Part A
Your problem statement already shows you the conversion.
Bottles purchased: 5×10¹⁰
Bottles recycled: 8.3×10⁹
Part B
The ratio of bottles purchased to bottles recycled is
... (5×10¹⁰)/(8.3×10⁹) = 0.6×10¹ = 6.0
The number of bottles purchased is 6 times the number of bottles recycle.
d) You have a <u>difference of squares</u>:
49y² - 9 = (7y)² - 3²
Recall the identity,
a² - b² = (a - b) (a + b)
So,
49y² - 9 = (7y - 3) (7y + 3)
e) Pull out the common factor 3 from each term:
3x² - 3x - 90 = 3 (x² - x - 30)
Now use the <u>sum-product method</u>. Notice that we can write 30 = 5 • 6, and 5 - 6 = 1, so
3x² - 3x - 90 = 3 (x + 5) (x - 6)
f) Same as in (e), use the <u>sum-product method</u>. Notice that 42 = 7 • 6, and -7 - 6 = -13, so
x² - 13x + 42 = (x - 7) (x - 6)
Answer:
9 = n
Step-by-step explanation:
12 = 6(n – 7)
Divide by 6 on both sides
12/6 = 6/6(n – 7)
2 = n-7
Add 7 to each side
2+7 = n-7+7
9 = n
Answer:
f(x) = x² - 2x - 15
Step-by-step explanation:
∵ The function intersect x-axis at -3 and 5
∴ f(x) = 0 at x = -3 , 5
∵ The form of the quadratic equation is ⇒ ax² + -b/a x + c/a = 0
ax² - b/a x + c/a = 0
Where the sum of its roots is b/a and their multiplication is c/a
∵ a = 1
∵ -3 , 5 are the roots of the quadratic equation
∴ b = -3 + 5 = 2
∴ c = -3 × 5 = -15
∴ f(x) = x² - 2x - 15
