Determine the number of solutions that exist to the equation below. 8(j - 4) = 2(4j - 16)

Mathematics

1 answer:

pishuonlain [190]3 years ago

5 0

There are infinitely many solutions

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The diameter of a circle is 6 in. Find its area to the nearest tenth.

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Answer and Step-by-step explanation:

The area formula for a Circle is:

A = $\pi r^2$

Diameter is equal to the radius times 2.

So, divide the diameter to get the radius.

6 divided by 2 equals 3.

Now, plug it into the formula.

$A = \pi (3)^{2}$

A = $9\pi$

Plug this into your calculator by multiplying 9 by pi.

We get the answer to be 28.3 when rounded to the nearest tenth.

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3 years ago

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= 2. Given the quadratic equation 3x2 – 8x + k = 0 has no real roots. Find the range of values of k.

VashaNatasha [74]

$\text{If there are no real roots, then}\\\\~~~~~\text{Discriminant} < 0\\\\\implies b^2 -4ac < 0\\\\\implies (-8)^2 -4 \cdot 3 k < 0\\\\\implies 64-12k < 0\\\\\ \implies 12k > 64\\\\\implies k > \dfrac{64}{12}\\\\\implies k > \dfrac{16}3\\\\\text{Interval,}~ \left( \dfrac{16}3, ~\infty\right)$