Multiply the fraction and simplify the answer 2/5×5/7×1/2

1 answer:

6 0

2/5 * 5/7 * 1/2 <== Group first pair of fractions to make
  multiplication easier

(2/5 * 5/7) * 1/2 <== Multiply fractions in parentheses, keeping in
  <span> (10/35) </span>   mind all rules of fraction multiplication (i.e.
(2/7)        cross-multiplying, etc.)

2/7 * 1/2 <== Multiply remaining fractions

1/7

The problem simplifies to 1/7.
Hope that helped =)

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Write down the quadratic equation whose roots are $x = -7$ and $x = 1,$ and the coefficient of $x^2$ is 1. Enter your answer in

pav-90 [236]

<h2>Steps:</h2>

So firstly, since we know that the coefficient of x² is 1, this means that this is our base equation:

y = x² + bx + c

Now, since we know that the roots are -7 and 1, set y = 0 and set x = -7 and 1 and simplify:

$0=(-7)^2+b(-7)+c\\0=49-7b+c\\-49=-7b+c\\\\0=1^2+b(1)+c\\0=1+b+c\\-1=b+c\\\\-49=-7b+c\\-1=b+c$

Now with this, we can set up a system of equations to solve for b and c. For this, I will be using the elimination method. For this, subtract the 2 equations:

$\begin{alignedat}{2}-49&=-7b+c\\-(-1&=b+c)\\-48&=-8b\end{alignedat}$