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grigory [225]
3 years ago
10

An office building has a cement block under its dumpster. The pad has an area of 108 square feet. The dumpster is 9 ft long and

8 ft wide. What is the most likely perimeter of the cement pad
Mathematics
1 answer:
juin [17]3 years ago
5 0

Answer:

Most likely Perimeter of the pad is 42 ft.

Step-by-step explanation:

Area of the Cement pad = 108 feet²

Length of the dumpster = 9 ft

Width of the dumpster = 8 ft

Cement pad surface is greater than dumpster to hold it.

Area of pad = 108 ft²

length × width = 108

we choose length and width such that they are greater than length and width of the dumpster.

So, length of the pad = 12 ft

Width of the pad = 9 ft

Thus, Perimeter = 2 × (length +  width) = 2 × ( 12 + 9 ) = 2 × 21 = 42 ft

Therefore, Most likely Perimeter of the pad is 42 ft.

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Given the center and radius of a circle, write the equation of the circle.
Mashutka [201]

Answer:

(x + 2)² + (y - 1)² = 25

General Formulas and Concepts:

<u>Algebra I</u>

  • Coordinates (x, y)

<u>Pre-Calc</u>

Circle Center Formula: (x - h)² + (y - k)² = r²

  • <em>(h, k)</em> is center
  • <em>r</em> is radius

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

<em>(h, k)</em> = (-2, 1)

<em>r</em> = 5

<u>Step 2: Find Equation</u>

  1. Substitute in variables [Circle Center Formula]:                                             (x - -2)² + (y - 1)² = 5²
  2. Simplify:                                                                                                             (x + 2)² + (y - 1)² = 25

Topic: Pre-Calculus

Unit: Conics

Book: Pre-Calculus (McGraw Hill)

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3 years ago
The length of the flower garden is 3 times as great as the width. What are the dimensions? The area is 48 sq m
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Which expressions are equivalent to the one below? Check all that apply. <br><br> 9^x
AveGali [126]

Answer:

A) 3^{x}*3^{x}

B) 3^{2x}

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Step-by-step explanation:

Given the exponential expression, 9^{x}:

A)  3^{x}*3^{x} is equivalent to 9^{x} due to the Product Rule of exponents:  a^{m} a^{n} = a^{m + n}.  

  • 3^{x}*3^{x} = 3^{x+x} = 3^{2x}

Next, apply the Power-to-Power Rule of exponents:  a^{mn} = (a^{m} )^{n}.  

  • 3^{x}*3^{x} = 3^{x+x} = 3^{2x} = (3^{2})^{x}  = 9^{x}

B)   3^{2x}  is equivalent to 9^{x} due to the Power-to-Power Rule of exponents:  a^{mn} = (a^{m} )^{n}.  

  • 3^{2x} = (3^{2})^{x} = (9)^{x} = 9^{x}.    

C)  (3 * 3)^{x}  is equivalent to 9^{x} due to the Product-to-Power Rule of exponents:  (ab)^{m} = a^{m} b^{m}.  

  • (3 * 3)^{x} = (9)^{x}  = 9^{x}  
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Answer:

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