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a_sh-v [17]
3 years ago
8

Jaime knows that 30² is 900. He wonders if knowing that 30² can help him finds 29x31. Raquel knows what 25² equals. How can she

use the knowledge to find 24x26?
Mathematics
1 answer:
iragen [17]3 years ago
3 0

9514 1404 393

Answer:

  Jaime: yes: 29·31 = 900 -1 = 899

  Raquel: 24·26 = 25^2 -1 = 624

Step-by-step explanation:

The difference of squares factors as the product of the sum and difference of the roots:

  a^2 -b^2 = (a -b)(a +b)

<u>Jaime</u>

  29·31 = (30 -1)(30 +1) = 30^2 -1^2 = 900 -1 = 899

  Jaime can subtract 1 from 30^2 to find 29·31

__

<u>Raquel</u>

  24·26 = (25 -1)(25 +1) = 25^2 -1^2 = 625 -1 = 624

  Raquel can subtract 1^2 from 25^2 to find 24·26.

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What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
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shape is rectangle which means the 2 long sides have equal distance and the 2 short sides have equal distance
we just need to find the distance of one long side and one short side for the perimeter which is the outline of the rectangle. Imagine the perimeter is the fence around the rectangle  that you would probably have to paint every 3 years and the area would be where the grass would grow in the rectangle which you would probably have to cut every weekend.

perimeter=2l+2w
 
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Using pythagorean method a² +b²=h² to find length:
From point (-6,1) to point (3,8) is a rise of 9 and a run of 9 right to get from one point to another, those are my a and b in the pythagorean formula.
a² +b²=h²
(9)²+(9)²=h²         substitution
81+81=h²            simplified
162=h²
√162=√h2           used radical properties
√162=h               length =√162

Using pythagorean method a² +b²=h² to find width:
From points (-6,-1) to point (-3,-4) is a down 3 units and left 3 units to reach from one point to another, these are my a and b for the pythagorean formula.

a² +b²=h²
(3)²+(3)²=h²
9+9=h²
18=h²
√18=√h²
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Now we find perimeter:
p=2l+2w
p=2(√162)+2(√18)
p≈33.9

D. 33.9 units

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