What is the angle of p

Mathematics

2 answers:

cluponka [151]3 years ago

3 0

Answer:

Step-by-step explanation:

180-(180-130) -(180-110)

liubo4ka [24]3 years ago

3 0

Answer:

answer 60

Step-by-step explanation:

50+70+p=180

p=180-120

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xenn [34]

The equation $f(x)=g(x)$ is

$|x-4|-11=-\sqrt{5x}$

Some observations:

$\sqrt{5x}$ is defined only as long as $5x\ge0$ , or $x\ge0$
wherever $\sqrt{5x}$ is defined, its value must be non-negative, so that $-\sqrt{5x}$ is never positive
by the definition of absolute value, we have $|x-4|=x-4$ if $x\ge4$ , and $|x-4|=-(x-4)=4-x$ if $x$ . Then

$|x-4|-11=\begin{cases}x-15&\text{for }x\ge4\\-x-7&\text{for }x$

If $x$ , the equation becomes

$-x-7=-\sqrt{5x}\implies x+7=\sqrt{5x}$

Taking the square of both sides gives

$(x+7)^2=\left(\sqrt{5x}\right)^2\implies x^2+14x+49=5x\implies x^2+9x+49=0$

but since the discriminant is $9^2-4\cdot1\cdot49$ , there are no real solutions.

If $x\ge4$ , then

$x-15=-\sqrt{5x}$

Taking squares gives

$(x-15)^2=\left(-\sqrt{5x}\right)^2\implies x^2-30x+225=5x$

and solving by the quadratic formula gives two potential solutions,

$x=\dfrac{35\pm5\sqrt{13}}2$

which have approximate values of 8.49 and 26.51.

We know for any value of $x$ that $g(x)\le0$ . We have $f(8.49)\approx-6.51$ and $f(26.51)\approx11.51$ , so only the first solution 8.49 is valid.