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2 years ago

Given ABCD, solve for x.

Mathematics

2 answers:

eduard2 years ago

8 0

Answer:

x=1

Step-by-step explanation:

Given is a picture of a parallelogram ABCD

As per properties of parallelograms opposite sides are parallel and equal.

Two opposite sides are given as 12.

But another pair is given in terms of x as 16+2x and 10+8x

Since opposite sides would be parallel we have

16+2x =10+8x

Simplify to get

6x =6

or x=1

Verify:

The top side = 16+2x =18

The bottom side 10+8x = 10+8 =18

Thus both are equal, thus verified

Monica [59]2 years ago

7 0

This shape is a parallelogram and the opposite sides of a parallelogram

are of equal length.

10 + 8x = 16 + 2x ⇔ 8x - 2x = 16 - 10 ⇔ 6x = 6 ⇔ x = 6:6 ⇔ x = 1

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Step-by-step explanation:

Given:

Side lengths of cube = $\frac{1}{4} \ foot$

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

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What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

$Volume\ of\ cube =a^{3}$

$=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot$

Length = 8 foot, Breadth = $6\frac{1}{4} =\frac{25}{4} \ foot$ , Height = $7\frac{1}{2} =\frac{15}{2} \ foot$

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$=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot$

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = $\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube$

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