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GalinKa [24]
3 years ago
10

harvey collects rare marbles. He has 125 marbles in collection 1, 36 fewer marbles in collection 2, and 53 more marbles than col

lection 1 in collection 3. Each display tray holds an equal number of marbles. If he uses 14 trays to to hold all of the marbles, how many marbles will he display on 3 trays? What simpler problems did you choose to solve first?
Mathematics
1 answer:
Usimov [2.4K]3 years ago
6 0

Collection 1, no of marbles = 125

Collection 2, no of marbles =36 fewer = 125-36 =89

Collection 3, no of marbles = 53 more =125+53 =178

Hence total marbles = 125+89+178

= 392

Given that he uses 14 trays to hold all the marables

Let us assume that he distributes equally all 392 marbles in 14 trays

Then marbles in each tray = 392/14 = 27

Thus division is used for finding out the no of marbles in a tray.

For finding out no of marbles in 3 trays, we get = 3x27 = 81 marbles

(Here direct variation is used)

Answer is 81 marbles

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A line passes through point A(10,15). A second point on the line has an x-value that is 125% of the x-value of point A and a y-v
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The equation of the line in the point-slope form is y - 15 = -\frac{3}{2} (x - 10)

Step-by-step explanation:

The point-slope form of a linear equation is y-y_{1}=m(x-x_{1}) , where

  • m is the slope of the line, where m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} , (x_{1},y_{1}) and (x_{2},y_{2}) are two points on the line
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∵ Point A = (10 , 15)

∵ The x-coordinate of the second point is 125% of x-coordinate

  of point A

∴ x-coordinate of second point = \frac{125}{100} × 10

∴ x-coordinate of second point = 12.5

∵ The y-coordinate of the second point is 75% of y-coordinate

  of point A

∴ y-coordinate of second point = \frac{75}{100} × 15

∴ y-coordinate of second point = 11.25

∴ The coordinates of the second point are (12.5 , 11.25)

Let us find the slope of the line by using the rule of it above

∵ (x_{1},y_{1}) = (10 , 15)

∵ (x_{2},y_{2}) = (12.5 , 11.25)

∴ m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}

Now we can write the equation

∵ The point-slope form is y-y_{1}=m(x-x_{1})

∵ m=-\frac{3}{2}

∵ (x_{1},y_{1}) = (10 , 15)

- Substitute these values in the form of the equation

∴ y - 15 = -\frac{3}{2} (x - 10)

The equation of the line in the point-slope form is y - 15 = -\frac{3}{2} (x - 10)

Learn more:

You can learn more about the linear equation in brainly.com/question/4152194

#LearnwithBrainly

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