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3 years ago

What is the solution to the following system of equations?

1 answer:

4 0

x+y=5
x-y=1
-------------add
2x = 6
x = 3

x+y=5
3+y=5
y = 2

solution
(3,2)

answer is c. (3, 2)

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Twenty toothpicks, each 6 cm long, form a figure consisting of six equilateral triangles and a rectangle as shown. What is the t

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The total area of the figure is 139.20 square centimeters

Areas

The area of a shape is the amount of space it occupies

<h3>Composite figure</h3>

The figure (see attachment) is a composite figure, and the total area is the sum of the areas of each shape that makes up the complete figure

The shape has 6 equilateral triangles, each of which has an area of:

$A_1 = \sqrt{\frac{3s^2}{4}}$

Where:

$s = 6$ --- the length of each toothpick

The area of the rectangle is then represented as:

$A_2 =3s \times s$

$A_2 =3s^2$

So, the total area of the figure is:

$Total = 6A_1 + A_2$

This gives

$Total =6 \times \sqrt{\frac{3s^2}{4}} + 3s^2$

Substitute 6 for s

$Total =6 \times \sqrt{\frac{3(6)^2}{4}} + 3(6)^2$

$Total =6 \times \sqrt{27} + 108$

$Total =6 \times 5.20+ 108$

$Total =139.20$

Hence, the total area of the figure is 139.20 square centimeters

Read more about areas at:

brainly.com/question/21135654

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2 years ago

A particular beach is eroding at a rate of 4 centimeters per year. A realtor converts this rate to millimeters per day. Which

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Answer:

$\frac{4cm}{1year}*\frac{10mm}{1cm}*\frac{1year}{365days}$

Step-by-step explanation:

Whenever we are doing unit conversions, we have to remember to make the first ratio and then each successive ratio should be put in such a way that the top and bottom cancels out with each unit and whatever we want, remains.

A simple example would be if we were to just convert from cm to mm. Suppose we want to convert 5 centimeters to millimeters. We can write the ratios is 2 ways:

First:

$5cm*\frac{10mm}{1cm}$

Second:

$5cm*\frac{1cm}{10mm}$

The first one is correct since we want mm, mm should be on top and cm should be on bottom form cm and cm to get canceled.

Now, for our problem, we want mm on top and day on bottom. So, cm and year should cancel. Looking at the first choice, the conversion factors are correct & skimming through, we see that

cm and cm cancels (top and bottom), also year and year cancels (top and bottom), it will leave us with mm on top and days on bottom, which is what we want.

First answer choice is right.

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