Answer:
A sequence of transformation can move two congruent figures to the same place (vertical / horizontal shifts). This causes them to perfectly overlap, proving their congruency.
A sequence of transformations can be used to show that something is similar, because if one were to transform a figure with only shrinks / stretches, one can shrink / stretch them to make them congruent. If only shrinks or stretches were done, and if the result of the transformation is congruent to the other figure, then the figures are similar (sides are proportional and shrinking/stretching them proves proportionality to other figure).
Answer:
<em>The slope of the line is m=6. </em>
<em>The y-intercept is (0,−24). </em>
<em>The equation of the line in the slope-intercept form is y=6x−24.</em>
Step-by-step explanation:
The slope of the line passing through the two points P=(x1,y1) and Q=(x2,y2) is given by m=y2−y1x2−x1.
We have that x1=2, y1=−12, x2=5, y2=6.
Plug the given values into the formula for the slope: m=(6)−(−12)(5)−(2)=183=6.
Now, the y-intercept is b=y1−m⋅x1 (or b=y2−m⋅x2, the result is the same).
b=−12−(6)⋅(2)=−24.
Finally, the equation of the line can be written in the form y=mx+b.
y=6x−24.
Answer:
The slope of the line is m=6.
The y-intercept is (0,−24).
The equation of the line in the slope-intercept form is y=6x−24.
Answer:
-19 = x
Step-by-step explanation:
Step 1: Write equation
-4(x + 1) - 3 = -3(x - 4)
Step 2: Solve for <em>x</em>
<u>Distribute:</u> -4x - 4 - 3 = -3x + 12
<u>Combine like terms:</u> -4x - 7 = -3x + 12
<u>Add 4x on both sides:</u> -7 = x + 12
<u>Subtract 12 on both sides:</u> -19 = x
Hey! Your answer would be A. (1/5)(-20)
Answer:
Step-by-step explanation:
Notice that they are asking you to write the equation of the parabola in vertex form, that is using the coordinates of the vertex 
in the expression:
we can start by directly replacing the given vertex coordinates (-3, -3) in the expression, and then using the extra info on the point the parabola goes through in order to find the parameter 
:
So, now we can write the full expression for the parabola:
