notice the equations in slope-intercept form, the first one has a slope of -1, the second one has a slope of 1.
if the slopes are equal, and the constant is different, they lines are parallel.
if the slopes are equal, and the constant is the same the equations are exactly the same thing, and the lines are coincident, on slapped on top of the other.
if the slopes differ, like here, then they have a solution, where they
intersect.
By the size , color, or if they have wings or no wings, etc. just think of what might be different on each one or group.
Side lengths of triangle are (6.2v-5.5) cm, (8.5v-6.7) cm, and (6.6w+7.6) cm.
To find:
The expression which represents the perimeter of the given triangle.
Solution:
We know that perimeter of a triangle is the sum of all sides of a triangle.
Answer: a) 6, 0, 10 b) yellow/orange line
Step-by-step explanation:
a) Plug the x in the y functions, y = 2x² + x
when x = -2, y = 2(-2)² + (-2) = 8 - 2 = 6
when x = 0, y = 2(0)² + (0) = 0 + 0 = 0
when x = 2, y = 2(2)² + (2) = 8 + 2 = 10
b) By looking the table, the equation has a point (0,0), only blue and yellow/orange line has the passed the point (0,0), so we delete the red line option.
And we choose a point (1,3), then only yellow/orange line has passed the point (1,3). So the yellow/orange line fits the equation.
Answer:
17 rows
Step-by-step explanation:
We know that f(x) = 2x² - 10x models the total number of spaces and x models the number of rows.
Since we are given the total number of spaces of 408. We let f(x) = 408
2x² - 10x = 408
Now we solve as a quadratic, subtract 408 to both sides
2x² - 10x - 408 = 0
Divide 2 on both sides
x² - 5x - 204 = 0
We look for terms that multiply to -204 and add to -5.
Those terms are -17 and 12
x² - 17x + 12x - 204 = 0
x(x-17) + 12(x-17)
(x+12)(x-17)
x = -12 x = 17
We can not have -12 rows but we can have 17 rows.
17 rows is the answer.
