Answer:
y = (1/4)x² - (5/4)x + 1
Step-by-step explanation:
The x-intercepts of the quadratic equation are simply it's roots.
Thus, we have;
(x + 1) = 0 and (x - 4) = 0
Now, formula for quadratic equation is;
y = ax² + bx + c
Where c is the y intercept.
At y-intercept: (0,1), we have;
At (-1,0), thus;
0 = a(1²) + b(1) + 1
a + b = -1 - - - (1)
At (4,0), thus;
0 = a(4²) + b(4) + 1
16a + 4b = -1
Divide both sides by 4 to get;
4a + b = -1/4 - - - (2)
From eq 1, b = -1 - a
Thus;
4a + (-1 - a) = -1/4
4a - 1 - a = -1/4
3a - 1 = -1/4
3a = 1 - 1/4
3a = 3/4
a = 1/4
b = -1 - 1/4
b = -5/4
Thus;
y = (1/4)x² - (5/4)x + 1
Answer:
The numbers are 17 and 5
Step-by-step explanation:
x + y = 22
x - y = 12
Add y to both sides of the equation
x = 12 + y
Substitute new value for x into first equation
12 + y + y = 22
Add the y's
12 + 2y = 22
Subtract 12 from both sides
2y = 10
y = 5
22 - 5 = 17
The numbers are 17 and 5
Hope this helps :)
Step-by-step explanation:
let debbie be x years
let felix be 6x years
in 12 years felix will be 2x older than debbie
do the calc
1. Check the picture attached. We can calculate the area of the orange region G by dividing it into right triangles with both legs equal to 1.
Area of one triangle is 1/2*1*1=1/2 units square.
There are 9 in total, so area G = 9/2 units square.
2. The square has side length equal to 10, so the square area is 100 units square.
3. P(landing in G)=Area of G/total area= (9/2)/100=9/200= 0.045