Is 5, 12, 14 a pythagorean triple ? Show why or why not?
2 answers:
Answer:
No
Step-by-step explanation:
Let's test these values using the Pythagorean Theorem.
a^2+b^2=c^2
where a and b are the legs and c is the hypotenuse.
a and b are the legs, or the shorter sides. 5 and 12 are the shorter sides, so they are a and b.
c is the hypotenuse, or the longest side. 14 is the longest side, so it is c.
5^2+12^2=14^2
Evaluate all the exponents
25+144=196
Add 25 and 144
169=196
169196
169 is not equal to 196, so 5, 12 and 14 cannot be a Pythagorean Triple
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The shop sold 36 sundaes and 28 banana spilts
<em><u>Solution:</u></em>
Let "a" be the number of sundaes sold
Let "b" be the number of banana spilts sold
Cost of 1 sundaes = $ 2
Cost of 1 banana spilt = $ 3
<em><u>On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156</u></em>
Therefore,
Number of sundaes sold = 8 + number of banana spilts sold
a = 8 + b ------- eqn 1
<em><u>Also, given that they made $ 156</u></em>
<em><u>Therefore, we frame a equation as</u></em>:
Number of sundaes sold x Cost of 1 sundaes + number of banana spilts sold x Cost of 1 banana spilt = 156
2a + 3b = 156 ---------- eqn 2
<em><u>Substitute eqn 1 into eqn 2</u></em>
2(8 + b) + 3b = 156
16 + 2b + 3b = 156
16 + 5b = 156
5b = 156 - 16
5b = 140
<h3>b = 28</h3><em><u>Substitute b = 28 in eqn 1</u></em>
a = 8 + 28
<h3>a = 36</h3>Thus the shop sold 36 sundaes and 28 banana spilts
The slope is 2
y=2x + b
Plug in a point to solve for b
8 = 2(3) + b
8 = 6 + b
b = 2
The equation is y = 2x + 2