 7 inches
Length BC = 24 inches
Length AB = 25 inches
Since it is a right angle triangle,
m∠C = 90°
To find the measures of the angle in ∠A and ∠B, we have :
For ∠A:
∠A = 73.7°
For ∠B:
∠B = 16.26 ≈ 16.3°
Therefore,
m∠A = 73.7°
m∠B = 16.3°
m∠C = 90°