In the diagram below, TUVW is a rectangle. Prove triangle TZW is congruent to triangle UZV.
1 answer:
Answer:
By S.S.S. congruence property; ΔTZW ≅ ΔVZU
Step-by-step explanation:
Given:
TUVW is a rectangle.
To Prove : TZW ≅ UZV
Proof:
Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.
So,
And also TV and WU are the diagonals of the rectangle.
And the diagonals of rectangle bisects each other.
Therefore;
Now In ΔTZW and ΔVZU
TW = UV (from 1)
TZ = ZV (from 2)
WZ = ZU (from 3)
So, by S.S.S. congruence property;
ΔTZW ≅ ΔVZU
Hence proved.
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Function B)
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This is an exponential function. This type of function is a non-algebraic function. It's also called <span>transcendental function.
</span>Function C)
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It's a straight line with slope equal to 100 and without y-intercept.
Function D)
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It's a cubic function. It's a third</span>-degree polynomial function.
So from the figure it is obvious that the function that grows at the fastest rate is the exponential function B). In fact, an exponential function always grows more quickly than a polynomial function.
Function A)
This is a quadratic function. This type of function is a second-degree polynomial function.
Function B)
</span>
This is an exponential function. This type of function is a non-algebraic function. It's also called <span>transcendental function.
</span>Function C)
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It's a straight line with slope equal to 100 and without y-intercept.
Function D)
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Refer to the diagram shown below.
The path of the rock is
y = -0.005x² + 0.4x - 5.1
When x = 0, y = -5.1 ft, which is the location of the hole level.
The rock reaches ground level two times when x = x₁ and when x = x₂.
At ground level, y = 0. Therefore
-0.005x² + 0.4x - 5.1 = 0
Divide through by -0.005.
x² - 82x + 1020 = 0
Solve with the quadratic formula.
x = (82 +/- √(82² - 4*1020))/2
= (82 +/- 51.4198)/2
x = 66.71 or x = 15.29
The smaller value of x is x₁ = 15.3 ft when the rock emerges out of the hole and reaches ground level.
The larger value of x is x₂ = 66.7 ft when the rock falls to the ground.
The rock lands 66.7 ft horizontally from Landon.
Answer: 66.7 ft
The path of the rock is
y = -0.005x² + 0.4x - 5.1
When x = 0, y = -5.1 ft, which is the location of the hole level.
The rock reaches ground level two times when x = x₁ and when x = x₂.
At ground level, y = 0. Therefore
-0.005x² + 0.4x - 5.1 = 0
Divide through by -0.005.
x² - 82x + 1020 = 0
Solve with the quadratic formula.
x = (82 +/- √(82² - 4*1020))/2
= (82 +/- 51.4198)/2
x = 66.71 or x = 15.29
The smaller value of x is x₁ = 15.3 ft when the rock emerges out of the hole and reaches ground level.
The larger value of x is x₂ = 66.7 ft when the rock falls to the ground.
The rock lands 66.7 ft horizontally from Landon.
Answer: 66.7 ft
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We have a = 18cm, b = 24cm and c = 30cm. Substitute and check: