What is the slope of 4x+5y= -10

Question:

1) The kick is good! The ball passes about 10 feet above the crossbar.

2) The kick is good! The ball clears the crossbar by approximately 14 feet.

3) The kick is good! The ball clears the crossbar by about 4 feet.

4) The kick is not successful. The ball is 2 feet too low.

Answer:

The correct option is;

3) The kick is good! The ball clears the crossbar by about 4 feet.

Step-by-step explanation:

Here we have

Horizontal distance from goal, x = 36 yards = 108 ft

Vertical distance of goal, y = 10 ft

Angle of elevation of ball = 34°

Initial velocity of ball, v₀ = 68 ft/s

∴ Vertical component of velocity = = v₀×sin(θ₀)×t - g×t

Horizontal component of velocity = vₓ = 68×cos(34) = 56.375 ft/s

The equation for projectile motion is as follows

x = x₀ + v₀×cos(θ₀)×t

y = y₀ + v₀×sin(θ₀)×t - 1/2×g×t²

Where:

x₀ = Initial horizontal displacement of the ball = 0

y₀ = Initial vertical displacement of the ball = 0

t = Time of flight of the ball

Therefore;

108 = 0 + 68×cos(34)×t which gives;

t = 108/56.375 = 1.916 seconds

Hence, y = y₀ + v₀×sin(θ₀)×t - 1/2×g×t² gives;

y = 0 + 68×sin(34)×1.916 - 1/2×32.2×1.916²

y = 72.85 - 59.09 = 13.76 ft, hence the vertical location of the ball at 36 yard is 13.76 ft where the crossbar is at 10 ft hence the ball clears the crossbar by 13.76 ft - 10 ft = 3.76 ft ≈ 4 ft

Therefore, the kick is good! The ball clears the crossbar by about 4 feet.

Answer:

Option B is correct.

Step-by-step explanation:

Solving using synthetic division

-8 | 2 14 9

The synthetic division is shown in image attached.

The remainder is: 25

The quotient is : 2x-2

So, Option B is correct.

Answer:

40° is  the temperature  for which the number of  degrees Fahrenheit is equal to the number  of degrees Celsius.

Step-by-step explanation:

Given : F = 1.8C + 32 gives the temperature  in degrees Fahrenheit (F ) for a given  temperature in degrees Celsius (C ).

To Find: There is  one temperature for which the number of  degrees Fahrenheit is equal to the number  of degrees Celsius. Write an equation you  can solve to find that temperature and  then use it to find the temperature.

Solution :

Given Formula :  F = 1.8C + 32

If number of  degrees Fahrenheit is equal to the number  of degrees Celsius

Then ,

⇒ -0.8C =32

⇒

⇒

Thus The equation we can use to find the temperature  for which the number of  degrees Fahrenheit is equal to the number  of degrees Celsius:

40° is  the temperature  for which the number of  degrees Fahrenheit is equal to the number  of degrees Celsius.