Answer:
Step-by-step explanation:
Given parameters:
Marbles in the bag = blue, yellow, and green
Pr(yellow) =
Pr(blue) =
Unknown:
Pr(green) = ?
Solution:
Probability is the likelihood of an event to occur;
For this problem;
Pr(yellow) + Pr(blue) + Pr(green) = 1
+ + Pr(green) = 1
Pr(green) = 1 - ( + )
Pr(green) = 1 -
Pr(green) =
Answer:
LK=12
Step-by-step explanation:
From the given figure, HI=7 and LH=9, and we know that
(1)
Now, from ΔKHL, we have
and from ΔOKH,
(2)
Also, ΔIKL is similar to ΔOHL, therefore
Using equation (2), we get
Thus, the value of LK is 12.
Answer:
2a) -2
b) 8
Step-by-step explanation:
<u>Equation of a parabola in vertex form</u>
f(x) = a(x - h)² + k
where (h, k) is the vertex and the axis of symmetry is x = h
2 a)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is 6, then
f(6) = 0
⇒ a(6 - 2)² - 6 = 0
⇒ 16a - 6 = 0
⇒ 16a = 6
⇒ a = 6/16 = 3/8
So f(x) = 3/8(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 3/8(x - 2)² - 6 = 0
⇒ 3/8(x - 2)² = 6
⇒ (x - 2)² = 16
⇒ x - 2 = ±4
⇒ x = 6, -2
Therefore, the other x-axis intercept is -2
b)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is -4, then
f(-4) = 0
⇒ a(-4 - 2)² - 6 = 0
⇒ 36a - 6 = 0
⇒ 36a = 6
⇒ a = 6/36 = 1/6
So f(x) = 1/6(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 1/6(x - 2)² - 6 = 0
⇒ 1/6(x - 2)² = 6
⇒ (x - 2)² = 36
⇒ x - 2 = ±6
⇒ x = 8, -4
Therefore, the other x-axis intercept is 8
All the answers except C has a Vertical Line when graphed. It must pass the Vertical line test in order to be a function.
Vertical Line Test: If you can draw a vertical line anywhere on a graph so that it hits the graph in more than one spot, then the graph is NOT a function.
C.) can pass the test since it's a horizontal line.
Hope this helps!
Y/x = 7/2
Cross multiply.
2y = 7x
Solve for y.
y = 7/2x
C) The slope of the line is 7/2
D) The y intercept is 0