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2 years ago

What is the area of the figure?

Mathematics

1 answer:

Minchanka [31]2 years ago

7 0

9514 1404 393

Answer:

Step-by-step explanation:

You know the area is almost, but not quite, the area of two squares that are 6 m on a side. The area of one of those squares is (6 m)² = 36 m². The area of two of them is 2×36 m² = 72 m².

Since the area is larger than 36 m² and smaller than 72 m², there is only one answer choice that makes any sense:

64.26 m²

Additional comment

That value is obtained using 3.14 for pi.

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If (5^2)p = 5^12, what is the value of p?

mr Goodwill [35]

Divide both sides by 5^2 (which is 25). So p = (5^12)/25. I can't be bothered to plug in into a calculator but be my guest.

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3 years ago

Each batch of granola Lena makes uses 3 cups of oats, 1 cup of raisins, and 2 cups of nuts. Lena wants to make 4 batches of gran

pogonyaev

Answer:

12 cups oats, 4 cups raisins, 8 cups nuts

Step-by-step explanation:

For this problem, just multiply each ingredient by 4

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3 years ago

Read 2 more answers

The resultant of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 2

kifflom [539]

The basic idea is that you form a parallelogram with those two vectors as the two different side lengths another way to see it: start at the tip of one vector and move in the same direction as the other vector (and the same length as the other vector)

With any parallelogram, the adjacent angles are supplementary

180-52-20= 108 degrees

5 0

3 years ago

Suppose ten students in a class are to be grouped into teams. (a) If each team has two students, how many ways are there to form

ValentinkaMS [17]

Answer:

(a) There are 113,400 ways

(b) There are 138,600 ways

Step-by-step explanation:

The number of ways to from k groups of n1, n2, ... and nk elements from a group of n elements is calculated using the following equation:

$\frac{n!}{n1!*n2!*...*nk!}$

Where n is equal to:

n=n1+n2+...+nk

If each team has two students, we can form 5 groups with 2 students each one. Then, k is equal to 5, n is equal to 10 and n1, n2, n3, n4 and n5 are equal to 2. So the number of ways to form teams are:

$\frac{10!}{2!*2!*2!*2!*2!}=113,400$

For part b, we can form 5 groups with 2 students or 2 groups with 2 students and 2 groups with 3 students. We already know that for the first case there are 113,400 ways to form group, so we need to calculate the number of ways for the second case as:

Replacing k by 4, n by 10, n1 and n2 by 2 and n3 and n4 by 3, we get:

$\frac{10!}{2!*2!*3!*3!}=25,200$

So, If each team has either two or three students, The number of ways form teams are:

113,400 + 25,200 = 138,600

6 0

3 years ago

When a sprinkler is installed in the ground, the spray of water goes up and falls in the pattern of a parabola. The height, in i

Westkost [7]

Answer:

(1) 256 inches

(2) 5 feet

(3) 400 inches

(4) 10 feet

Step-by-step explanation:

(1) The function that gives the height in inches of the spray of water at a distance x from the sprinkler head is given as follows;

h(x) = 160·x - 16·x²

At x = 2 feet, we have;

h(2) = 160 × 2 - 16 × 2² = 256

Therefore, the height of the spray water at a horizontal distance of 2 feet from the sprinkler head h(2) = 256 inches

(2) The x-coordinate, $x_{max}$ , of the maximum point of a parabola given in the form, y = a·x² + b·x + c is found using the following formula;

$x_{max}$ = -b/(2·a)

The x-coordinate, $x_{max}$ , of the maximum point of the given equation of the parabola, h(x) = 160·x - 16·x², (a = -16, b = 160) is therefore;

$x_{max}$ = -160/(2 × (-16)) = 5

Therefore, the number of feet along the way, the function will reach maximum height, $x_{max}$ = 5 feet

(3) The function, h(x) = 160·x - 16·x², will reach maximum height, $h_{max}$ , at x = 5, therefore;

$h_{max}$ = h(5) = 160 × 5 - 16 × 5² = 400

The maximum height of the spray, $h_{max}$ = 400 inches

(4) The water is at ground level where h(x) = 0, therefore;

At ground level, h(x) = 0 = 160·x - 16·x²

160·x - 16·x² = 0

∴ 16·x × (10 - x) = 0

By zero product rule, we 16·x = 0, or (10 - x) = 0, from which we have;

x = 0, or x = 10

The water is at ground level at x = 0 and x = 10 feet, therefore, the water will hit the ground again (the second time after leaving the sprinkler head at x = 0) at x = 10 feet.

7 0

3 years ago