Answer:
D. (3; -4)
Step-by-step explanation:
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Answer: it will take her 56.67 seconds or 0.945 minutes to race 2 laps
Step-by-step explanation:
It takes Ella 1 minute and 25 seconds to complete the cheep beach course.
We can express this time in seconds or minutes. Expressing it in seconds,
1 minute = 60 seconds
Therefore,
1 minute and 25 seconds = 60 +25 = 85 seconds
If the course is 3 laps long, that means she completed 3 laps in 85 seconds. The time it will take her to race 2 laps would be
(2 × 85)/3
= 56.67 seconds
Converting to minutes, it will be
56.7/60 = 0.945 minutes
a) To find the volume of a cube, you cube the side length.
So, that will be V = 9/2³ = 729/8 in³.
b) To find the volume of a rectangular prism, you multiply the length by the width by the height.
So, that is V = 18 * 9 * 9/2 = 729 in³.
c) To find how many times the smaller box can go into the larger one, you divide the larger one's volume over the smaller one's.
That is <em>729/(729/8) = 729*8/729 = </em><em>8 boxes</em><em>.</em>
Answer:
Part A: 3x²(x⁸ - 16)
Part B: 3x²(x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)
Step-by-step explanation:
Part A. Factor out the greatest common factor
3x¹⁰ - 48 x²
= 3x²(x⁸ - 16)
Part B. Factor the expression completely
(i) Factor the difference of squares
x⁸ - 16
= (x⁴ - 4)(x⁴ + 4)
= (x² - 2)(x² + 2)(x⁴ + 4)
3x¹⁰ - 48 x² = 3x²(x² - 2)(x² + 2)(x⁴ + 4)
(ii) Factor the sum of squares
Use the Sophie Germain Identity to factor x⁴ + 4.
x⁴ + 4
= (x²)² + 2² (Still a sum of squares)
= (x² + 2)² - 4x² (Factor this as a difference of squares)
= (x² + 2 - 2x)(x² + 2 + 2x)
3x¹⁰ - 48 x² = 3x² (x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)
