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3 years ago

5

The current of a river is 4 miles per hour. A boat travels to a point 30 miles upstream and back in 4 hours. What is the speed o

f the boat in still water?

1 answer:

Maurinko [17]3 years ago

7 0

16 mph is the answer I found after doing the work

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3 years ago

Which statement describes the first step to solve the equation by completing the square?

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The first step I would take is
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Show that 2x +1 is a factor of 2x3 +5x2+4x+1 and factories completely

larisa [96]

$\text{According to the factor theorem, if f(b) = 0, then x-b is a factor of f(x).}\\\\\text{Given that,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\f\left(-\dfrac 12 \right) = 2\left( - \dfrac 12 \right)^3 +5 \left( - \dfrac 12 \right)^2 +4 \left( - \dfrac 12 \right) +1 \\\\\\~~~~~~~~~~~~=-2 \cdot \dfrac 18 + 5 \cdot \dfrac 14 -2 +1 \\\\\\~~~~~~~~~~~=\dfrac 54 -\dfrac14 -1\\\\\\~~~~~~~~~~~=\dfrac 44 -1 \\\\\\~~~~~~~~~~~=1-1\\\\\\~~~~~~~~~~~=0\\\\\text{So,}~ 2x +1 ~ \text{is a factor of f(x).}$

$\text{Now,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\~~~~~~=2x^3+x^2 +2x^2 +2x +2x+1\\\\~~~~~~=x^2(2x+1) +2x(2x+1) + (2x+1)\\\\~~~~~~=(2x+1)(x^2 +2x +1)\\\\~~~~~~=(2x+1)(x+1)^2$

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2 years ago

how.can you write the prime factorization and find the greatest common factor and the least common multiple of two numbers

alisha [4.7K]

Answer:

Step-by-step explanation: you just need to find the greatest factors and least multiple then do it to two numbers

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3 years ago