9 times 12 is 108. so 42/108=21/54
for nine they are not for 10 yes
Answer:
A) (-8, -16)
B) (0, 48)
C) (-4, 0), (-12, 0)
Step-by-step explanation:
A) the vertex is the minimum y value.
extremes of a function we get by using the first derivation and solving it for y' = 0.
y = x² + 16x + 48
y' = 2x + 16 = 0
2x = -16
x = -8
so, the vertex is at x=-8.
the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16
B) is totally simple. it is f(0) or x=0. so, y is 48.
C) is the solution of the equation for y = 0.
the solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac)) / (2a)
in our case here
a=1
b=16
c=48
x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =
= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)
x1 = -8 + 4 = -4
x2 = -8 - 4 = -12
so the x- intercepts are (-4, 0), (-12, 0)
Answer:
$4000
Step-by-step explanation:
the cars value is going sown by 2000 dollars each year so in seven years the car will be worth 4000 dollars
Note: I'm not completely positive on this.
The ratio between the amount of blue and yellow paint needed to make green paint is 2: 3.
That is, for every 2 liters of blue paint you need 3 liters of yellow paint.
In the same way, for every 4 liters of blue paint, 6 liters of yellow paint are needed.
Then, to continue filling the table, you must consecutively sum 2 liters of blue paint and 3 liters of yellow paint in the corresponding column. This will increase the amount of green paint by a factor of 5 liters.
The same procedure is followed until 45 liters are summed to the green paint column. Then, the data in that row will indicate how much blue and yellow paint is needed:
18 liters of blue paint
27 liters of yellow paint
To verify the result divided 18/27
The result should be 0.6667 = 2/3, which is the ratio sought
