Answer:
<h3>
f(x) = 6(x - 2)² + 3</h3>
Step-by-step explanation:
f(x) = a(x - h)² + k - vertex form of the equation of the parabola with vertex (h, k)
"the parabola opens upward" means: a>0
"the parabola has x = 2 as an axis of symmetry" means: h = 2
so f(x) = a(x - 2)² + k
"the parabola contains the point (1, 9)" means:
9 = a(1 - 2)² + k
9 = a(-1)² + k
9 = a + k
k = 9 - a
"the parabola contains the point (4, 27)" means:
27 = a(4 - 2)² + k
so:
27 = a(2)² + 9 - a
27 = 4a + 9 - a
3a = 18
a = 6
and k = 9 - 6 = 3
Therefore the vertex form for this parabola is:
<u> f(x) = 6(x - 2)² + 3</u>
Answer:
see explanation
Step-by-step explanation:
1 revolution is equivalent to the circumference of the wheel
1 revolution = πd ( d is the diameter )
= 70π cm
50 revolutions = 70π × 50 = 3500π cm = 35π m ≈ 110m ( nearest metre )
9514 1404 393
Answer:
(c) Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Step-by-step explanation:
Try the numbers in the constraints to see if they work.
<u>Build hours</u>:
(4 h/child bike)(10 child bikes) = 40 hours
(6 h/adult bike)(12 adult bikes) = 72 hours
total build hours: 40 +72 = 112, less than 120; constraint is met
<u>Test hours</u>:
(4 h/child bike)(10 child bikes) = 40 hours
(4 h/adult bike)(12 adult bikes) = 48 hours
total test hours: 40 +48 = 88, less than 100; constraint is met
__
Both constraints are met, so the order can be filled.
Simple, convert it to a decimal, first
move the decimal two places to the left
45%

0.45.
Then you change it into a fraction
45/100.
But, you can simplify it even more by dividing the numerator and denominator by 5.
45/5=9
and
100/5=20
Thus, it would be simplified, 9/20.