This is the quadratic function:
h(x)=ax²+bx+c
We have two points:
(1,58)
(2,112)
Now, we calculate this quadratic funtion.
we assume that h(0)=0
Therefore:
a(0)²+b(0)+c=0
c=0
(1,58)
a(1)²+b(1)=58
a+b=58 (1)
(2,112)
a(2)²+b(2)=112
4a+2b=112
2a+b=56 (1)
With the equations (1) and (2) we make a system of equations:
a+b=58
2a+b=56
we can solve this system of equations by reduction method.
-(a+b=58)
2a+b=56
---------------------
a=-2
-2(a+b=58)
2a+b=56
-------------------
-b=-60 ⇒ b=60
The function is:
h(x)=ax²+bx+c
h(x)=-2x²+60x
Now find the height, in feet, of the rock after 10 seconds in the air.
h(10)=-2(10)²+60(10)
h(10)=-200+600=400
Answer: 400 ft.
-12x+3 greater than or equal to 5
-12x greater than or equal to to 2
To turn the negative sign of -12x into positive, we multiply both sides by minus, which shifts the inequality sign.
So, 12x less than or equal to 2
x is less than or equal to 1/6
Therefore, 0, -1, -3, -4 and -6 satisfy this inequality.
Answer:
La edad actual de Beatriz es de:
30 años
Step-by-step explanation:
Planteamiento:
5e = 4b
(e+3) + (b+3) = 60
e = edad actual de José
b = edad actual de Beatriz
Desarrollo:
de la segunda ecuación del planteamiento:
e + b + 6 = 60
e + b = 60 - 6
e + b = 54
e = 54 - b
sustituyendo este último valor en la primer ecuación del planteamiento:
5(54-b) = 4b
5*54 + 5*-b = 4b
270 - 5b = 4b
270 = 4b + 5b
270 = 9b
b = 270/9
b = 30
e = 54 - b
e = 54 - 30
e = 24
Comprobación:
5e = 4b
5*24 = 4*30 = 120
The answer would be twenty five because
equals
leaving you with x = 5 at a minimum. So 5x: 5 x 5 = 25
Hope this helps! :)
Answer:
61
Step-by-step explanation:
82+37=119. 180-119=61. remember triangles always add up to 180°
