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3 years ago

15

two years ago jenny was four times as old as helen. six years from now , jenny will be twice as old as helen. how old are each o

f the girls now?

1 answer:

Dmitry_Shevchenko [17]3 years ago

7 0

They would be the same age, because 4 minus 2 = 2 so the would be the same age

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Which expression is equivalent to |b| >2?

vovangra [49]

Answer:

The equivalent expression for |b| > 2 is {b : b < -2} ∪ {b : b > 2}.

Step-by-step explanation:

The expression |x| < a is equivalent to -a < x < a and the expression |x| > a is equivalent to {x : x < -a} ∪ {x : x > a}.

This means, the set of all points that satisfy the inequality |x| < a is the set of all points between -a and a exclusive of -a and a.

The set of all points that satisfy the inequality |x| > a is the set of all points that are less than -a and the set of all points that are greater than a.

Hence, the equivalent expression for |b| > 2 is {b : b < -2} ∪ {b : b > 2}.

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Please explain why. Thanks

xxTIMURxx [149]

<h3><u>Question</u> :-</h3>

Is (x-2) is a factor of x³-3x²-x +7 –

Yes
No ☑

<h3><u>Explanation</u> :-</h3>

We are given –

Polynomial function, P(x) = x³-3x²-x +7

In order to check if x - 2 is a factor of x³-3x²-x +7 or not, we must show that P(2) = 0.

Let's find value of x!

$\qquad$ $\twoheadrightarrow\bf P(x) = x³-3x²-x +7$

$\qquad$ $\twoheadrightarrow\bf Q(x) =x - 2$

$\qquad$ $\twoheadrightarrow\bf If \:Q(x) = 0$

$\qquad$ $\twoheadrightarrow\bf x - 2 = 0$

$\qquad$ $\twoheadrightarrow\bf x = 2$

Now Put x = 2 into the polynomial –

$\qquad$ $\purple{\twoheadrightarrow\bf P(2) = 2³-3(2)²-2+7}$

$\qquad$ $\twoheadrightarrow\sf P(2) = 8 - 3 \times 4 +5$

$\qquad$ $\twoheadrightarrow\sf P(2) = 8 -12 +5$

$\qquad$ $\twoheadrightarrow\sf P(2) = 13-12$

$\qquad$ $\purple{\twoheadrightarrow\bf P(2) =1 }$

Since the value of the polynomial function st x = 2 is not Zero (0). Henceforth, ( x - 2) is a factor of x³-3x²-x +7.

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