Answer:
see explanation
Step-by-step explanation:
(a)
To find the x- intercepts , let y = 0 , that is
6x - x² = 0 ← factor out x from each term
x(6 - x) = 0
Equate each factor to zero and solve for x
x = 0
6 - x = 0 ⇒ x = 6
Coordinates of P (6, 0 )
(b)
The axis of symmetry is a vertical line, positioned at the midpoint of the zeros
x = 
= 
= 3
Equation of axis of symmetry is x = 3
(c)
Given a parabola in standard form y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
= - 
y = 6x - x² = - x² + 6x ← is in standard form
with a = - 1, b = 6 , then
= - 
= 3
Substitute x = 3 into y = 6x - x² for y- coordinate
y = 6(3) - 3² = 18 - 9 = 9
coordinates of maximum point = (3, 9 )
Answer:
(3.5, 17)
Step-by-step explanation:
It would be nice to see the whole graph, so we can see where the functions cross.
Without that information, we can still eliminate unreasonable choices.
A) the quadratic at y=3.5 is well above the exponential
B) the most likely choice (3.5, 17)
C) at x=-8, the quadratic is above the exponential
D) neither graph goes anywhere near y = -8
There are 2 orange marbles, 3 green marbles, & 5 purple marbles
two consecutives draws <em>without</em> replacement
Orange first, green second
Orange/total = 2/10, or 1/5
green/total - 1 = 3/9, or 1/3
1/5(1/3) = 1/15
There is a 1/15 chance of <em>Orange first, green second</em>
Both marbles are purple
Purple/total = 5/10, or 1/2
Purple/total = 4/9, or <em>44% chance of both being purple</em>
first is purple, the next is anything but purple
purple/total = 1/2, or 50% chance
(everything - purple)/total = 5/10, or 50% chance
1/2(1/2) = 1/4, or 25% chance of <em>first purple, then anything but purple</em>
hope this helps
X=59 all triangles have a sum of 180. So we subtract our given. 180 - 74 = 106. Then we subtract our givin again. 106 - 47 and boom our answer is 59.
Answer:
4 students
Step-by-step explanation:
As shown in the diagram, let U=[The total number of students questioned]
A=[Those who liked peanut butter ]
B=[Those who liked jam ]
x = those who like both peanut butter and jam.
Also 6 liked neither peanut butter nor jam.
From the diagram we can write the mathematical equation as follow and solve for x
We add x and subtract 30 to both sides.
Therefore 4 students like both peanut butter and jam.
