Simplify ( √ 5 ) ( 3 √ 5 )

Mathematics

1 answer:

Amiraneli [1.4K]3 years ago

8 0

Answer:

$5^\frac{5}{6}$

Step-by-step explanation:

$\sqrt{5}$ can be represented as $5^{\frac{1}{2}}$ and $\sqrt[3]5}$ can be represented as $5^{\frac{1}{3}}$ . Therefore, the expression can be rewritten as:

$5^{\frac{1}{2}}*5^{\frac{1}{3}}$

The rule for multiplying two exponents with the same base is you add the exponents. For example: $x^m*x^k=x^{m+k}$

We can use the same property to get:

$5^{\frac{1}{2} +\frac{1}{3}}$

which is just $5^\frac{5}{6}$ after you add the fractions

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Which graph correctly solves the system of equations below? y = −x2 − 1 y = 2x2 − 4 (6 points)

myrzilka [38]

The equations are

$i) y=-x^2-1\\\\ii) y=2x^2-4$ ,

The graphs of the solutions (x, y) of these equations are 2 parabolas, since the right hand side expressions are polynomials of degree 2.

The solution/s of the system are the x-coordinates of the point/s of intersection of the parabolas.

The solutions of the first equation form a parabola looking downwards (since the coefficient of x^2 is -), and the second, a parabola opening upwards (since the coefficient of x^2 is +).

We can draw both parabolas, but to find the solution we still need to solve the system algebraically.

The algebraic solution of the system is:

$-x^2-1=2x^2-4\\\\3x^2-3=0\\\\3(x^2-1)=0\\\\x^2-1=0$ , so

the solutions are x=-1 and x=1.

The graph of the system is drawn using desmos.com

If we are allowed to use a graphic calculator, we can draw both graphs and point at the solution.