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3 years ago

In the coordinate plane, find the distance between the points using absolute value.

Mathematics

1 answer:

alukav5142 [94]3 years ago

8 0

Answer:

The distance between the two points is 8 units

Step-by-step explanation:

In the given figure

∵ The coordinates of the 2 points are (4, 5) and (4, -3)

∴ x1 = 4 and y1 = 5

∴ x2 = 4 and y2 = -3

∵ Their x-coordinates are equal

→ That means the distance between them is vertical

∴ The length of the vertical distance between two points is

the difference between the y-coordinates of the points

∵ The distance between them = Iy2 - y1I

∵ y1 = 5 and y2 = -3

∴ The distance between them = I-3 - 5I

∴ The distance between them = I-8I

→ Remember absolute value gives always positive values

∴ The distance between them = 8 units

∴ The distance between the two points is 8 units

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Find the measure of <_B (show work if possible)

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Answer: <b is 59.3 degrees

Step-by-step explanation:

Triangles have total of 180 degrees

The bottom two points are both 4y

To solve: 4y+4y+(3y+14)=180

11y+14=180

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11y=166

Divide by 11

Y=15.1

So plug that in for y

3(15.1)+14=B

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Hope this helped

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Read 2 more answers

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times.

tatyana61 [14]

Answer:

(a) $g(n)=0.05\cdot 2^n$

(b) $g^{-1}(n)=\log_{2}20g(n)$

Step-by-step explanation:

Part A

The paper's thickness = 0.05mm

When the paper is folded, its width doubles (increases by 100%).

The thickness of the paper grows exponentially and can be modeled by the function:

$g(n)=0.05(1+100\%)^n\\\\g(n)=0.05\cdot 2^n$

Part B

$g(n)=0.05\cdot 2^n\\2^n=\dfrac{g(n)}{0.05}\\ 2^n=20g(n)\\$Changing to logarithm form, we have:\\\log_{2}20g(n)=n\\$Therefore:\\g^{-1}(n)=\log_{2}20g(n)$

Part C

If the thickness of the paper, g(n)=384,472,300,000 mm

Then:

$g^{-1}(n)=\log_{2}20g(n)\\g^{-1}(n)=\log_{2}20\times 384,472,300,000\\=\dfrac{\log 20\times 384,472,300,000}{\log 2} \\g^{-1}(n)=42.8 \approx 43\\n=43$

You must fold the paper 43 times to make the folded paper have a thickness that is the same as the distance from the earth to the moon.

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