Y1 is the simplest parabola. Its vertex is at (0,0) and it passes thru (2,4). This is enough info to conclude that y1 = x^2.
y4, the lower red graph, is a bit more of a challenge. We can easily identify its vertex, which is (-4,0), and several points on the grah, such as (2,-3).
Let's try this: assume that the general equation for a parabola is
y-k = a(x-h)^2, where (h,k) is the vertex. Subst. the known values,
-3-(-4) = a(2-0)^2. Then 1 = a(2)^2, or 1 = 4a, or a = 1/4.
The equation of parabola y4 is y+4 = (1/4)x^2
Or you could elim. the fraction and write the eqn as 4y+16=x^2, or
4y = x^2-16, or y = (1/4)x - 4. Take your pick! Hope this helps you find "a" for the other parabolas.
Answer:
The population is: all glass recycled
The sample is: the 10 selected glass items.
The parameter is the proportion of: all his glass that is clear
The statistic is the proportion of: the selected glass that is clear
Step-by-step explanation:
This is a linear equation in slope intercept form which is
where m is the slope and b is the y intercept.
The equation
Has a slope of -1/3 so this means that the slope will be decreasing. A negative linear equation increases as we go left. and decreases as we go right. The y intercept is 2. So this means the graph must pass through (0,2) and when x=0, y must be 2.
In other words, look for a line that the y values increase as we go left and decrease we go right. Also look for a point (0,2) and make sure the graph pass through it.
Answer:
19cm
Step-by-step explanation:
An equilateral triangle is a triangle where the length of the 3 sides are the same.
the perimeter is the sum of the 3 sides
for example, if the length of the side of the an equilateral triangle is 5, the perimeter is 5 x 3 = 15
let x = unknown length of side
length after increase = x + 5
(x + 5) x 3 = 72
divide both sides of the equation by 3
x + 5 = 24
subtract 5 from both sides of the equation
x = 24 - 5 = 19cm
Answer:
B = 40° and D = 60°
Step-by-step explanation:
Just subtract the angles you already know from 90° (since perpendicular means right angle, which is 90°).
