Answer:
125
Step-by-step explanation:
Given
f(x) = 5x²
g(x) = 2x + 3
Now
g(-4) = 2 * (- 4) + 3
= - 8 + 3
= - 5
Also
f(g(-4)) = f( -5)
= 5 * ( -5)²
= 5 * 25
= 125
Answer:
y = -4/3x -9
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
8x+6y = -54
Subtract 8x from each side
8x+6y-8x = -8x-54
6y = -8x-54
Divide each side by 6
6y/6 = -8x/6 -54/6
y = -4/3x -9
Answer:
School needs to collect at least 144 box tops each day to meet their goal.
Step-by-step explanation:
The total requirement of box tops = 2,000
The number of box tops they have already received = 872
So, the box tops left = Total number required- Number of tops received
=2,000 - 872
= 1,128 box tops are left so far.
Number of days left = 8
So, number of minimum tops needed each day = 
= 
Hence, they need to collect at least 144 box tops each day to meet their goal.
The question involves the concept & equations associated with projectile motion.
Given:
y₁ = 1130 ft
v₁ = +46 ft/s (note positive sign indicates upwards direction)
t = 6.0 s
g = acceleration due to gravity (assumed constant for simplicity) = -32.2 ft/s²
Of the possible equations of motion, the one we'll find useful is:
y₂ = y₁ + v₁t + 1/2gt²
We can just plug and chug to define the equation of motion:
<u><em>y = (1130 ft) + (46 ft/s)t + 1/2(-32.2 ft/s²)t²</em></u>
<em>(note: if you were to calculate y using t = 6.0 s, you'd find that y = 826.4 ft, instead of 830 ft exactly because of some rounding of g and/or the initial velocity)</em>
