On average, Donna's Cafe has 84 customers, which represents 24% of the total approved occupancy by the fire department. a. What
1 answer:
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Answer:
Correct choices are a, b, e
Step-by-step explanation:
As per diagram, the circles are equal.
<u>Since the distance AB is the radius of both circles:</u>
- AB = AC = BC = BD = AD = r
<u>So the answer choices:</u>
a. AC = BC
- Correct, both equal to r
b. AC = BD
- Correct, both equal to r
C. CD = AB
- Incorrect. Half of CD is the leg of 30-60-90 triangle and is equal to r√3/2, so CD = AB√3
d. ABCD is a square
- Incorrect. ACBD is rhombus
e. ABD is an equilateral triangle
- Correct, all three sides are equal to r
f. CD = AB + AB
- Incorrect as CD = AB√3
The cost of pen and pencils are related to the number that can be bought
with a given amount of money.
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Reasons:
The given parameters are;
If the number number of pens and pencils James buys = 3 pens and 2 pencils, the amount James will have left = $2
If the number of pens and pencils James buys = 2 pens and 3 pencils, the amount James will have left = $6
The amount of money Judith has = The amount of money with James
The number of pens and pencil James and Judith can buy = 6 pens and 6 pencils
The cost of one pen = a
The cost of one pencil = b
Required:
To find the ordered pair (a, b)
Solution:
Let <em>X</em> represent the initial amount of money James has, we get;
X - (3·a + 2·b) = 2...(1)
X - (2·a + 3·b) = 6...(2)
2·X = 6·a + 6·b...(3)
Therefore;
X = (6·a + 6·b) ÷ 2 = 3·a + 3·b
Which from equation (1) gives;
3·a + 3·b - (3·a + 2·b) = 2
3·a + 3·b - 3·a - 2·b = 2
3·b - 2·b = 2
b = 2
Subtracting equation (1) from equation (2) gives;
(X - (2·a + 3·b)) - (X - (3·a + 2·b)) = 6 - 2 = 4
-2·a - 3·b + 3·a + 2·b = 4
a - b = 4
a = 4 + b
∴ a = 4 + 2 = 6
a = 6
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