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SIZIF [17.4K]
3 years ago
10

Which expression is equivalent to 6m+(m-2)(m+7)+3

Mathematics
1 answer:
Vika [28.1K]3 years ago
5 0

Answer:

m^{2} + 11m - 11

Step-by-step explanation:

6m+(m-2)(m+7)+3  =   6m   +  [ m*m - 14 -2m + 7m]  + 3

=  6m  + mm - 14 + 5m  + 3

=  mm + 11m - 11

6m+(m-2)(m+7)+3   = m^{2} + 11m - 11

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What is the justification for the first step in proving the formula for factoring the sum of cubes?
Anna11 [10]

Explanation:

The formula isnt correctly written, it should state:

a^3+b^3 = (a+b)(a^2-ab+b^2)

You have to start from (a+b)(a^2-ab+b^2)  and end in a³+b³. On your first step, you need to use the distributive property.

(a+b)(a^2-ab+b^2) = a*(a^2-ab+b^2) + b*(a^2-ab+b^2)

This is equal to

a*a^2-a*(ab) + a*b^2 + b*a^2-b*(ab) + b*b^2 = a^3 - a^2b + ab^2 +ba^2 -b^2a +b^3

Note that the second term, -a²b, is cancelled by the fourth term, ba², and the third term, ab², is cancelled by the fifht term, -b²a. Therefore, the final result is a³+b³, as we wanted to.

5 0
3 years ago
The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 40 to 75 mi
jeka57 [31]

Answer:

0.8333 = 83.33% probability that the cycle time exceeds 50 minutes if it is known that the cycle time exceeds 45 minutes

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

P(X > x) = \frac{b - x}{b - a}

Uniformly distributed over the interval 40 to 75 minutes.

This means that a = 40, b = 75

It is known that the cycle time exceeds 45 minutes

This means that we can use a = 45

What is the probability that the cycle time exceeds 50 minutes?

P(X > 50) = \frac{75 - 50}{75 - 45} = 0.8333

0.8333 = 83.33% probability that the cycle time exceeds 50 minutes if it is known that the cycle time exceeds 45 minutes

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