Answer: B
Step-by-step explanation: Since all triangles have angles that add to 180 degrees, add the two known angles and then subtract that from 180.
29 + 108 = 137
180 - 137 = 43
Answer:
The ball is in the air for approximately 3.27 seconds ⇒ answer A
Step-by-step explanation:
* Lets explain how to solve the problem
- The height of the ball is modeled by the function
h(t) = -4.9 t² + 16 t
- We need to find the time that the ball is in the air
- The ball is in the air from its initial position and then return to the
same position
- That means h(t) = 0 because h(t) represent the height of the ball
from its initial position
∵ h(t) = -4.9 t² + 16 t
∵ h(t) = 0
∴ 0 = -4.9 t² + 16 t
- Add 4.9 t² to both sides
∴ 4.9 t² = 16 t
- Subtract 16 t from both sides
∴ 4.9 t² - 16 t = 0
- Take t as a common factor
∴ t (4.9 t - 16) = 0
- Equate each factor by 0
∴ t = 0 and 4.9 t - 16 = 0
∵ 4.9 t - 16 = 0 ⇒ add 16 for both sides
∴ 4.9 t = 16
- Divide both sides by 4.9
∴ t = 3.2653
∴ t = 0 ⇒ initial position
∴ t = 3.2653 seconds ⇒ final position
* <em>The ball is in the air for approximately 3.27 seconds</em>
we have

Combine like terms in both sides

we know that

substitute in the expression above
-----> equation A
Multiply equation A by
both sides

---------> equation B
Group terms that contain the same variable, and move the constant to the opposite side of the equation

---------> equation C
Solve for x

We are going to proceed to verify each case to determine the solution.
<u>Case a)</u> 
the case a) is equal to the equation A
so
the case a) have the same solution that the given equation
<u>Case b)</u> 
Combine like terms in left side


the case b) is equal to the equation B
so
the case b) have the same solution that the given equation
<u>Case c)</u> 
Combine like terms in left side




therefore
the case c) not have the same solution that the given equation
<u>Case d)</u> 
Combine like terms in left side

the case d) is equal to the equation C
so
the case d) have the same solution that the given equation
<u>Case e)</u> 
Combine like terms in left side



therefore
the case e) not have the same solution that the given equation
therefore
<u>the answer is</u>
case a) 
case b) 
case d) 
Answer:
(5/2)√13 ≈ 9.0139
Step-by-step explanation:
The longer hypotenuse is found using the Pythagorean theorem as ...

The right triangles are AA similar, and vertical sides correspond. Their ratio, smaller/larger is 5/8. That means the hypotenuse of the smaller triangle, A, is 5/8 of the hypotenuse of the larger one.
