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7nadin3 [17]
3 years ago
14

One side of a kite is 6 cm less than 4 times the length of another. The perimeter of the kite is 68 cm. Find the length of each

side of the kite.
Mathematics
1 answer:
strojnjashka [21]3 years ago
3 0
Perimeter:

p = 2b + 2h = 68

b = 4h - 6 (per problem statement)

substituting for b in the perimeter equation:

p = 2(4h - 6) + 2h = 68

(2)(4h) - (2)(6) + 2h = 68

8h - 12 + 2h = 68

10h - 12 = 68

10h = 68 + 12

10h = 80

h = 80/10

h = 8

b = 4(8) - 6 = 32 - 6 = 26

p = 2(26) + 2(8)

p = 52 + 16 = 68 . . . [OK]


b = 26 cm
h = 8 cm

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Let us start with the A.O.S. (Axis Of Symmetry). For a parabola, it is the line that passes in the minimum point, that can be identified in the present figure as being in the x = - 1 point. And for this reason, we are able to answer the first part as:

A.O.S.: x = -1

Now, as mentioned above, the vertex lies in the minimum point, which is located in the x = -1 and with height y = 2. This allow us to answer the second part as:

Vertex: (-1, 2)

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Y-intercept: y = 4

Because the parabola has concavity facing up, the graph presents a value of minimum, but no maximum. And this is possible to be identified as the point where x = -1 and y = 2, which lead us to the following answer for the third part of the question:

Min.: (-1 , 2)

The domain for any second-order polynomial is the entire real number because there is no restriction for the value of x. And for this reason, the answer of the fourth part of the answer is:

Domain: All real numbers

About the range, for a parabola with the concavity facing up, it can be determined as all the real numbers bigger or equal to the minimum value of the function, which is y = 2. From this reason, we are able to answer the last part of the question as:

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8 0
1 year ago
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diamong [38]

Answer:

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BigorU [14]

Answer:

2,160 pencils

Step-by-step explanation:

Large boxes = 12

Small boxes = 18

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Total pencil in large boxes = Total large boxes × number of pencils per box

= 12 × 144

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Total pencil in small boxes = Total small boxes × number of pencils per box

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Total number of pencils = total pencils in large boxes + total pencil in small boxes

= 1,728 pencils + 432 pencils

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3 0
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igor_vitrenko [27]
5x -3 = 12
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The answer I get is the number 3.
7 0
3 years ago
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