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4 years ago

Select the correct answer.

Mathematics

2 answers:

kipiarov [429]4 years ago

8 0

Answer:

Step-by-step explanation:

v - 2u

= < - 2, 4 > - 2 < 2.5, - 4 > ← multiply each component by 2

= < - 2, 4 > - < 5, - 8 > ← subtract corresponding components

= < - 2 - 5, 4 + 8 > = < - 7, 12 >

Graph A shows the resulting vector

kow [346]4 years ago

3 0

Answer: Graph A

Step-by-step explanation:

Hi, to answer this we have to solve the expression.

u = <2.5, -4>

v= <-2,4>

v - 2u = <-2,4>- 2<2.5, -4>

v - 2u = <-2,4>- <5, -8>

v - 2u = <-7,12>

Correct option is A.

For the graph , we have to move 7 places to the left in the x axis (negative), go up in the y axis by 12 units, and connect that point with the (0,0).

Feel free to ask for more if needed or if you did not understand something.

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Two points are selected randomly on a line of length 32 so as to be on opposite sides of the midpoint of the line. In other word

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Solution :

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If x ranges from the 0 to 16 and the y ranges from 16 to 32, we see that the boundary of the region $y-x \geq 9 \text{\ is}\ y - x = 9$ which goes from the $(7, 16 ) \text{ to}\ (16, 25)$ .

And so it is easier to find the area of region where $y-x \leq 9$ . This is the triangle with points $(7,16),(16,25) \text{ and}\ (16,16)$ as its vertices.

The area if the triangle is = $\frac{1}{2} \times 9 \times 9$

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or $P(y-x \geq 9) = 1 - \frac{81}{512}=\frac{431}{512}$

Thus the answer is $\frac{431}{512}$

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