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Gnesinka [82]
3 years ago
14

A homeowner has 200 feet of fence to enclose an area for a pet.

Mathematics
1 answer:
marishachu [46]3 years ago
7 0
<h3>Answer:</h3>
  • (a) x = 50 maximizes the area. We assume that means 50 ft × 50 ft
  • (b) 2500 ft²
  • (c) domain: 0 ≤ x ≤ 100; range: 0 ≤ A ≤ 2500
<h3>Step-by-step explanation:</h3>

(a) The function describes a parabola that opens downward. The value of A(x) is zero when x=0 and when x=100. The vertex (maximum) is halfway between those zeros, at x=50. The dimensions are 50 and 100-50 = 50. The maximum area pen will be 50 ft square.

(b) A(50) = (50 ft)² = 2500 ft² . . . the maximum area

(c) A(x) will be negative if x < 0 or x > 100, so the domain is 0 ≤ x ≤ 100.

The value of A(x) ranges from 0 to its maximum, 2500. Hence the range is 0 ≤ A(x) ≤ 2500.

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The product of 2 numbers is -24 and their sum is -5. What are the two numbers and why are they the two numbers?
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The numbers are (-8, 3) or (3, -8).

Step-by-step explanation:

  • Step 1: Given the product of the numbers are -24 and their sum are -5. Let the numbers be a and b. Form equations out of these details.

⇒ a + b = -5 ⇒ b = -5 - a

⇒ a × b = -24 -------- (1)

  • Step 2: Substitute the value of b in eq(1)

⇒ a × (-5 - a) = - 24

⇒ -5a - a² = -24

⇒ a² + 5a - 24 = 0

  • Step 3: Solve the quadratic equation for a.

a = (-5 ± √25 - 4 × 1 × -24)/2

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  • Step 4: For each value of a, find b.

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6 0
2 years ago
What's the hcf and lcm of 5and 7​
svetlana [45]

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(x + 5)² + (y - 4)² = 36

Step-by-step explanation:

The equation of a circle in standard form id

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (- 5, 4) and r = 12 ÷ 2 = 6 , thus

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3 + 15 =

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2 years ago
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