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Sveta_85 [38]
3 years ago
13

One side of a right triangle is 8 cm shorter than the hypotenuse and 7 cm shorter than the third side. Find the lengths of the s

ides of the triangle.
Mathematics
1 answer:
Reptile [31]3 years ago
7 0

Answer:

5 cm

Step-by-step explanation:

Let the shorter side be a, longer side be b, hypotenuse be c

By Pythagorean theorem:

a² + b² = c²

a² + (a + 7)² = (a + 8)²

a² + a² + 14a + 49 = a² + 16a + 64

a² - 2a - 15 = 0

a² + 3a - 5a - 15 = 0

a(a + 3) - 5(a + 3) = 0

(a + 3)(a - 5) = 0

a = -3 or a = 5

Because a is a side length and is a positive number

a = 5

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For numbers to be divisible by 2 they must end in an even number

For numbers to be divisible by 9 the sum of the digits must be divisible by 9

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Find the vector projection of B onto A if A = 5i + 11j – 2k,B = 4i + 7k​
valkas [14]

Answer:

\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\

Step-by-step explanation:

Given A = 5i + 11j – 2k and B = 4i + 7k​, the vector projection of B unto a is expressed as proj_ab = \dfrac{b.a}{||a||^2} * a

b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)

note that i.i = j.j = k.k  =1

b.a = 5(4)+11(0)-2(7)

b.a = 20-14

b.a = 6

||a|| = √5²+11²+(-2)²

||a|| = √25+121+4

||a|| = √130

square both sides

||a||² = (√130)

||a||²  = 130

proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\

<em>Hence the projection of b unto a is expressed as </em>\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\<em></em>

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3 years ago
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3 years ago
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Anni [7]

Answer:

5.8% or 6%

Step-by-step explanation:

6 face cards in a deck minus the red ones so it would be [6-3=3]

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Then to get your percentage it would be [0.0576 x 100=5.76%]

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3 years ago
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