1) f(x)=2x+6
f(2)=2(2)+6
=4+6
=10
2)f(x)=3x
f(a+1)=3(a+1)
=3a+3
3)f(x)=3x-1 and g(x)=5x+3
f(2)=3(2)-1
f(2)=6-1
=5
g(3)=5x+3
=5(3)+32
=15+3
=18
f(2)+f(3)=5+18
=23.
Answer: The y-value of the vertex is
Step-by-step explanation: we know that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
In this problem we have
-----> this a vertical parabola open upward
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
The vertex is the point
The y-value of the vertex is
Answer:
parentheses
Step-by-step explanation:
Hope this helps <3
Answer:
ρ_air = 0.15544 kg/m^3
Step-by-step explanation:
Solution:-
- The deflated ball ( no air ) initially weighs:
m1 = 0.615 kg
- The air is pumped into the ball and weight again. The new reading of the ball's weight is:
m2 = 0.624 kg
- The amount of air ( mass of air ) pumped into the ball can be determined from simple arithmetic between inflated and deflated weights of the ball.
m_air = Δm = m2 - m1
m_air = 0.624 - 0.615
m_air = 0.009 kg
- We are to assume that the inflated ball takes a shape of a perfect sphere with radius r = 0.24 m. The volume of the inflated ( air filled ) ball can be determined using the volume of sphere formula:
V_air = 4*π*r^3 / 3
V_air = 4*π*0.24^3 / 3
V_air = 0.05790 m^3
- The density of air ( ρ_air ) is the ratio of mass of air and the volume occupied by air. Expressed as follows:
ρ_air = m_air / V_air
ρ_air = 0.009 / 0.05790
Answer: ρ_air = 0.15544 kg/m^3
Answer:
a) 
b) The population increases 7.1% each year.
Step-by-step explanation:
The continuous population growth model is given by:
In which 
is the population after t years, 
is the initial population and r is the growth rate.
In this problem, we have that:
A population grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.
This means that 
a) Write a function to model the population increase.
b) By what percent does the populaiion increase each year?
So the population increases 7.1% each year.
