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Jlenok [28]
3 years ago
6

Srinivasa Ramanujan, the great East Indian mathematician, was invited to Cambridge University in England in 1914 by the English

mathematician G. H. Hardy. One day Ramanujan was ill in the hospital, and Hardy came to visit him. Hardy remarked that he had come in taxicab #1729, and said that he thought that this was an entirely uninteresting number. Ramanujan instantly replied, "Oh no! 1,729 is the smallest number that can be written as the sum of two cubes in two different ways."
The table below shows two patterns of numbers. The pattern in the top row represents the counting numbers. The pattern in the second row consists of the cubes of the counting numbers.

Which two pairs of numbers have cubes that add up to 1,729? Because there are two pairs of numbers to find, you should select a total of four numbers from the list below.

A. 8
B. 7
C. 12
D. 11
E. 10
F. 9
G. 1
H. 2
I. 3
J. 4
K. 5
L. 6
Mathematics
2 answers:
ale4655 [162]3 years ago
6 0

Answer:

1,10,9,12 for APEX

Step-by-step explanation:


kotegsom [21]3 years ago
3 0
(12,1):12³+1³=1728+1=1729
(10,9): 10³+9³=1000+729=1729
☺☺☺☺
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OLga [1]

Answers:

  • 6. Slope = -5/3; y intercept = 5
  • 7. Slope = -1; y intercept = 2
  • 8. Slope = 3; y intercept = 0

The graphs are below

========================================================

Explanation:

6)

Let's solve for y to get the equation in slope intercept form y = mx+b

5x+3y = 15\\\\3y = -5x+15\\\\y = \frac{-5x+15}{3}\\\\y = \frac{-5x}{3}+\frac{15}{3}\\\\y = -\frac{5}{3}x+5\\\\

That last equation matches with y = mx+b to get

m = -5/3 = slope

b = 5 = y intercept

To graph this, we plot the y intercept at (0,5). Then move down 5 and to the right 3 to arrive at (3,0) as the second point. This movement is directly tied to the slope. We only need two points to graph a straight line.

---------------------------------

7)

The equation y = -x+2, aka y = -1x+2, is already in slope intercept form

m = -1 = slope

b = 2 = y intercept

Start at (0,2) which is the location of the y intercept. Move down 1 and to the right 1 due to the slope -1/1 = -1. This should move us to the point (1,1). Connect the two points (0,2) and (1,1) with a straight line to finish up the graph.

---------------------------------

8)

We start with the origin (0,0) because the y intercept of y = 3x is 0. It might help to think of y = 3x as y = 3x+0

Then we move up 3 units and to the right 1 unit to get to (1,3) as our next point. Connect the two points with a straight line

slope = 3

y intercept = 0

Once again, the graphs are shown below.

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