Answer:
50 feet
Step-by-step explanation:
Set up a 3-dimensional coordinate system (see the attached image).
This setup shows an axis that runs North-South (South is <u>negative</u>, North is positive), an axis that runs East-West (East is positive, West is negative), and an axis that runs Up-Down (Up is positive, Down is negative).
The two points in question are then:
First person's location (12, -20, -12), and the second person's location is (-20, 10, 12).
The distance between two points
and
is
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%2B%28z_2-z_1%29%5E2)
![d=\sqrt{(-20-12)^2+(10-(-20))^2+(12-(-12))^2}\\\\d=\sqrt{(-32)^2+30^2+24^2}\\\\d=\sqrt{2500}\\\\d=50](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-20-12%29%5E2%2B%2810-%28-20%29%29%5E2%2B%2812-%28-12%29%29%5E2%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B%28-32%29%5E2%2B30%5E2%2B24%5E2%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B2500%7D%5C%5C%5C%5Cd%3D50)
Answer:
Step-by-step explanation:
The point slope form of the equation is expressed as
y - 7/2 = 1/2(x - 4)
Comparing with the point slope form of an equation which is expressed as
y - y1 = m(x - x1)
m represents slope
Therefore
m = 1/2
y1 = 7/2
x1 = 4
The slope intercept form of the equation of a straight line is expressed as
y = mx + c
Where c represents the intercept
Substituting y = 7/2, m = 1/2 and x = 4 into y = mx + c, it becomes
7/2 = 1/2 × 4 + c
7/2 = 2 + c
c = 2 - 7/2 = (4 - 7)/2 = - 3/2
Therefore, the y intercept is - 3/2
Answer:
![c = -6](https://tex.z-dn.net/?f=c%20%3D%20-6)
![d = -1](https://tex.z-dn.net/?f=d%20%3D%20-1)
Step-by-step explanation:
Given
See attachment for grid
Required
Find c and d
From the attachment, we have:
--- Point on A
--- Corresponding point on B
When A is reflected across the x-axis, the rule is:
![(x,y) \to (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2C-y%29)
So, we have:
![(3,5) \to (3,-5)](https://tex.z-dn.net/?f=%283%2C5%29%20%5Cto%20%283%2C-5%29)
Next, is to calculate the translation from
to ![(-3,-6)](https://tex.z-dn.net/?f=%28-3%2C-6%29)
This is calculated using:
![3 + c = -3](https://tex.z-dn.net/?f=3%20%2B%20c%20%3D%20-3)
and
![-5 + d = -6](https://tex.z-dn.net/?f=-5%20%2B%20d%20%3D%20-6)
So, we have:
![3 + c = -3](https://tex.z-dn.net/?f=3%20%2B%20c%20%3D%20-3)
![c = -3-3](https://tex.z-dn.net/?f=c%20%3D%20-3-3)
---- i.e. Shift by 6 units to the left
![-5 + d = -6](https://tex.z-dn.net/?f=-5%20%2B%20d%20%3D%20-6)
![d = 5 - 6](https://tex.z-dn.net/?f=d%20%3D%205%20-%206)
--- i.e. Shift by 1 unit down
Answer:
350%
Step-by-step explanation:
6 questions would be a 100% increase, and 6 times 3 is 18 questions, so that is 300%. the 3 questions left equal 50%, so the total is 350%.