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4 years ago

In the diagram shown at the right, a 2-foot-wide flower border surrounds the heart-shaped pond. What is the area of the border?

Mathematics

1 answer:

True [87]4 years ago

6 0

The area is 139.02 sq. ft.

This can be broken into two shapes: a 12 by 12 square and a circle with a diameter of 12. Adding the 2 ft border increases it to a 14 by 14 square and a circle with a radius of 16 (2 on each side).

With border:

Area of square = 14*14 = 196
Area of circle = 3.14(8*8) = 200.96

Together = 396.96

Without border:

Area of square = 12*12 = 144
Area of circle = 3.14(6*6) = 113.04

Together = 257.04

This is a difference of 396.96-257.04 = 139.02 sq. ft.

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scoray [572]

Answer:

"Solving'' an inequality means finding all of its solutions. A "solution'' of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality.

Step-by-step explanation:

Example 1:

Consider the inequality

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The basic strategy for inequalities and equations is the same: isolate x on one side, and put the "other stuff" on the other side. Following this strategy, let's move +5 to the right side. We accomplish this by subtracting 5 on both sides (Rule 1) to obtain

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after simplification we obtain

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or simplified,

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All real numbers less than 1 solve the inequality. We say that the "set of solutions'' of the inequality consists of all real numbers less than 1. In interval notation, the set of solutions is the interval tex2html_wrap_inline187 .

Example 2:

Find all solutions of the inequality

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Let's start by moving the ``5'' to the right side by subtracting 5 on both sides (Rule 1):

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or simplified,

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or simplified

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Example 3:

Solve the inequality

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Let us simplify first:

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There is more than one route to proceed; let's take this one: subtract 2x on both sides (Rule 1).

displaymath209

and simplify:

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Next, subtract 9 on both sides (Rule 1):

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Then, divide by 4 (Rule 3a):

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and simplify again:

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It looks nicer, if we switch sides (Rule 2).

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2 years ago

How do you do this question

maxonik [38]

Answer:

I am not sure about the actual answer but hopefuly you figure this out

Step-by-step explanation:

To get the number of boys and girls you do 3+5 to get 8. 120 divided by 8 is 15. so every digit in the ratio is 15 students. 15x3 is 45 and 15x5 is 75. there are 45 girls and 75 boys. 16/25 of the boys go climbing. There are 75 boys so you do 16x3 because 25x3 is 75 so 16x3 is 48. 48 boys go climbing. 120-48 is 72. and 27 boys go sailing.

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3 years ago

How do I work this out?

riadik2000 [5.3K]

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3 years ago

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Mashcka [7]

Answer:

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Step-by-step explanation:

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3 years ago

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What is the solution set of -|x|=-8

Novosadov [1.4K]

-|x|=-8

-x = - 8

x = 8

and

- (-x) = - 8

x = - 8

Answer

x = -8 , 8

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3 years ago