Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Mathematics

1 answer:

BabaBlast [244]2 years ago

3 0

Answer:

Step-by-step explanation:

We want to solve the equation:

$x^2+2x+7=0$

Using the quadratic formula. The quadratic formula is given by:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 1, b = 2, and c = 7.

Substitute:

$\displaystyle x=\frac{-(2)\pm\sqrt{(2)^2-4(1)(7)}}{2(1)}$

Evaluate:

$\displaystyle x=\frac{-2\pm\sqrt{-24}}{2}$

Simplify the square root:

$\sqrt{-24}=\sqrt{4\cdot 6\cdot -1}=\sqrt{4}\cdot\sqrt{6}\cdot\sqrt{-1}=2i\sqrt{6}$

Hence:

$\displaystyle x=\frac{-2\pm2i\sqrt{6}}{2}$

Simplify:

$\displaystyle x=-1\pm i\sqrt{6}$

Hence, our solutions are:

$\displaystyle x=\left\{-1+i\sqrt{6}, -1-i\sqrt{6}\right\}$

Our answer is C.

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Hello I need help Finding the probability

Stolb23 [73]

Each petal of the region $R$ is the intersection of two circles, both of diameter 10. Each petal in turn is twice the area of a circular segment bounded by a chord of length $5\sqrt2$ , which implies the segment is subtended by an angle of $\dfrac\pi2$ . This means the area of the segment is

$\text{area}_{\text{segment}}=\text{area}_{\text{sector}}-\text{area}_{\text{triangle}}$
$\text{area}_{\text{segment}}=\dfrac{25\pi}4-\dfrac{25}2$

This means the area of one petal is $\dfrac{25\pi}2-25$ , and the area of $R$ is four times this, or $50\pi-100$ .

Meanwhile, the area of $G$ is simply the area of the square minus the area of $R$ , or $10^2-(50\pi-100)=200-50\pi$ .

So

$\mathbb P(X=R)=\dfrac{50\pi-100}{100}=\dfrac\pi2-1$
$\mathbb P(X=G)=\dfrac{200-50\pi}{100}=2-\dfrac\pi2$
$\mathbb P((X=R)\land(X=G))=0$ (provided these regions are indeed disjoint; it's hard to tell from the picture)
$\mathbb P((X=R)\lor(X=G))=\mathbb P(X=R)+\mathbb P(X=G)=1$