For this case we must indicate which of the ordered pairs shown belongs to the given table.
Option A:
, this pair is not found in the table
Option B:
, this pair is not found in the table
Option C:
, this pair is not found in the table
Option D:
, it is observed that this pair belongs to the table, it is in the last row of the table.
Answer:
Option D
I honestly don’t remember what a dilation is, but I can tell you that those triangles are not similar. 3:18 and 8:24 do not share the same ratio. 3 fits into 18 *6* times and 8 only fits into 24 *3*times.
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One of the rules of triangles is that if you have a 45 45 90 angle triangle, the two sides besides the hypotenuse are equal to each other. In this case, one of the sides is equal to x, so other side is equal to x as well. Now, to solve for x, you need to know the Pythagorean theorum:
Both 'a' and 'b' are equal to x, and 'c' is equal to 3, so I'll make the substitutions below:
This can be simplified to:
Now we just solve for x:
Solution:
To solve this problem, we must first remember that slope-intercept form is y=mx + b, where the variable m represents the slope of the line and the variable b represents the y-intercept of the equation.
To begin, we can take this form and substitute in the slope for the variable m.
y = mx + b
y = 4x + b
Next, because we weren't given the y-intercept, we can find it by substituting the value of 6 for x and the value of -1 for y (these values came from the ordered pair that we were given in this problem).
-1 = 4(6) + b
After that, we can begin to simplify and solve for the variable b by computing the multiplication on the right side of the equation.
-1 = 24 + b
Next, we should subtract 24 from the right side of the equation in order to get the variable b alone.
-25 = b
Now, if we substitute in this value for the variable b in our equation with the slope, we get:
y = 4x - 25
Therefore, your answer is y = 4x - 25.
Hope this helps!