4^2 4x4 =16
4^3 4x4x4 =64
4^4 4x4x4x4 =256
4^5 4x4x4x4x4 =1,024
what do you see
The answer is: 13 units.
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Each side of the park is 13 units long.
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(Assuming hexagonal shape will have 6 (SIX) sides of equal length).
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Explanation:
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Let us assume you meant to write that the: "...new park, in the shape of hexagon, will have 6 (six) side of equal length."
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From the coordinates given, we can infer that this is a "regular" hexagon.
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Here is one way to solve the problem: Find the length of ONE side of the hexagon.
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Let us choose the following coordinates: (18,0), and (6.5, 5). Let the distance between these points , which would equal ONE side of our hexagon, represent "c", the hypotenuse of a right triangle. We want to solve for this value, "c".
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Let the distance on the x-axis, from (6.5, 0) to (18.5, 0); represent "b", one side of a right triangle.
→ We can solve for "b" ; → b = 18.5 - 6.5 ; → b = 12 .
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Let the distance from (6.5, 0) to (6.5, 5) ; represent "a"; the remaining side of the right triangle.
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→ a = y₂ - y₁ = 5 - 0 = 5 ;
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{Note: We choose the particular coordinates, including "(6.5, 0)", because the distances between the coordinates chosen form a "right triangle"; (with "c", representing a "hypotenuse", or "slanted line segment"; which would be also be "ONE line segment of the given regular hexagon", which is our answer, because each line segment is the same values, so we only have to find the value of ONE line segment, or side, of the hexagon.).
When considering the given coordinates: "(6.5, 5)", and "(18.5, 0)", a "right triangle" can be formed at the coordinate, "(6.5, 0),
By choosing this particular letters (variables) to represent the sides of a "right triangle", we can solve for the "hypotenuse, "c", using the Pythagorean theorem for the sides of a right triangle:
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→ a² + b² = c² ; in which "c" represents the hypotenuse of the right triangle
and "a" represents the length of one of the other sides; and "b" represents the length of the remaining side. (Note: All triangles have three sides).
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We have: a = 5 ; b = 12 ; → Solve for "c" ;
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→ a² + b² = c² ; ↔ c² = a² + b² ; Plug in the known values for "a" & "b" ;
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→ c² = a² + b² ; → c² = 5² + 12² ;
→ c² = 25 + 144 = 169 ; → c² = 169 ;
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→ Take the square root of each side; to isolate "c" on one side of the equation; and to solve for "c" ;
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→ c² = 169 ; √(c²) = √(169) ; → c = ± 13;
→ ignore the negative value; since the side of a polygon cannot be a negative number;
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→ c = 13 ; The answer is: 13 units.
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Answer:
at matilda's new job, she will make a rounded salary of $69,000 per year.
Step-by-step explanation:
when solving a problem like this, you have to take her current salary ($64,000 per year) and multiply it to the salary increase percentage by first turning the percentage into a decimal. to turn the percentage into a decimal, you imagine a tiny dot to the right of the 8 like this:
8.
and then you have to move that little dot to the left two times recreating it into .08. you multiply .08 (the salary increase percentage) by her current salary ($64,000) and then also add that number to matilda's current salary to come up with the answer you can round. I'll give you an example of my proscess just so I can give a clear visual of my explanation.
step one:
$64,000
x .08
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5,120
step 2:
$64,000
+$5,120
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$69,120
step 3:
$69,120 is rounded up to the nearest thousands is approximately $69,000
answer: $69,000
From ages 6-12 months a baby would increase in weight by an average of 3-5 ounces a week