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3 years ago

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Solve 8 − |2x − 1| ≥ 6. State your answer in interval notation

1 answer:

Gnoma [55]3 years ago

3 0

Answer:

$\huge\boxed{x\in[-0.5,\ 1.5]}$

Step-by-step explanation:

$8-|2x-1|\geq6\qquad\text{subtract 8 from both sides}\\\\8-8-|2x-1|\geq6-8\\\\-|2x-1|\geq-2\qquad\text{change the signs}\ /\text{multiply both sides by (-1)}/\\\\|2x-1|\leq2\iff2x-1\leq2\ \wedge\ 2x-1\geq-2\qquad\text{add 1 to all sides}\\\\2x-1+1\leq2+1\ \wedge\ 2x-1+1\geq-2+1\\\\2x\leq3\ \wedge\ 2x\geq-1\qquad\text{divide all sides by 2}\\\\\dfrac{2x}{2}\leq\dfrac{3}{2}\ \wedge\ \dfrac{2x}{2}\geq\dfrac{-1}{2}\\\\x\leq1.5\ \wedge\ x\geq-0.5\Rightarrow-0.5\leq x\leq1.5$

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The coordinates of A and B are (3k, 8) and (k, -3) respectively. Given that the gradient of the line segment AB is 3, find the v

Vladimir [108]

Step-by-step explanation:

gradient = slope or several other words.

it describes how strongly a line (or tangent to a bent curve) is going up or down or ... if it is changing at all.

it is represented by the ratio

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in our case, when going from A to B we have

x changes by -2k (from 3k to k).

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so, the gradient or slope is

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B = (11/6, -3)

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2 years ago

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IRISSAK [1]

Answer:

Probablity of getting six in at most three roll= 0.199.

Step-by-step explanation:

Given: Dice rolled at most 3 times untill a 6 occurs.

First, finding the probablity of getting 6 in a dice if rolled once.

Probablity= $\frac{chances\ of\ occurance}{Total\ number\ of\ event}$

We know, dice have six side, therefore, total number of event will be 6.

∴ Probablity of getting six in one roll= $\frac{1}{6}$

As given, Dice is rolled at most 3 times.

Now, finding the probablity of getting 6 in a dice if rolled 3 times.

∴ Probablity of getting six in three roll= $\frac{1}{6}+(\frac{1}{6})^{2} +(\frac{1}{6})^{3}$

⇒ Probablity of getting six in three roll= $\frac{1}{6}+\frac{1}{36} +\frac{1}{216}$

Taking LCD 216

⇒Probablity of getting six in three roll= $\frac{1\times 36+ 6\times 1+1}{216}$

⇒Probablity of getting six in three roll= $\frac{43}{216}$

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