Answer: The system of
equations that best models this situation are
y = 30x + 120
z = 75x + 15
Step-by-step explanation:
Let x represent the number of months for which John Urschel wants to use either plans of the gym.
Let y represent the total cost of using plan A for x months
Let z represent the total cost of using plan B for x months.
Plan A has a $120 sign-up fee and costs an additional $30 per
month. This means that the total cost of using plan A for x months is expressed as
y = 30x + 120
Plan B costs $75 per month with a signup fee of $15. This means that the total cost of using plan B for x months is expressed as
z = 75x + 15
<span>0 = x² + 10x + 16
Subtract </span><span>x^2+10x+16 from each side
</span><span>0−<span>(<span><span>x^2+10x</span>+16</span>) </span></span>= x^2+10x+16−(<span>x^2+10x+16</span>)
<span><span>−x^2−10x</span>−16</span>=<span>0
</span>
Factor left side
<span><span>(<span>−x−2</span>)</span><span>(x+8)</span></span>=<span>0
</span>
Set all factors to equal 0
<span><span><span>−x</span>−2</span>=<span><span><span>0<span> or </span></span>x</span>+8</span></span>=<span>0
</span>
The solutions are x = -2 and x = -8
Answer:
52.24 km
Step-by-step explanation:
Given that,
The distance needed to stop a car, d, varies directly as the square of the speed, s, at which it is travelling.
d = ks²
Where
k is constant
When s₁ = 70 km/hr, d₁ = 40 m, s₂ = 80 km/hr, d₂ = ?
So,
![\dfrac{d_1}{d_2}=\dfrac{s_1^2}{s_2^2}\\\\d_2=\dfrac{d_1s_2^2}{s_1^2}\\\\d_2=\dfrac{40\times 80^2}{70^2}\\\\d_2=52.24\ km](https://tex.z-dn.net/?f=%5Cdfrac%7Bd_1%7D%7Bd_2%7D%3D%5Cdfrac%7Bs_1%5E2%7D%7Bs_2%5E2%7D%5C%5C%5C%5Cd_2%3D%5Cdfrac%7Bd_1s_2%5E2%7D%7Bs_1%5E2%7D%5C%5C%5C%5Cd_2%3D%5Cdfrac%7B40%5Ctimes%2080%5E2%7D%7B70%5E2%7D%5C%5C%5C%5Cd_2%3D52.24%5C%20km)
So, the new distance is 52.24 km.
True, this is in accordance to the side-side-side postulate.