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3 years ago

Parallel and Transversal Lines

Mathematics

1 answer:

Len [333]3 years ago

6 0

Answer:

Step-by-step explanation:

1) Vertical angles - (G) are the opposite angles formed by two intersecting lines that are congruent because the angles have the same measure

2)Alternate interior angles: (H) Are formed when a transversal line passes

through a pair of parallel lines and formed on opposite sides of the transversal inside the parallel lines.

3) Corresponding angles: F) Two equal angles on the same side of a line

that crosses two parallel lines and on the same side of each parallel line

4) Exterior angles:(A) Are the angles above and below the pair of parallel lines

5) Supplementary angles:(B) Two angles that have measures with a sum

of 180°

6) Alternate Exterior angles:(D) Are formed when a transversal line passes

through a pair of parallel lines and formed on opposite sides of the transversal above and below the parallel lines.

7) Adjacent angles: (C) are pair of angles that share a vertex and one side but do not overlap

8) Complementary angles: (I) Two angles that have measures with a sum 90°

9) Interior angles: (E) are the angles inside the pair of parallel lines

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A firework is fired into the air from the top of a barn. Tis hight (h) above the ground in yards after (t) seconds is given by t

Grace [21]

The given function for the height of the firework is a quadratic function

1. Time at which the firework reaches the maximum height is 1 seconds

2. The maximum height of the firework, is 25 yards

3. Time after which the firework will fall to the ground is (1 + √5) seconds

Reason:

The given function that represents the height of the fireworks with time is

presented as follows;

h(t) = -5·t² + 10·t + 20

1. The time at which the firework reaches its maximum height is given by

the maximum point of the given function as follows;

The x-value of the maximum point of a quadratic function is $x = \dfrac{b}{2 \cdot a}$

Where;

a, and b, are the coefficient of x² and x, in the general form of a quadratic function f(x) = a·x² + b·x + c

By comparison, we have;

$t = -\dfrac{10}{2 \times (-5)} = 1$

The time at which the firework reaches the maximum height is t = 1 seconds

2. The maximum height is given by plugging in the value of t, at the maximum point into the given function as follows;

h(1) = -5×1² + 10×1 + 20 = 25

The maximum height of the firework, f(1) = 25 yards

3 The time at which the firework will fall to the ground, is given by the zero of the function as follows;

When the firework falls to the ground, h(t) = 0 = -5·t² + 10·t + 20

Dividing both sides by (-5) gives;

$\dfrac{0}{-5} = \dfrac{ -5 \cdot t^2 + 10 \cdot t + 20}{-5} = t^2 - 2 \cdot t - 4$

t² - 2·t - 4 = 0

By the quadratic formula $x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$ , we get;

$t = \dfrac{2\pm \sqrt{(-2)^{2}-4\times 1\times (-4)}}{2\times 1} = \dfrac{2\pm \sqrt{20}}{2\times 1} = \dfrac{2\pm 2 \times \sqrt{5}}{2\times 1} = 1 \pm \sqrt{5}$

Therefore;

The time after which the firework will fall to the ground, t = 1 + √5 seconds

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