Answer:
ABCD is a parallelogram
Step-by-step explanation:
Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a
parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC
1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2.
definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3.
alternate interior angles are congruent 4. AC ≅ AC 4.
reflexive property 5. △CAD ≅ △ACB 5. SAS congruency
theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7.
-7 and 8 are the solutions to the given equation system.
Therefore, the maximum distance between the y values of the two equations must lie exactly between their points of intersection. That is on x value:
x = (-7 + 8)/2 = 0.5
The maximum distance is:
y = 0.5 + 56 = 56.5
y = 0.5² = 0.25
56.5 - 0.25 = 56.25 units
Answer:the original height of the candle is 14.8 inches
Step-by-step explanation:
A Candlestick burns at a rate of 0.2 inches per hour. It means that the height of the candle is decreasing by 2 inches per hour. This decrease is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
d = - 0.2 (it is decreasing)
n = 8
T8 = 13.4 inches
We want to determine the value of the first term, a. Therefore,
13.4 = a - 0.2(8 - 1)
13.4 = a - 1.4
a = 13.4 + 1.4 = 14.8 inches
We know that
volume of <span>a rectangular prism =B*h------> equation 1
where
B is the area of the base
h is the height
volume of </span><span>a rectangular pyramid=(1/3)*B*h-----> equation 2
where
</span>B is the area of the base
h is the height
<span>
substitute equation 1 in equation 2
</span>volume of a rectangular pyramid=(1/3)*volume of a rectangular prism
<span>
the answer part a) is
</span>volume of a rectangular pyramid=(1/3)*volume of a rectangular prism
<span>
Part b) </span><span>If the pyramid was full of water, how much of the prism would it fill up?
</span>
the answer part b) is
<span>If the pyramid was filled with water, the prism would only fill 1/3 of its volume
Part c) </span><span>Name another pair of three-dimensional objects that have a relationship similar to this
cones and cylinders
</span>volume of a cylinder =B*h------> equation 1
where
B is the area of the base
h is the height <span>
</span>volume of a cone=(1/3)*B*h-----> equation 2
where
B is the area of the base
h is the height
substitute equation 1 in equation 2
volume of a cone=(1/3)*volume of a cylinder
