Mathematics, 15.06.2021 06:10 ohgeezy

What are the lengths of each segment? Thank you!

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Answer from: kaitlynk0

$\displaystyle a=\sqrt{17}\text{ units} \text{ and } b=3\sqrt{2}\text{ units}$

Step-by-step explanation:

To determine the distance between any two points, we can use the distance formula. The distance formula is given by:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

a is the distance between the points (-2, 3) and (-1, -1). Let (-2, 3) be (x₁, y₁) and let (-1, -1) be (x₂, y₂). Substitute and evaluate:

$\begin{aligned} a&=\sqrt{(-1-(-2))^2+(-1-3)^2}\\\\&=\sqrt{(1)^2+(-4)^2}\\\\&=\sqrt{1+16}=\sqrt{17}\text{ units} \end{aligned}$

b is the distance between the points (2, 2) and (-1, -1). Again, we can let (2, 2) be (x₁, y₁) and (-1, -1) be (x₂, y₂). Substitute and evaluate:

$\displaystyle \begin{aligned} b&=\sqrt{(-1-2)^2+(-1-2)^2}\\\\&=\sqrt{(-3)^2+(-3)^2}\\\\&=\sqrt{9+9}=\sqrt{18}=\sqrt{3^2\cdot 2}=3\sqrt{2}\text{ units}\end{aligned}$

Answer from: Quest

Answer: choice c and choice d

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

Which functions have an additive rate of change of 3? check all that apply

Answer from: Quest

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

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