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2 years ago

Workers in an office of 60 staff were asked their favourite type of take-away.

Mathematics

1 answer:

nikdorinn [45]2 years ago

5 0

Answer:

a = 84°

b = 36°

c = 24°

d = 84°

e = 132°

Step-by-step explanation:

The parameters of the workers in the office are;

The number of staffs in the office = 60 staffs

The take-aways are pizza, curry, fish & chips, kebab and other

The frequency for the above take-aways = 14, 6, 4, 14, and 22 respectively

The variables for the angles representing the above take-aways on the pie chart = 'a', 'b', 'c', 'd', and 'e'; respectively

In order to find the size of the angles that represent each group of workers in the pie chart, we find the ratio of the group size to the total number of workers and we multiply the result by 360° as follows;

∠a = 360° × 14/60 = 84°

∠b = 360° × 6/60 = 36°

∠c = 360° × 4/60 = 24°

∠d = 360° × 14/60 = 84°

∠e = 360° × 22/60 = 132°

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Which expression shows a sum of three terms.

vladimir1956 [14]

Answer: B) 3+y+3

This can be simplified to y+6, but the current un-simplified expression has 3 terms.

======================================

Explanation:

Terms are separated by a plus sign. If you had something like 10x-5y, then you would write that as 10x+(-5y) showing that 10x and -5y are the two terms.

Choices A and C, xy and 6y respectively, have one term each. They are considered monomials. Mono = one, nomial = name.

Choice D is the product of the constant 3 and the binomial y+3. Binomials have two terms.

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3 years ago

Determine whether quadrilateral ABCD is a rhombus, a rectangle, a square, a parallelogram, or none. List all that apply. Explain

svlad2 [7]

Answer:

ABCD is a rhombus, and a parallelogram

==================================

<h3>Given </h3>

Points A(-6, - 1), B(4, - 6), C(2, 5), D(- 8, 10)

First, plot the points (see attached picture).

Then, connect all the points.

Opposite sides are parallel,
Diagonals are perpendicular.

From our observation the figure is rhombus.

Let's confirm it with the following.

1) Find midpoints of diagonals and compare.

AC → x = (- 6 + 2)/2 = - 2, y = (- 1 + 5)/2 = 2
BD → x = (4 - 8)/2 = - 2, y = (- 6 + 10)/2 = 2

The midpoint of both diagonals is same (- 2, 2).

2) Find slopes of diagonals and check if their product is -1, this will confirm they are perpendicular.

m(AC) = (5 - (-1))/(2 - (-6)) = 6/8 = 3/4
m(BD) = (10 - (-6))/(-8 - 4) = - 16/12 = - 4/3

m(AC) × m(BD) = 3/4 * (- 4/3) = - 1

<u>Confirmed.</u>

So this is a rhombus and also a parallelogram but <u>not</u> rectangle or square, since opposite angles are not right angles.

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9 months ago