Using the following data, calculate the mean. 5, 4, 7, 4, 5, 8, 6, 5

Mathematics

1 answer:

Helga [31]3 years ago

8 0

Answer:

5.5

Step-by-step explanation:

The mean is the average of the numbers.

mean=(5+4+7+4+5+8+6+5)/8=44/8

=5.5

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A rectangle has a perimeter of 44 inches and an area of 72 square inches. What are the lengths of the sides of the rectangle?

kondor19780726 [428]

A rectangle has a perimeter of 44 inches and an area of 72 square inches.
Perimeter = 44 inches, area = 72 square inches.
Let the length and breadth be l and b respectively.
We know, perimeter of a rectangle = 2(l + b)
Therefore,
2(l + b) = 44

or, l + b = 22

or, b = 22 - l ...(i)

We know, area of a rectangle = lb
Therefore,
lb = 72
Putting (i) in b, we get
l(22 - l) = 72

or, 22l - l^2 -72 = 0

or, l^2 - 22l + 72 = 0

or, l^2 - 4l - 18l + 72 = 0

or, l(l - 4) - 18(l - 4) = 0

or, (l - 4)(l - 18) = 0

or, l = 4 or l = 18

Therefore, if the length is 4 inches, then the breadth is (22-4) inches, i.e., 18 inches.
And if the length is 18 inches, then the breadth is (22-18) inches, i.e., 4 inches.

Answer:

B) 4 inches and 18 inches.

Hope you could get an idea from here.

Doubt clarification - use comment section.

5 0

3 years ago

A canoe rental shop is being built near a river. An equation of the line representing the river is y=14x+8. Each unit in the coo

julsineya [31]

Answer:

412.3 feet

Step-by-step explanation:

A canoe rental shop is being built near a river. An equation of the line representing the river is y=1/4x+8. Each unit in the coordinate plane corresponds to 100 feet. Approximately how far is the canoe rental shop from the river? Round your answer to the nearest whole foot. The rental shop is at (-3,3).

Solution:

The distance between a point and a line is the perpendicular distance. The perpendicular distance is the shortest distance between the point and the line.

Given a point ( $x_1,y_1$ ) and a line with the equation Ax + By + C = 0, the perpendicular distance (d) is given as: