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kolezko [41]
3 years ago
5

Emily says she can prove the Pythagorean Theorem using the following diagram. She explains that she can divide the squares on th

e two shorter sides into grids with equal-sized grid squares. She says she can then rearrange the grid squares to cover the area of the square on the hypotenuse, which proves that the sum of the squares on the two shorter sides equals the square on the hypotenuse.
Is this a valid geometrical proof that a2 + b2 = c2 for all right triangles?

Mathematics
1 answer:
lubasha [3.4K]3 years ago
5 0

Answer:

The last bit is correct, a2 + b2 = c2 for all right triangles? You do not divide the measurements you can only add up the squares to find the square of the hypotenuse as the sum, and then square root the totaled squares back to a new number. It does not cover the area like the statement said so only the question is true as Pythagoras theorem can be used to find a missing side or to find the missing hypotenuse.

Step-by-step explanation:

Is this a valid geometrical proof that a2 + b2 = c2 for all right triangles?

Answer yes but only for c2 if we area adding.

This is because if we were looking and missing for a smaller side to the triangle measure and was already given the hypotenuse as one measure, then we can subtract either given alternative side would be; c2 - b2 = a2 to find an alternative side we subtract.

and c2- b2 = a2 works the same as c2 -a2 = b2.

None of the above formula finds the area, for the area we would need to multiply to find the height.

A = 1/2 x a x b

We have a different understanding to area

The area of a triangle is 1/2 given by the equation:

AΔ=(1/2)∗(base)∗(height) which is the smae as A= 1/2 x a x b

Eg)

Given: Measurements of A + B In attachment picture.

A = 3 cm

B = 4 cm

What is the area of the right triangle ABC?

Since the base leg of the given triangle is 4 cm, while the height is 3 cm, this gives:

AΔ=(1/2)∗3∗4=6cm2

So to find area we multiply A by 1/2 and multiply that product by the length of B (base).

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in a class of 34 students 19 of them are girls what percentage of the class are girls to 1 decimal place
motikmotik

Answer:

55.9% of the class are girls

Step-by-step explanation:

19/34 = 0.559

0.559 x 100 = 55.9%

6 0
3 years ago
Read 2 more answers
Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.
DENIUS [597]

Answer:

\frac{7}{\sqrt{3}}

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |                   --------------------(i)

From the question,

the point is (5, 0, -6)

the plane is x + y + z = 6

Therefore,

a = 5

b = 0

c = -6

m = 1

n = 1

t = 1

r = 6

Substitute these values into equation (i) as follows;

d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |

d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |

d = |\frac{(-7)}{\sqrt{3}} |

d = \frac{7}{\sqrt{3}}

Therefore, the shortest distance from the point to the plane is  d = \frac{7}{\sqrt{3}}

5 0
3 years ago
Which of the following is fartherest to the left on a number line 1/5, (0.1)to second power, 0.02
Alexxx [7]
1/5 is .2
.1^2 is .01
.02 is .02

So the furthest left  would be the smallest number, which in this case is 0.1^2
5 0
3 years ago
the mean of a set of numbers is 120. if one number is increased by 300, the mean increases to 135. how many numbers are in the s
stiks02 [169]

There are 20 numbers in the set.

Given,

Set of numbers is 120

one number is increased by 300

and, mean increases to 135.

To find the how many numbers are in the set?

Now, According to the question:

Let the number of numbers be 'n'

Then, (sum of numbers)/n = 120

or, old sum = 120n

if one number is increased by 300, the new sum = (old sum + 300)

Then, (new sum)/ n= 135

or new sum = 135n = old sum + 300 = 120n + 300

The equation will  be:

135n = 120n + 300

15n = 300

n = 20

Hence, There are 20 numbers in the set.

In the question:

The mean of a set of numbers is 120. if one number is increased by 300, the mean increases to 135.

Learn more about Equation at:

brainly.com/question/28551889

#SPJ4

3 0
1 year ago
Simplify the expression 417000 x 0.0002
Amanda [17]
Please see picture above.

5 0
3 years ago
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