The perfect cubes less than 1000 are:

1^3 = 1 
2^3 = 8 
3^3 = 27 
4^3 = 64 
5^3 = 125 
6^3 = 216 
7^3 = 343 
8^3 = 512 
9^3 = 729

so
2^3 = 8 could only be 1 + 1, but this is 2, not 8. 
3^3 = 27 could be 1 + 1, 1 + 8 or 8 + 8, but all of these are too small 
4^3 = 64 could be 1 + 1, 1 + 8, 1 + 27, 8 + 8, 8 + 27, 27 + 27.
 general proof that a^3 + b^3 = c^3 holds for no positive integers
hope it helps

6 0

3 years ago

Solve system with substitution

SpyIntel [72]

Answer:

The cost of 1 Rose Bush= $ 8

The cost of 1 Shrub = $12.

Step-by-step explanation:

The cost of 11 rose bushes and 4 shrubs = $136

The cost of 2 rose bushes and 11 shrubs = $148

Let the cost of one rose bush = $x

and the cost of one shrub = $ y

Now, according to the question:

11 x + 4 y = 136

and 2 x + 11 y = 148

From (1), we get that 11x = 136 - 4y

or, $x = \frac{136 - 4y}{11}$

Substitute this value of x in equation (2), we get

$2 x + 11 y = 148 \implies 2( \frac{136 - 4y}{11}) + 11y = 148$

or, $( \frac{272 - 8y}{11}) + 11y = 148 \implies 272 - 8y + 121y = 1628$

or, 113 y = 1356

or, y = 1356/113 = 12

⇒ y = 12, So $x = \frac{136 - 4y}{11} = \frac{136 -12(4)}{11} = \frac{136 - 48}{11} = 8$

or, x =8 and y = 12 is the solution of the above system.

Hence, the cost of 1 rose bush = $x = $8

and The cost of 1 shrub = $ y = $12.

4 0

3 years ago