We can convert the equation of the line in vector form by imposing i cap ,j cap and k cap with direction ratios.
The movement of an object from one place to another is described using vectors. Vectors can be represented as points in a coordinate system in the cartesian system. Similar to this, a "n" tuple can be used to represent vectors with "n" dimensions.
In physics, a vector is a quantity with both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity. Simply subtract the starting point from the terminal point to determine the vector in component form given the initial and terminal points.
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The value of f(r - 2) is 6r - 5
<h3>What is a function?</h3>
Function can be defined as an expression, rule, or law that defines a relationship between one variable known as the independent variable and another called the dependent variable.
From the information given ,we have;
f(x)= 6x+7, with f ( r - 2)
From here, we have that x = r -2
Now, let's substitute x as r - 2 in the function given;
f(x) = 6x + 7
f(r - 2) = 6 ( r - 2) + 7
Expand the bracket
f(r - 2) = 6r - 12 + 7
collect like terms
f(r - 2) = 6r - 5
Thus, the value of f(r - 2) is 6r - 5
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Simplify:
5(a + 5) + -3 = 3(2 + -1a)
Reorder the terms:
5(5 + a) + -3 = 3(2 + -1a)
(5 * 5 + a * 5) + -3 = 3(2 + -1a)
(25 + 5a) + -3 = 3(2 + -1a)
Reorder the terms again:
25 + -3 + 5a = 3(2 + -1a)
Combine like terms:
]25 + -3 = 22
22 + 5a = 3(2 + -1a)
22 + 5a = (2 * 3 + -1a * 3)
22 + 5a = (6 + -3a)
Solve:
22 + 5a = 6 + -3a
To solve for variable 'a':
You have to move all terms containing A to the left, all other terms to the right.
Then add '3a' to each side of the equation:
22 + 5a + 3a = 6 + -3a + 3a
Combine like terms:
5a + 3a = 8a
22 + 8a = 6 + -3a + 3a
Combine like terms again:
-3a + 3a = 0
22 + 8a = 6 + 0
22 + 8a = 6
Add '-22' to each side of the equation.:
22 + -22 + 8a = 6 + -22
Combine like terms:
22 + -22 = 0
0 + 8a = 6 + -22
8a = 6 + -22
Combine like terms once more:
6 + -22 = -16
8a = -16
Divide each side by '8'.
a = -2
Simplify:
a = -2
Answer: a=-2
Hope I could help! :)
