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Nataliya [291]
3 years ago
12

It’s my last question :(

Mathematics
1 answer:
jenyasd209 [6]3 years ago
6 0

Answer:

Perimeter =  28·√2 + 24 feet

Step-by-step explanation:

The dimensions of the initial sheet of plywood are;

The length of the sheet of plywood = 25 ft.

The width of the sheet of plywood = 14 ft.

The shape cut from each corner of the sheet of plywood  = A right triangle

The leg length of each of the cut out right triangles = 7 ft.

The number of leg lengths of the right triangle cut from the length side of the initial sheet of plywood = 2

The length of the parallel sides of the remaining hexagonal piece of plywood = Initial length of the plywood - 2 × The leg length of the cut out right triangle

∴ The length of the parallel sides of the remaining hexagonal piece of plywood = 26 ft. - 2 × 7 ft.  = 12 ft.

The other side length of the remaining hexagonal piece of plywood = The hypotenuse side of the cut out right triangle

The hypotenuse side of the cut out right triangle = √((7 ft.)² + (7 ft.)²) = 7·√2 ft.

∴ The other side length of the remaining hexagonal piece of plywood = 7·√2

The number of side lengths in the remaining hexagonal piece of plywood = 4

The perimeter of the remaining hexagonal piece of plywood = 2 × The length of the parallel sides + 4 × The other side lengths

∴ The perimeter of the remaining hexagonal piece of plywood = 2 × 12 ft. + 4 × 7·√2 = (28·√2 + 24) ft.

The perimeter of the remaining hexagonal piece of plywood = (28·√2 + 24) feet

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Given:

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70-hour review course average a score of 749.

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The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

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70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

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y=\dfrac{129}{40}(57)+\dfrac{2093}{4}

y=183.825+523.25

y=707.075

y\approx 707.1

Therefore, the required linear equation for the given situation is y=\dfrac{129}{40}x+\dfrac{2093}{4} and the average score for persons taking a 57-hour review course is 707.1.

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