Answer:
a. (-1, 3)
Step-by-step explanation:
The "glide" 4 units right and up is the transformation ...
(x, y) ⇒ (x+4, y+4)
The reflection across y=1 is the transformation ...
(x, y) ⇒ (x, 2-y)
Combined, you have the transformation ...
(x, y) ⇒ (x +4, 2-(y +4)) = (x +4, -2-y)
Then, ...
K(-5, -5) ⇒ K'(-5 +4, -2-(-5)) = K'(-1, 3)
Answer: The equation in slope-intercept form is y=2x-11
Step-by-step explanation: Slope-intercept is y=mx+b where m is the slope and b is the y-intercept. To find the slope, you find the difference between the y values divided by the difference between the x values. -5-(-9) = 4, and 3-1 is 2. 4/2 is 2, so m = 2. Since the slope is 2, it states for every x you move on the right you move 2 up. But we are trying to get the y-intercept, so x = 0. We are subtracting 1 in our x value, so we move 2 downwards. We subtract 2 from -9 which gives us -11, which is our y-intercept.
Hope this helps!
The dimensions of the prism can be 2x, 2x+3 and x+6.
We first factor out the GCF of the trinomial. The GCF of the coefficients is 2. Each term has an x in common as well, so the GCF is 2x.
Factoring out the 2x, we have
2x(2x²+15x+18).
To factor the remaining trinomial, we find factors of 2*18=36 that sum to 15. 12*3 = 36 and 12+3 = 15. We split up 15x into 12x and 3x:
2x(2x²+12x+3x+18)
Now we group together the first two terms in parentheses and the last two:
2x((2x²+12x)+(3x+18))
Factor out the GCF of the first group:
2x(2x(x+6)+(3x+18))
Factor out the GCF of the second group:
2x(2x(x+6)+3(x+6))
Factoring out what these have in common,
2x(x+6)(2x+3)
Answer:
6 times.
Exclamation:
You can do 15 divided by 2,50 to get you answer, when you do that you get 6.
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