The figure shown has a parallelogram on top and a rectangle below it:

Mathematics

1 answer:

Verdich [7]3 years ago

5 0

Area of a parallelogram = b×h
= 13.4×48.2
= 645.88 inches square
Area of rectangle = l×b
=7.3×48.2
= 351.86
Area of the figure = (b×h) + (l×b)
=645.88+351.86
= 997.74 inches square
Therefore, the answer is option C

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The Country Buffet restaurant has tables that seat 6 people and booths that can seat 4 people. The restaurant has 38 seating uni

Alina [70]

Answer:

There are 20 booths and (38 - 20), or 18, tables

Step-by-step explanation:

Represent the number of tables with t and the number of booths with b.

We need to find the values of t and b.

(6 people/table)(t) + (4 people/booth)b = 188 (units are "people")

t + b = 38 (units are "seating units")

Solving the second equation for t, we get 38 - b = t.

Substitute 38 - b for t in the first equation:

(6 people/table)(38 - b) + (4 people/booth)b = 188

Then solve for b: 6(38) - 6b + 4b = 188, or:

228 - 2b = 188, or 2b = 228 - 188, or 2b = 40. Thus, b = 20 (booths)

There are 20 booths and (38 - 20), or 18, tables.

6 0

4 years ago

Figure ABCDE has vertices a(-3, 3), b(2, 3), c(5, -2), d(0, -3), and e(-3, -2). Plot the points on your own coordinates grid and

Ilya [14]

<h2>Answer:</h2>

Shown below

<h2>Step-by-step explanation:</h2>

First of all, we have the following points:

$a(-3, 3) \\ \\ b(2, 3) \\ \\ c(5, -2) \\ \\ d(0, -3) \\ \\ e(-3, -2)$

To plot these points, we need to graph a coordinate grid. Recall that a coordinate grid is composed of two perpendicular lines, that we call the axes and are labeled like number lines. The horizontal axis is called the x-axis while the vertical axis is called the y-axis, and these two axes intersect at a point called the origin. Next, let's plot each point as follows:

<h2>PART 1. Plot the points on your own coordinates grid and connect in alphabetical order. </h2><h2></h2>

Point a:

Let's stand at the origin and then move three units to the left and three units up. The resulting point is shown in the firs figure below.

Point b:

Let's stand at the origin and then move two units to the right and three units up. The resulting point is shown in the firs figure below.

Point c:

Let's stand at the origin and then move five units to the right and two units down. The resulting point is shown in the firs figure below.

Point d:

Let's stand at the origin and then move three units to down. The resulting point is shown in the firs figure below.

Point e:

Let's stand at the origin and then move three units to the left and two units down. The resulting point is shown in the firs figure below.

Next, let's connect connect the points in alphabetical order, so that the line are connected from a to b, from b to c, from c to d, from d to e and from e to a again. So the resulting graph is shown in the second figure. As you can see, this is an irregular pentagon.

<h2>PART 2. Decompose figure ABCDE into rectangles and triangles.</h2>

Every pentagon can be divided up into three triangles. Hence, from the third figure. the triangles are:

ΔABE

ΔBDE

ΔBCD

Since a rectangle is a quadrilateral whose angles are all right angles, then there is no chance to obtain a rectangle from ABCDE. To obtain a rectangle, we'd need other points and this is not what the problem asks.