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IgorC
2 months ago
13

The extensions of the legs AB and CD of a trapezoid ABCD intersect at point E. Find the lengths of the altitude of △AED drawn to

the base AD, if BC=7cm, AD=21cm, and the length of an altitude of a trapezoid is 3cm.

Mathematics
1 answer:
Inessa [12.5K]2 months ago
8 0

Let G represent the intersection of EF & BC.

According to Thales' theorem:

\frac{eg}{ef} = \frac{bc}{ad}

And EF = EG + GF = EG + 3

\frac{eg}{eg + 3} = \frac{7}{21}

21eg = 7eg + 21

14eg = 21

eg = \frac{21}{14} = \frac{3}{2} = 1.5

The height of △AED = EF

Thus, EF = EG + GF = 1.5 + 3 = 4.5

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In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is t
Inessa [12570]

Answer:

La conclusión sobre p utilizando una desigualdad de valor absoluto es

0.325 < p < 0.375

Explicación paso a paso:

Según el enunciado, nos informan que

La proporción de la muestra es \r p = 0.35

El margen de error es E = 0.025

El intervalo de confianza se representa matemáticamente como

\r p -E < p < \r p +E

=> 0.35 - 0.025 < p < 0.35 + 0.025

=> 0.325 < p < 0.375

7 0
3 months ago
Lonzell said the function shown in the graph is positive on the interval (−,) and negative on the interval (−,−)open negative 5
Inessa [12570]

Answer:

The segments of the positive graph are located at the coordinates (-5,-4) and (2,5).

In contrast, the negative segment is identified as (-4,2).

Step-by-step explanation:

The positive graph is above the x-axis, while the negative portion lies beneath the y-axis.

Within the interval (-1,5),

The graph appears below the x-axis between (-1,2)

And above it between (2,5).

At this juncture, Lonzell’s assertion is inaccurate.

Within the interval (-5,-1),

The graph again resides below the x-axis in the range (-4,-1)

And above it between (-5,4).

At this point, Lonzell's assessment remains incorrect.

Thus,

The segments of the positive graph are at the coordinates (-5,-4) and (2,5).

Meanwhile, the negative segment is identified at (-4,2).

5 0
3 months ago
In the picture, the angle made by the goniometer is classified as a(n) ___ angle. ___ ° &lt; θ &lt; ___ .
Leona [12618]
An obtuse angle is one that measures more than 90 degrees but less than 180 degrees.

5 0
3 months ago
Read 3 more answers
The third angle of an isosceles triangle is 16 o less than the sum of two equal angles. Find
tester [12383]

Solution:    49°, 49°, 82°

Detailed explanation:

Let x denote the base angles

and therefore the vertex angle is expressed as 2x - 16.

According to the Triangle Sum Theorem, the angles in a triangle total 180°

(x) + (x) + (2x - 16) = 180

                 4x - 16 = 180

                       4x = 196

                         x = 49

Base angles are: x = 49

The vertex angle: 2(49) - 16 = 82

                                   

6 0
1 month ago
A sphere with a diameter of 9 units fits exactly in the clear glass cube as shown.
babunello [11817]

Answer:

347.3 cubic units

Step-by-step explanation:

To calculate the volume of the empty space, we derive the total volume of the two shapes and subtract the volume of the sphere from that of the cube.

The volume of a cube is calculated as l^3.

Here, the length is given as 9, so we compute 9x9x9, resulting in 729 cubic units.

The formula for the volume of a sphere is 4/3 pi r^3.

The radius is 4.5 (half of the diameter), thus:

4/3*91.125 pi

which becomes 121.5 pi = 381.7 (to one decimal place).

Subtracting these gives us 729-381.7 = 347.3.

The volume of the empty space equals 347.3 cubic units.

The comprehensive expression in reference to the given d:

Volume of empty space = d^3 - 4/3 pi (d/2)^3

I hope this was helpful!

3 0
3 months ago
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