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arsen [322]
2 years ago
14

In △ABC, point D∈AC

Mathematics
1 answer:
Maslowich2 years ago
6 0
<h3>Answer:</h3>
  • ABDC = 6 in²
  • AABD = 8 in²
  • AABC = 14 in²
<h3>Explanation:</h3>

A diagram can be helpful.

When triangles have the same altitude, their areas are proportional to their base lengths.

The altitude from D to line BC is the same for triangles BDC and EDC. The base lengths of these triangles have the ratio ...

... BC : EC = (1+5) : 5 = 6 : 5

so ABDC will be 6/5 times AEDC.

... ABDC = (6/5)×(5 in²)

... ABDC = 6 in²

_____

The altitude from B to line AC is the same for triangles BDC and BDA, so their areas are proportional to their base lengths. That is ...

... AABD : ABDC = AD : DC = 4 : 3

so AABD will be 4/3 times ABDC.

... AABD = (4/3)×(6 in²)

... AABD = 8 in²

_____

Of course, AABC is the sum of the areas of the triangles that make it up:

... AABC = AABD + ABDC = 8 in² + 6 in²

... AABC = 14 in²

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Find the radius of a circle with circumference of 45.84 meters. Use 3.14
alukav5142 [94]

Answer:

3.8 meters

Step-by-step explanation:

In order to find the circumference for a circle, we use the formula π(radius)²

The circumference give is 45.84 and the π given is 3.14

All we have to do is to just substitute them.

45.84 = 3.14(radius)²

45.84 / 3.14 = radius²

14.6 = radius²

radius = √14.6

radius = 3.82 ≅ 3.8

5 0
3 years ago
Read 2 more answers
It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(
Rudik [331]
It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(t) = .25t + 1, for t > 10. Find the number of fish that can be caught if you fish for 15 minutes. Round your answer to the nearest whole number.

8 0
3 years ago
If the sum of six consecutive even integers is 390 what is the smallest of the six integers
saveliy_v [14]
The answer is 60 but im going to explain it down below if you want to know how to do it :)

first because we dont know the values of the 6 numbers we have to lay it out like this.
x
x+2
x+4
x+6
x+8
x+10
-------- (then we add it together)
6x+30 = 390 (the sum of the 6 numbers)

using this equation we find out what x is 

so we do 390-30 to find what 6x is, which is 360
because now we know that 6x=360, we divide 360 by 6 to find out what x is
360 divided by 6 =60..... x = 60

so now we know that the smallest integer is 60
to check the answer we could add the 6 numbers which are:
60+62+64+66+68+70=390 :)

so the smallest integer is 60

5 0
3 years ago
A gear with a diameter of 12.0 inches makes 35 revolutions every three minutes. Find the linear and angular velocities of a poin
alina1380 [7]

Answer:

Angular velocity: \omega = \frac{7\pi}{18} \,\frac{rad}{s} (1.222\,\frac{rad}{s})

Linear velocity: v = \frac{14\pi}{3}\,\frac{m}{s} (14.661\,\frac{m}{s})

Step-by-step explanation:

The gear experiments a pure rotation with axis passing through its center, the angular (\omega), in radians per second, and linear velocities (v), in inches per second, of a point on the outer edge of the element are, respectively:

\omega = \frac{2\pi}{60}\cdot \dot n (1)

v = R\cdot \omega (2)

Where:

\dot n - Rotation rate, in revolutions per minute.

R - Radius of the gear, in inches.

If we know that \dot n = \frac{35}{3}\,\frac{rev}{min} and R = 12\,in, then the linear and angular velocities of the gear are, respectively:

\omega = \frac{2\pi}{60}\cdot \dot n

\omega = \frac{7\pi}{18} \,\frac{rad}{s} (1.222\,\frac{rad}{s})

v = R\cdot \omega

v = \frac{14\pi}{3}\,\frac{m}{s} (14.661\,\frac{m}{s})

7 0
2 years ago
Which of the following statements are true? The product of two numbers with the same sign is negative. The quotient of a positiv
ozzi

The answer is II and III

3 0
3 years ago
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