Answer:
Step-by-step explanation: 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.
Answer:
the area of the triangle is 41
the perimiter of the triangle is 33.25
Step-by-step explanation:
The distance of the two points should be (18+23) 41
Answer:
1) 
2) 
3) 
4) 
5) 
Step-by-step explanation:
According to the information given in the exercise, the value of "x" is:
Then:
1) You must substitute into the expresion 
:
Now, you must evaluate:
2) You have to substitute the given value of "x" into the second expression:
Finally, evaluating, you get the following result:
3) According to the Zero exponent Rule, any non-zero number with an exponent of zero is equal to 1.
Then, substituting into the expression 
and then evaluating, you get:
4) By definition:
Then, substituting into 
and evaluating, you get:
5) Since:
When you substitute the given value of "x" into the last expression and then you evaluate, you get:
Example 1 – Solve: 3x3 = 12x
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order.
 3x^3-12=0
Step 2: Use a factoring strategies to factor the problem.
 3x(x^2-4)=0
3x(x+2)(x-2)=0
Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.
 3x=0 or x+2=0 or x-2=0
Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.
 x=0 or x=-2 or x=
I hope this helped you!
