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Nesterboy [21]
2 years ago
12

A graph displays point A (5, 3, 4) and point B (−4, 2, 6). Calculate the approximate distance each point is from the origin. Rou

nd to the nearest tenth. Which point is farther from the origin, and by how much?
Mathematics
1 answer:
SIZIF [17.4K]2 years ago
5 0

Distance from the origin to the points  ≈ 0.41.

<h3>What is the distance between two points ( p,q) and (x,y)?</h3>

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

D = √[(x-p)² + (y-q)²]  

Point A (5, 3, 4) and point B (−4, 2, 6) are located away from the origin (0,0,0), and the points from the origin to this points are expressed as OB - OA where;

Let OB is the distance from the origin to the point B

Let OA is the distance from the origin to the point A

Using the formula for calculating the distance between two points;

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(4-0)²+(3-0)²+(5-0)²

OA = √(16)+(9)+(25)

OA = √50

OA = 7.071

Similarly;

OB = √(6-0)²+(2-0)²+(-4-0)²

OB = √(6)²+(2)²+(-4)²

OB = √36+4+16

OB = √56

OB = 7.4833

Distance from the origin to the points = 7.4833 - 7.071= 0.4123

Distance from the origin to the points  ≈ 0.41

Learn more about distance between two points here:

brainly.com/question/16410393

#SPJ1

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Write various of the equation of a line that passes through (-6, 3) and has a slope of - 1/3
pishuonlain [190]

Answer:

\large\boxed{y-3=-\dfrac{1}{3}(x+6)-\text{point-slope form}}\\\boxed{y=-\dfrac{1}{3}x+1-\text{slope-intercept form}}\\\boxed{x+3y=3-\text{standard form}}

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

m - slope

We have

m=-\dfrac{1}{3},\ (-6,\ 3)\to x_1=-6,\ y_1=3

Substitute:

y-3=-\dfrac{1}{3}(x-(-6))\\\\y-3=-\dfrac{1}{3}(x+6)

Convert to the slope-intercept form

y=mx+b

y-3=-\dfrac{1}{3}(x+6)           <em>use the distributive property</em>

y-3=-\dfrac{1}{3}x-2           <em>add 3 to both sides</em>

y=-\dfrac{1}{3}x+1

Convert to the standard form

Ax+By=C

y=-\dfrac{1}{3}x+1           <em>multiply both sides by 3</em>

3y=-x+3             <em>add x to both sides</em>

x+3y=3

5 0
3 years ago
Bob bought a broken motor scooter, repaired it, and sold the scooter for $130. That was $50 less than 1.5 times what he paid for
FromTheMoon [43]

Answer: $120

Step-by-step explanation:

Assume the original price is x.

He sold the scooter for $130 and this was $50 less than 1.5 times what he paid for it.

Relevant formula is therefore:

1.5x - 50 = 130

1.5x = 130 + 50

x = 180/1.5

x = $120

4 0
3 years ago
What is the simplified value of the exponential expression 16 superscript one-fourth? 2 4
USPshnik [31]

The simplified value of the exponential expression is 2.

<h3>How to get the simplified expression?</h3>

Here we need to simplify the expression:

16^{1/4}

First, you need to remember that:

\sqrt[n]{x} = x^{1/n}

Then we can just write:

16^{1/4} = \sqrt[4]{16}

And now, you can remember that:

2*2 = 4

Then:

2*2*2*2 = 4*4 = 16

From this, we can conclude that:

2^4 = 16\\\\\sqrt[4]{16} = 2

So we conclude that the simplified value is 2.

If you want to learn more about exponential expressions:

brainly.com/question/11464095

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3 0
2 years ago
What is -12(x-12)=-9(1+7x)​
katen-ka-za [31]

Answer:

-3

Step-by-step explanation:

-12(x-12)=-9(1+7x)

-12x+144=-9-63x

-12x+63x=-9-144

51x=-153

x=-153/51=-3

3 0
3 years ago
Sketch seven points. Then, connect the points to form a closed plane figure. What kind of polygon did you draw?
weqwewe [10]

It’s a heptagon, which has seven points.

7 0
3 years ago
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