Hello,
The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.
Now let's find the y-intercept by using the formula of point-slope form,
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points.
Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.
In conclusion, the rate of change is -3 and the y-intercept is 18.
I hope this helps!
May
Complete the square:
<span>y = 3x^2 - 12x + 4 </span>
<span>y = 3(x^2 - 4x) + 4 </span>
<span>y = 3(x^2 - 4x + 4 - 4) + 4 </span>
<span>y = 3(x^2 - 4x + 4) - 12 + 4 </span>
<span>y = 3(x - 2)^2 - 8</span>
The length is 30 meters and the width is 12 meters.
Answer:
809 km²
Step-by-step explanation:
I can split this into 3 rectangles. One is 25 by 17, another is 24 by 13, and the last one is 6 by 12. (I had gotten 13 for the second rectangle because 25 - 12 = 13.)
(25 * 17) + (24 * 13) + (6 * 12) <em>{17 is the first number after a multiple of 4 (16). As a result, 25 by 17 will end in "25." 25 by 17 is 425.}</em>
425 + (24 * 13) + (6 * 12) <em>{24 by 13 is 312.}</em>
425 + 312 + (6 * 12) <em>{6 by 12 is 72.}</em>
425 + 312 + 72 <em>{From left to right, add 425, 312, and 72 to get 809}</em>
737 + 72
809 km²
The area of this figure is 809 km².
