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RSB
2 months ago
6

Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5? The differ

ence is a binomial with a degree of 5.
The difference is a binomial with a degree of 6.

The difference is a trinomial with a degree of 5.

The difference is a trinomial with a degree of 6.
Mathematics
2 answers:
lawyer [12.5K]2 months ago
6 0
<span>Let A = a3b + 9a2b2 - 4ab5, and B = a3b - 3a2b2 + ab5. The difference can be expressed as A - B = a3b + 9a2b2 - 4ab5 - (a3b - 3a2b2 + ab5). When the negative sign is in front of the parentheses, all the internal signs change: this leads to: A - B = a3b + 9a2b2 - 4ab5 - a3b + 3a2b2 - ab5 = a3b - a3b + 9a2b2 + 3a2b2 - 4ab5 - ab5 = 12a2b2 - 5ab5. The first term’s degree is 2 + 2 = 4, while the second term’s degree is 1 + 5 = 6. Thus, the correct response is that the difference is a binomial of degree 6.</span>
zzz [12.3K]2 months ago
5 0
By using the property of inverse addition, we find that a3b and a3b negate each other. The positive terms, 9a2b2 and 3a2b2, combine to yield 12a2b2, while the negative components, -4ab5 and -ab5, sum to -5ab5. Therefore, the final simplification of your equation is 12a2b2 - 5ab5.

This represents a binomial with a total degree of 6.

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A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation val
zzz [12365]

Answer:

A correlation coefficient of +1 or -1 reflects a perfect linear relationship, but a 0.94 indicates a strong positive correlation between the aspen leaf's length and surface area, though not guaranteeing linearity.

Step-by-step explanation:

The correlation coefficient (r) ranges between +1 and −1, where +1 means perfect positive correlation, −1 means perfect negative correlation, and 0 means no correlation.

The closer r is to ±1, the stronger the correlation. Generally, values between 0.7 and 1, or −0.7 and −1, indicate a significant correlation.

While 0.94 shows a strong direct association between the leaf's length and surface area, it does not definitively prove a linear relationship is the best fit.

4 0
3 months ago
A machine can stamp 40 envelopes in 8 mins. How many of these machines working simultaneously are required or needed to stamp 12
lawyer [12517]

Answer:

24 minutes

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Let y represent the rate of 120 envelopes per minute.

40/8 = 120/y

40y = 8 * 120

40y = 960

y = 960/40

= 24 minutes

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