The correct way to write slope intercept is y=3x+4
Let the first brother = x
second brother = x + 2
third brother = x + 4
<span>The product of the first and third boys' ages is 20 more than twice the second boy's age:
x(x+4) = 2(x+2) + 20
x</span>² + 4x = 2x + 4 + 20
x² + 4x - 2x - 24 = 0
x² + 2x - 24 = 0
(x - 4)(x + 6) = 0
x = 4 or -6 (rejected, age cannot be negative)
First brother = 4
Second brother = 4 + 2 = 6
Third brother = 4 + 4 = 8
The three boys are 4, 6, and 8 years old.
Given:
Markers are sold in packages of 12 and pens are sold in packages of 8.
To find:
Least amount of markers and pens Rick needs to buy to have an equal number of markers and pens
Solution:
To find the least amount of markers and pens, we need to find the LCM of 12 and 8.
Prime factors of 8 and 12 are
To find the LCM, multiply all factors but the common factors are included only once.
Therefore, the least amount of markers and pens Rick needs to buy to have an equal number of markers and pens is 24.
A unit vector in the direction of a would be the vector a multiplied by a factor such that the length of vector a is unity.
The magnitude of a is given by:
|a|
=sqrt(4^2+3^2+2^2) [ I got lazy instead of writing (-4)^2+(-3)^2+2^2]
=sqrt(29).
So the univector is a/sqrt(29), or (-4/sqrt(29),-3/sqrt(29), 2/sqrt(29), or simply (-4,-3,2)/sqrt(29).
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