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Mathematics

1 answer:

mojhsa [17]1 year ago

8 0

Answer:

x = 44

Step-by-step explanation:

(3x + 30) = 162 (opposite angles are equal )

3x = 162 - 30

x = 132/3

x = 44

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A single, six-sided die is rolled. Find the probability of rolling an even number or a number less than 5.

Svetach [21]

The probability of rolling an odd number or a number less than 5 is 5/6.

Probability is the likelihood of the occurrence of an event. It is the ratio of number of events to number of possible outcomes.

The possible outcome from rolling a six-sided die is 1, 2, 3, 4, 5 and 6

P(odd number) = 3/6; P(less than 5) = 4/6; P(odd number and less than 5) = 2/6

Hence:

P(odd number or less than 5) = 3/6 + 4/6 - 2/6 = 5/6

The probability of rolling an odd number or a number less than 5 is 5/6.

8 0

1 year ago

For what values of $x$ is $$\frac{x^2 + x + 3}{2x^2 + x - 6} \ge 0?$$ note: be thorough and explain why all points in your answe

Rus_ich [418]

To solve the inequality $\frac{x^2+x+3}{2x^2+x-6}\ge \:0$

$\mathrm{Factor\:the\:left\:hand\:side\:}\frac{x^2+x+3}{2x^2+x-6}:$

The numerator $x^2+x+3$ is not factorizable.

so factor the denominator $2x^2+x-6$ :

$2x^2+x-6=\left(2x^2-3x\right)+\left(4x-6\right)=x\left(2x-3\right)+2\left(2x-3\right)\\ \mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-3x\mathrm{:\quad }x\left(2x-3\right)\\ \mathrm{Factor\:out\:}2\mathrm{\:from\:}4x-6\mathrm{:\quad }2\left(2x-3\right)\\$