How is the Pythagorean theorem related to the distance formula? Explain.

Answers

Answer 1

Answer:

The distance formula is used to find the distance between two points and the Pythagoras theorem is used to find the missing length in a right-angled triangle.

What is Pythagoras's Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

$|AC|^2 = |AB|^2 + |BC|^2$

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

The distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y)

$D = √((x-p)^2 + (y-q)^2) \: \rm units.$

The distance formula is a formalization of the Pythagorean Theorem using (x,y).

The distance formula is used to find the distance between two points and the Pythagoras theorem is used to find the missing length in a right-angled triangle.

So, they are the same thing in two different contexts.

Learn more about Pythagoras' theorem here:

brainly.com/question/12105522

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Answer 2

Answer:

Answer:

The distance formula is a formalisation of the Pythagorean Theorem using (x,y) . They are the same thing (but the distance formula is for working out the distance between two points and Pythagoras theorem is for working out the missing length in a right-angled triangle) in two different contexts.

Step-by-step explanation:

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Which of the following describes the quotient of 2 and -22?A. The quotient is an irrational number.
B. The quotient is undefined
C. The quotient is an integer.
D.The quotient is a rational number.

Answers

The quotient is a rational number.

How do I show six less than a quotient of a number and two equals fifteen

Answers

x/2 - 6 = 15

That's how you write it out.

x/2 - 6 = 15
x/2 = 15 + 6
x/2 = 21
x = 21 * 2
x = 42

Answer: 42

First you add 6 on both sides to get x ÷ 2 alone giving you x ÷ 2 = 21. Then to get x alone you have to mutliply 2 on both sides giving you the answer of 42.

$(x)/(2)-6=15$

Describe the steps you can use to find an average of fractional amounts

Answers

Answer:

Average of number is equal to sum of numbers by total no.

i.e., $Average\,=\,(Sun\,of\,numbers)/(Total\,no)$

Now when numbers/amounts are fraction then there is one extra step which is to add the fractions.

Lets say we have to find average of 2 fractions i.e., $(3)/(4)\,,\,(5)/(3)$

$\implies\,Average\,=\,((3)/(4)+(5)/(3))/(2)$

Step 1 : First to add the fractions find the LCM of denominator as There are unlike fractions

3 = 1 × 3

4 = 1 × 4

LCM of 3 and 4 = 3 × 4 = 12

Step 2: To make them like fraction we find equivalent fraction of each fraction whose denominator equal to 12

$(3)/(4)*(3)/(3)=(9)/(12)$

$(5)/(3)*(4)/(4)=(20)/(12)$

Step 3: Adding both fractions

$(9)/(12)+(20)/(12)=(9+20)/(12)=(29)/(12)$

Step 4: put these value in average formula

$\implies\,Average\,=\,\frac{(29)/(12){2}$

Step 5: Now we divide $(29)/(12)$ by 2 using fraction division .i.e., multiply the reciprocal of divisor with dividend

here 2 is divisor

Reciprocal = $(1)/(2)$

$\imples Average=(29)/(12)*(1)/(2)=(29*1)/(12*2)=(29)/(24)$

Following these steps Average of fractional amount of any no can be found.

1. first make the denominators of the set the same.
E.g. $(2)/(7)+ (4)/(3)$ = $(6)/(21) + (28)/(21)$ = $(34)/(21)$

2. Divide the total by the number of fractions added together: In this case it was 2 so:
$(34)/(21) * (1)/(2)$ = $(34)/(42)$

3. Simplify the total: $(17)/(21)$

if one letter is chosen at random from the word combed, what is the probability that the letter chosen will be a "d"?

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I might be wrong. This is what I think. The probability is 3.85% You can round up to 4 %. I might be wrong. I hope I helped. :D

Urgent! Can someone help me on these questions?

Answers

I'm pretty sure y=3 because if it's reflected on the y-axis it would have t be the same number just positive. for the first one

What is 87.235 to the nearest hundredth

Answers

87.24

3 is in the hundredths place and since 5 is in the thousandths place you round up to 4.

87.235 becomes 87.24

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Use multiplication and the distributive property to find the quotient of 54/3