The numbers of courses taught per semester by a random sample of university professors are shown in the histogram.
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Answer:
- 8
Step-by-step explanation:
Given the expression
(3x² - 5)(4 + 4x²)
Each term from the second factor is multiplied by every term in the first factor, meaning
3x²(4 + 4x²) - 5(4 + 4x²) ← distribute both parentheses
= 12x² + 12 - 20 - 20x² ← combine like terms
= 12 - 8x² - 20
The coefficient for the x² term is - 8
Answer:
10
Step-by-step explanation:
If there’s a direct correlation between variables x and y, it can be expressed as
y = kx,
where y is the dependent variable
x is the independent variable
k signifies the constant of variation
_____________________________
For the first scenario
y = 400
x = r
using y = kx, we can derive the relation:
400 = kr
To find k here:
k = 400/r
For the second scenario
y = r
x = 4
again using y = kx, the relationship is given by:
r = 4k
Solving for k:
k = r/4
Since both conditions provide the same equation, k will have the same value in both cases.
Thus, we conclude:
400/r = r/4
=> 400*4 = r*r
=> 1600 = r^2
Hence, r is calculated to be 40.
Thus, k = r/4 = 40/4 = 10.
The constant of variation is confirmed to be 10, which is the correct answer.
Verification:
k = 400/r = 400/40 = 10