All categories

3 years ago

In triangle ABC, D is the midpoint of side AC and E is the midpoint of side BC.

Mathematics

1 answer:

cestrela7 [59]3 years ago

8 0

Answer:

Step-by-step explanation:

Since all sides are half of greater triangle.Then 7 × 2 = 14 is length of greater hypotenuse.

Suppose two triangles with similar conditions

1^2+1^2=2

Hypotenuse=2^1/2

We assume another triangle which is exactly double of previous triangle I.e

2^2+2^2=8

Hypotenuse=2×2^1/2

Which is exactly twice of previous triangle.

Hence proved hyootenuse is double of smaller triangle I.e 14

You might be interested in

A hiker is walking down a mountain. She walked 5,978 feet in 17 minutes. In that time, she descended 1,024 feet from the top

olya-2409 [2.1K]

Answer:

63.5 feet/minute

Step-by-step explanation:

She first descended 1,024 feet in 17 minutes

Then she descended 500 feet in 7 minutes

The total feet descended is 1,024 + 500 = 1,524 feet

The total time to descend is 17 + 7 = 24 minutes

The average rate of change in altitude is

Altitude descended / time

1,524 feet / 24 minutes

63.5 feet /minute

3 0

3 years ago

Find the length of the darkened arc. Leave your answer in terms of pi.

jonny [76]

Answer:

$\frac{15 }{4} \pi \:$

Step-by-step explanation:

Radius of circle (r) = 18/2 = 9 ft

Central angle = 180° - 30° = 150°

$length \: of \: arc \\ = \frac{150 \degree}{360 \degree} \times 2\pi \: r \\ \\ = \frac{150 \degree}{360 \degree} \times 2 \times \pi \: \times 9\\ \\ = \frac{5 }{12 } \times 18 \times \pi \: \\ \\ = \frac{5 }{4} \times 3\times \pi \:\\ \\ = \frac{15 }{4} \pi \:$

6 0

3 years ago

Find the value of a and b

andriy [413]

Answer:

a = 133 degrees

b = 78 degrees

Step-by-step explanation:

the top and bottom lines are parallel.

the two sidelines are lines that intercept the top and bottom lines.

as they intercept parallel lines, they actually must have the same angles with them.

so, the 47 degrees inner angle at the bottom line, must be also somewhere at the interception point with the top line. and right, it must be now mirrored the outward angle at the top line. and that means a (the inward angle at the top line) is also the outward angle at the bottom line.

the sum of inward and outward angles at a point must always be 180 degrees.

so, the outward angle of 47 = the inward angle a =

= 180 - 47 = 133 degrees.

similar in the other side.

102 is the inward angle.

the outward angle of that is 180 - 102 = 78 degrees.

and that is also the inward angle b.

b = 78 degrees

4 0

2 years ago

What is the simplified form of the expression 1/3(21m + 27)?

Lana71 [14]

1/3 ( 21m + 27 )
= 1/3 X 21m + 1/3 X 27
= 7m + 9 ..

Hope it helps !!!
if u hav any doubt then u can ask ....

5 0

3 years ago

Read 2 more answers

The table shows the relationship between the number of minutes Rodney spends practicing playing the piano p, and the number of m

vagabundo [1.1K]

<u>Answer-</u>

The equation that describes the pattern is,

$\boxed{\boxed{y=2{x}+30}}$

<u>Solution-</u>

P = Number of minutes Rodney spends practicing playing the piano

G = Number of minutes Rodney spends practicing playing the guitar

Taking P on x axis and G on y axis, the points are,

$(0,30),(15,60),(30,90),(45,120)$

Taking first two points i.e $(0,30),(15,60)$ , the line equation will be,

$\Rightarrow \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}$

$\Rightarrow \dfrac{y-30}{60-30}=\dfrac{x-0}{15-0}$

$\Rightarrow \dfrac{y-30}{30}=\dfrac{x}{15}$

$\Rightarrow 15(y-30)=30{x}$

$\Rightarrow y-30=2{x}$

$\Rightarrow y=2{x}+30$

Putting the other two points i.e $(30,90),(45,120)$ in the equation, they also satisfy the equation. That means they are also on the same line $y=2{x}+30$ .

From the result, it is evident that P and G are linearly related.

3 0

3 years ago