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Luba_88 [7]
3 years ago
5

In right angle ABC, angle C is the right angle, AC = 3 and AB = 5. Point D is on hypotenuse AB, such that DB = 1. Find the area

of the triangle DBC.

Mathematics
1 answer:
Ivan3 years ago
4 0
Look at the picture.

To find the area of triangle DBC we need to find its base, x, and its height, h.

Triangle ABC is a right triangle, so using the Pythagorean theorem we can find x.
(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{the hypotenuse})^2 \\
3^2+x^2=5^2 \\
9+x^2=25 \\
x^2=25-9 \\
x^2=16 \\
x=\sqrt{16} \\
x=4

Now look at triangles ABC and DBH. They both are right triangles and have the same angle α. That means they're similar and their corresponding sides are proportional. The ratio of the side opposite to angle α to the hypotenuse is the same in both triangles - so the ratio of h to 1 is the same as the ratio of 3 to 5.
\frac{h}{1}=\frac{3}{5} \\
h=\frac{3}{5}

The base x is 4, the height h is 3/5. Calculate the area:

A=\frac{xh}{2}=\frac{4 \times \frac{3}{5}}{2}=2 \times \frac{3}{5}=\frac{6}{5}

The area of triangle DBC is 6/5.

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An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of mov- ing violatio
Rudik [331]

Answer:

a) E(y) = 0.8

b) The average subcharge is $165

Step-by-step explanation:

We are given the following distribution in the question:

y:           0        1        2         3

P(y):   0.50   0.25   0.20   0.05

a) E(y)

E(y) = \displaystyle\sum y_iP(y_i)\\\\E(y) = 0(0.50)+1(0.25)+2(0.20)+3(0.05)\\E(y) = 0.8

b) Expected value of subcharge

Subcharge =

\$110y^2

Expected value of subcharge =

=110E(y^2)\\\\=110\displaystyle\sum y_i^2P(y_i)\\\\=110(0^2(0.50)+1^2(0.25)+2^2(0.20)+3^2(0.05))\\=110(1.5)=165

Thus, the average subcharge is $165

5 0
3 years ago
Which expression is equivalent to 9 x 9 x 9 + 12 x 12 x 12?
zloy xaker [14]

Answer:

i think probably 2457 is answer

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Describe how you would classify the shape below on the hierarchy. Start at the top and describe how you know if the shape fits i
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I would classify that shape as a pentagon because it has 5 sides/edges.

It is shaped like the houses in the old times.

Hope I helped :) :)
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3 years ago
adrian began riding his scooter at 7:00am. He stopped riding it at 8:10am. How long did adrian ride his scooter for?​
Alenkinab [10]

Answer:

Adrian rode his scooter for a total of 70 minutes, or an hour and ten minutes.

Step-by-step explanation:

There are 60 minutes in an hour, so if Adrian started riding his scooter at 7:00AM, to get to 8:10AM he needs to add 70.  Again, since there are 60 minutes in an hour, 70 minutes converts to one hour and 10 minutes.  Adrian rode his scooter for 70 minutes, or an hour and ten minutes.

7:00 + :70 = 8:10

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