MATHEMATICS MIDDLE SCHOOL

What are the similarities in the pythagorean theorem and the distance formula

Answers

Answer 1

Answer:

Answer:

Short answer: They are essentially the same thing.

The distance formula is derived from the Pythagorean Theorem

We have distance formula:

$D = √((x_1 - x_2)^2 + (y_1 - y_2)^2)$

Pythagorean Theorem:

$a^2+b^2=c^2 \Rightarrow c=√(a^2+b^2)$

The shortest distance between two points if a line. If you draw a line in the cartesian plane both points will have an x-coordinate and y-coordinate. Note that it forms a right triangle! Therefore, the distance between those points is the hypotenuse.

We can have a point $a=(x_(1), y_(1))$ and point $b=(x_(2), y_(2))$

But once $a$ and $b$ can be positive or negative:

$c = √(a^2+b^2)= D = √((\pm a)^2+(\pm b)^2)$

Answer 2

Answer:

Answer:

The Pythagorean theorem states that, for all 90-degree triangles, the relationship between the lengths of the sides is given by the formula a^2 + b^2 = c^2.

DISTANCE FORMULA

The study of geometry in a graphical environment is called co-ordinate geometry.

In co-ordinate geometry, the standard formula for calculating the distance between 2 points is called the distance formula.

Step-by-step explanation:

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What is the decimal number of 3 cents

Answers

The decimal number of three cents is 0.03

The answer is 0.03 becuase of the decimal place

PLEASE HELP I DON'T UNDERSTAND

Answers

Do you remember how to find the equation of a line when you know two points on the line ? Well, that little table gives you FIVE points on the line, and in case some students didn't notice that, the table even labels the columns 'x' and 'y' as a hint. With 5 points given, there are 20 different ways to find the equation of the line. Get to work.

Okay first we need to find the line of best fit. We would need the slope and the y-intercept. First let's solve for slope.

$Slope = (y_2 - y_1)/(x_2 - x_1)$

We would need two coordinates from the table to fill in the data. Let's use (0, 23) and (1, 20).

$(x_1, y_1) = (0, 23); (x_2, y_2) = (1, 20)$

Then we can solve for the y-intercept using the slope-intercept form: y = mx + b.

If the force being applied to a moving cart is doubled and the mass remains constant, what will happen to the acceleration of the cart?It will double

It will be cut in half

It will increase by a factor of 10

It will triple

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if an force will be double result the acceleration will be double.

F = m * a

2 F = m * 2 a

Write 333 ones 444 tenths and 222 hundredths as a decimal.

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333.
44.4
2.22
lol it confused me first

PLEase help I really need this

Answers

Answer:

54 - 8 = $46

Step-by-step explanation:

ok the answer is 46 dollars

what is the answer for:

r = 9 ft

r = 21 m

d = 30 cm

d = 24 cm

r = 15.2 in

r = 16.01 ft

please answer them i just want the answer like example the answer for r= 9 ft is 56.52 ft

thanks!!!

Answers

$r-a\ radius\ of\ the\ circle\n\nd-a\ diameter\ of\ the\ circle\n\na\ circumference\ of\ the\ circle:2\pi r=d\pi\n\nr=9ft\to2\pi r=2\pi\cdot9=18\pi\approx18\cdot3.14=56.52\ (in)\n\nr=21\ m\to2\pi r=2\pi\cdot21=42\pi\approx42\cdot3.14=131.88\ (m)\n\nd=30cm\to d\pi=30\pi\approx30\cdot3.14=94.2\ (cm)\n\nd=24cm\to d\pi=24\pi\approx24\cdot3.14=75.36\ (cm)\n\nr=15.2\ in\to 2\pir=2\pi\cdot15.2=30.4\pi\approx30.4\cdot3.14=95.456\ (in)\n\nr=16.01\ ft\to2\pi r=2\pi\cdot16.01=32.02\pi\approx32.02\cdot3.14=100.5428(ft)$

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