Answer:
Step-by-step explanation:
<h3>Part A</h3>
<u>Solve the equation:</u>
- 6x² + 48x + 120 = 0
- x² + 8x + 20 = 0
- x² + 8x + 16 + 4 = 0
- (x + 4)² + 4 = 0
- (x + 4)² = - 4
The left side is positive and right side is negative so no solution
<h3>Part B</h3>
There is no intercession with the x-axis, the graph of the function is entirely above the x-axis.
It means the diver won't reach the bottom of the lake
The equation of a sphere is:
(x – h)^2 + (y – k)^2 + (z – l)^2 = r^2
where h, k and l are the coordinates of the center of the
sphere
Using the midpoint formula, the coordinate of the center
is:
h = (-4 + 6) / 2 = 1
k = (7 + -5) / 2 = 1
l = (6 + 7) / 2 = 6.5
so the equation becomes:
(x – 1)^2 + (y – 1)^2 + (z - 6.5)^2 = r^2
we plug in any point, in this case point P to solve for r:
(-4 -1)^2 + (7 – 1)^2 + (6 - 6.5)^2 = r^2
r^2 = 61.25
So the full equation is:
<span>(x – 1)^2 + (y – 1)^2 + (z - 6.5)^2 = 61.25</span>
Answer:
91 radical
Step-by-step explanation:
because because two radicals make a radical and when you add those numbers together there 91 so 91 radical
Answer: 20 oranges and 5 mangoes
Step-by-step explanation:
Define the following:
x = number of oranges
y = number of mangoes
Make the following system of equations:
x + y = 25
0.35x + 1.00y = 12.00
Solve for x:
y = 25 - x
⇒ 0.35x + 1.00(25 - x) = 12.00
⇒ 0.35x + 25 - x = 12.00
⇒ -0.65x = -13.00
⇒ x = 20
Solve for y:
20 + y = 25
y = 5
∴ 20 oranges and 5 mangoes were purchased.
