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Lilit [14]
2 years ago
11

Can anyone please help me solve!!!!!

Mathematics
1 answer:
kumpel [21]2 years ago
6 0

Answer:

30 square units

Step-by-step explanation:

We know that the area of a triangle is equal to half of the product between the base and the height.

In this case, we can see that one of the sides of the triangle is parallel to the x-axis, then we can define:

Base = difference between the two extreme x-values

In this case, the extremes (the point at the left and the point and the right) are:

(-5, 3) and (7, 3)

The difference between the x-values is:

D = (7 - (-5)) = 7 + 5 = 12

Then the base is 12 units long.

For the height, we can find the difference in the y-value between the lowest point and the highest one.

In this case, we have two points at the same height (both with y-value = 3)

and the top point is (4, 8)

The difference in the y-value is:

D = (8 - 3) = 5

Then the height is 5 units.

Now that we know the height and the base of the triangle, the area is:

A = (5 units)*(12 units)/2 = 30 square units.

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The sum of the interior angles of a polygon is 1080 degrees. How many sides does the polygon have?
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  8

Step-by-step explanation:

The formula for the number of degrees in the sum of the interior angles of an n-sided polygon is ...

  sum of angles = 180°(n -2)

Filling in the given value and solving for n, we get ...

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Step-by-step explanation:

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Write three sentences that compare the values 12 and 3 in different ways
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Given data:

The numbers given are 12 and 3.

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The 12 and 3 are both natural as well as rational number, 12 is nine more than 3.

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1 year ago
A perfectly straight 24 ft tall tree grows on the edge of the bank of a 45 foot wide river. A bird sitting at the top of the tre
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Answer:

Distance covered by the bird before meeting the water is: 51.264 ft

Step-by-step explanation:

Notice that if the bird catches the fish in 2 seconds, then the fish was able to dive down a total of 6 feet before being caught:

distance=Vel\,* time=3\,\frac{ft}{s} *\,2\,\,s=6 \,\,ft

So the bird needs to fly in the direction of the hypotenuse of a right angle triangle (see attached image) that has one leg of length (24 ft + 6 ft) = 30 ft, and another one 22.5 ft (half the width of the river.

Such hypotenuse is (using Pythagoras theorem):

hyp =\sqrt{(60\,ft)^2+(22.5\.ft)^2} =\sqrt{4106.25} \,ft=64.08\,ft

Now, in order to find the distance D the bird covers from the top of the tree to the water (marked in red in our image), we use similar triangles. The bigger triangle is that of legs 60 ft and 22.5 ft and hypotenuse 64.08 ft.

The smallest triangle we use in the proportion is the one shaded yellow in the image, which has one leg equal to 24 ft, and unknown hypotenuse:

So we make the proportion between known legs, and hypotenuses:

\frac{24\,ft}{30\,ft} =\frac{D}{64.08\,ft} \\D=\frac{64.08\,ft\,*\,24\,ft}{30\,ft} \\D=51.264\,ft

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3 years ago
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