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3 years ago

12 equals x times the square root of 2

Mathematics

1 answer:

garik1379 [7]3 years ago

4 0

Answer:

x = 6√2

Step-by-step explanation:

Divide by the coefficient of x, then rationalize the denominator.

$12=x\sqrt{2} \qquad\text{given}\\\\\dfrac{12}{\sqrt{2}}=x \qquad\text{divide by $\sqrt{2}$}\\\\\dfrac{12}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=x \qquad\text{rationalize the denominator}\\\\\boxed{x=6\sqrt{2}} \qquad\text{simplify}$

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It takes Leon 17 hours to seal his driveway working by himself. If Michael helps Leon, they can seal the driveway in 2 hours. Ho

Norma-Jean [14]

Answer:

It takes Michael 1 hour, 14 minutes and 7 seconds to seal the driveway close

Step-by-step explanation:

Leon do the work in 17 hours that means the rate of his work is $\frac{1}{17} work/hr$ , so he do $\frac{2}{17}$ of the work in two hours, therefore Michael do the other $\frac{15}{17}$ of the work, thus Michael rate will be $\frac{15}{17} \div\frac{1}{2} =\frac{30}{17} work/hour$ .

So it takes Michael $1h+\frac{4}{17}h$ to complete the work, or $\frac{4h}{17} \times \frac{60min}{1hour} =14\frac{2}{17} min\\\\\frac{2}{17} min \times \frac{60 secs}{1min}=7secs$

$1h \ 14 min \ 7secs$

8 0

3 years ago

Sam and Mary collect marbles. “If you give me 5 marbles I’ll have twice as many as you.” said Sam to Mary.

ivann1987 [24]

Answer:

54 marbles

Step-by-step explanation:

The question is a word problem leading to a simultaneous equation

Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,

If Mary gives Sam 5 marbles, we have;

x + 5 = 2 × (y - 5)...(1)

If Sam gives Mary 4 marbles, we get;

x - 4 = y + 4...(2)

From equation (1), we get;

x + 5 = 2 × (y - 5) = 2·y - 10

x = 2·y - 10 - 5 = 2·y - 15

x = 2·y - 15...(3)

From equation (2), we have;

x - 4 = y + 4

∴ x = y + 4 + 4 = y + 8

x = y + 8...(4)

Equating the two values of 'x' in equation (3), and equation (4), we get;

2·y - 15 = y + 8

2·y - y = 8 + 15 = 23

∴ y = 23

From equation (4), we get;

x = y + 8 = 23 + 8 = 31

x = 31

The total number of marbles they have altogether = x + y

However, x + y = 23 + 31 = 54

Therefore;

The total number of marbles they have altogether = 54 marbles.

7 0

3 years ago

Ok maribelalmaraz2404 what’s this? Isosceles, Scalene, or equilateral?

Alexxx [7]

Answer:

scalene

Step-by-step explanation:

Since none of the sides are equal, the triangle is a scalene triangle

Isosceles would have 2 sides equal

Equilateral would have all 3 sides equal

3 0

3 years ago

alex wants to buy the same number of stamps and envelopes dancer sold in packs of 14 and envelopes are sold and packs of 10 what

lianna [129]

5 packs of stamps and 7 packs of envelopes. There will be a total of 70 envelopes and stamps.

6 0

3 years ago

What are the coordinates of the point on the directed line segment from (-10, -3)(−10,−3) to (2, -3)(2,−3) that partitions the s

azamat

Answer:

the coordinates of the point would be (-2.5,3)

Step-by-step explanation:

We want to split the segment from (-10,-3) to (2,-3) into segments with a ratio of 5:3. Since the y-coordinate is -3 for both coordinates, the y-coordinate of the partitioning point will be -3. The ratio of 5:3 corresponds to 5/8 of the distance between the x-coordinates of the two points. So we would be moving 5/8 of the distance from -10 to 2 for the x-coordinate, so the x-coordinate would be -10 + 5/8 (12) = -2.5. So the coordinates of the point would be (-2.5,3)

6 0

3 years ago