<span>When you have an equation of the form y = mx + b (which you do in this case), the slope is always equal to the coefficient of x, which is m or 12 in this case. Since there is no "b" in your equation, you could say that b=0, and the line is known to cross the y axis at zero.
In case you are interested, if the equation said y = 12 x + 3 the slope of the line would still be 12 but the line would cross the y axis at 3. If the equation said y = 12x -4, the line would have a slope of 12 and would cross the y axis at -4.</span>
Answer:

Step-by-step explanation:
Given the rational expression:
, to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator





Thus, we now have: 
Step 2: Apply the concept of Partial Fraction
Let,
= 
Multiply both sides by (x - 1)(x - 4)
= 

Step 3:
Substituting x = 4 in 





Substituting x = 1 in 





Step 4: Plug in the values of A and B into the original equation in step 2


If x+2 is a factor of x^3+6x^2+kx+10, then if we replace x by -2 in the polynomial x^3-6x^2+kx+10, we must get zero:
x=-2→(-2)^3-6(-2)^2+k(-2)+10=0→
-8-6(4)-2k+10=0→
-8-24-2k+10=0
-2k-22=0
Solving for k. Adding 22 both sides of the equation:
-2k-22+22=0+22
-2k=22
Dividing both sides of the equation by -2:
-2k/(-2)=22/(-2)
k=-11
Answer: k = - 11
I think when you subtract 4 from x, you are shifting the graph right horizontally 4 units. When you add 84 at the end of the function, you are shifting it up vertically 84 units. When you times it by -5, you are stretching it by a factor of 5 and flipping it upside down.
just think of how each term effects the y value.
This is algebra disguised as geometry. I object. There are much better ways to combine algebra and geometry.
Anyway, in a parallelogram the diagonals meet at their midpoints, so bisect each other. So we have two pairs of congruent segments; geometry over.
3x + 1 = x+27
79 - y = 2y + 22
We can ignore the one about x.
79 - 22 = 2y + y
57 = 3y
y = 19
Answer: 19