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2 years ago

Roberto scored 3 points in 2 soccer

Mathematics

1 answer:

wariber [46]2 years ago

4 0

Roberto scored 3 points in 2 soccer games. At this rate, how many points will he score in 10 games?

What we know

Roberto scored 3 points in 2 soccer games.

Roberto played 10 soccer games.

How to solve

If we know that Roberto scored 3 goals in 2 soccer games, we can find out how many goals he scored in 10 soccer games.

2 soccer games → 3 goals

4 soccer games → 6 goals

6 soccer games → 9 goals

8 soccer games → 12 goals

10 soccer games ⇒ 15 goals

Therefore, Roberto scored 15 goals in 10 soccer games.

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A right-angled triangle has shorter side lengths exactly c^2-b^2 and 2bc units respectively, where b and c are positive real num

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Answer: hypotenuse = $c^{2} + b^{2}$

Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side ( $s_{1},s_{2}$ ) of the right triangle, .i.e.:

$h^{2} = s_{1}^{2} + s_{2}^{2}$

In this question:

$s_{1}$ = $c^{2}-b^{2}$

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Substituing and taking square root to find hypotenuse:

$h=\sqrt{(c^{2}-b^{2})^{2}+(2bc)^{2}}$

Calculating:

$h=\sqrt{c^{4}+b^{4}-2b^{2}c^{2}+(4b^{2}c^{2})}$

$h=\sqrt{c^{4}+b^{4}+2b^{2}c^{2}}$

$c^{4}+b^{4}+2b^{2}c^{2}$ = $(c^{2}+b^{2})^{2}$ , then:

$h=\sqrt{(c^{2}+b^{2})^{2}}$

$h=(c^{2}+b^{2})$

Hypotenuse for the right-angled triangle is $h=(c^{2}+b^{2})$ units

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