Answer:
<u>Part A</u>
- Reflect over the y-axis: (x, y) → (-x, y)
A (-4, 4) → (4, 4)
B (-2, 2) → (2, 2)
C (-2, -1) → (2, -1)
D (-4, 1) → (4, 1)
- Shift 4 units down: (x, y-4)
(4, 4-4) → A' (4, 0)
(2, 2-4) → B' (2, -2)
(2, -1-4) → C' (2, -5)
(4, 1-4) → D' (4, -3)
<u>Part B</u>
Two figures are <u>congruent</u> if they have the same shape and size. (They are allowed to be rotated, reflected and translated, but not resized).
Therefore, ABCD and A'B'C'D' are congruent. They are the same shape and size as they have only be reflected and translated.
Angles are classified based on their measures.
<u>Classification of angles</u>
The following are the classification of angles
- Acute Angles
- Right Angles
- Obtuse Angles
- Straight lines
- Reflex Angles
The smallest angle is 0 degrees and the largest is 360 degrees.
When the measure of an angle is less than 90 degrees, such angle is an acute angle
When the measure of an angle is exactly 90 degrees, such angle is a right angle
Angles greater than 90 degrees, but less than 180 degree are obtuse angles, while angles that measure exactly 180 degrees are straight lines.
The last type of angle is the reflex angle, and it has a measure between 180 degrees and 360 degrees (exclusive)
<em>The question is incomplete, so I gave a general explanation</em>
Read more about angles at:
brainly.com/question/17972372
Exponential functions are known to increase geometrically. An example of exponential function is p(x) = 500(1.02)^x
<h3>Exponential functions</h3>
Exponential functions are known to increase geometrically. The standard exponential function is given as:
y = ab^x
a is the base
x is the exponent
From the given options, the function written in this form is
p(x) = 500(1.02)^x. Hence an example of exponential function is
p(x) = 500(1.02)^x
Learn more on exponential function here: brainly.com/question/12940982
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Answer:
a = length of the base = 2.172 m
b = width of the base = 1.357 m
c = height = 4.072 m
Step-by-step explanation:
Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?
lets call a = length of the base
b = width of the base
c = height
V = a.b.c = 12
Area without the top:
Area = ab + 2bc + 2ac
Cost = 12ab + 8.2bc + 8.2ac
Cost = 12ab + 16bc + 16ac
height = 3.width
c = 3b
Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab
abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²
Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b
C(b) = 48b² + 240/b
C'(b) = 96b - 240/b²
Minimum cost: C'(b) = 0
96b - 240/b² = 0
(96b³ - 240)/b² = 0
96b³ - 240 = 0
96b³ = 240
b³ = 240/96
b³ = 2.5
b = 1.357m
c = 3b = 3*1.357 = 4.072m
a = 4/b² = 2.172m
16 is the answer to this question.
