All categories

2 years ago

What is the measure of P?

Mathematics

1 answer:

vesna_86 [32]2 years ago

4 0

Answer:

∠P = 111°

Step-by-step explanation:

∠P = 84 + 27

= 111

You might be interested in

General solutions of sin(x-90)+cos(x+270)=-1<br> {both 90 and 270 are in degrees}

mixer [17]

Answer:

$\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

Step-by-step explanation:

Given:

$\sin (x-90^{\circ})+\cos(x+270^{\circ})=-1$

First, note that

$\sin (x-90^{\circ})=-\cos x\\ \\\cos(x+270^{\circ})=\sin x$

So, the equation is

$-\cos x+\sin x= -1$

Multiply this equation by $\frac{\sqrt{2}}{2}:$

$-\dfrac{\sqrt{2}}{2}\cos x+\dfrac{\sqrt{2}}{2}\sin x= -\dfrac{\sqrt{2}}{2}\\ \\\dfrac{\sqrt{2}}{2}\cos x-\dfrac{\sqrt{2}}{2}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos 45^{\circ}\cos x-\sin 45^{\circ}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos (x+45^{\circ})=\dfrac{\sqrt{2}}{2}$

The general solution is

$x+45^{\circ}=\pm \arccos \left(\dfrac{\sqrt{2}}{2}\right)+2\pi k,\ \ k\in Z\\ \\x+\dfrac{\pi }{4}=\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{4}\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

4 0

3 years ago

What is the positive solution to the equation 0=⅓x²-3

sammy [17]

Add 3, multiply by 3, and take the positive square root.
3 = (1/3)x²
9 = x²
√9 = 3 = x

The positive solution to the equation is x = 3.

7 0

3 years ago

If Nembutal is used to anesthetize rabbits at a dosage of .09 mg/g of body weight, and the concentration of the solution is 60 m

Vitek1552 [10]

Answer:

2.72 ml

Step-by-step explanation:

4 lb = 1814.37 gm

1814.37 gm * .09 mg/gm / ( 60 mg/ml) = 2.72 ml

3 0

2 years ago

Sarah had a bag of 16 marbles that are green and yellow. The number of yellow marbles is 2 less than double the number of green

Alex777 [14]

Answer:

10 yellow marbles

Step-by-step explanation:

(y is the amount of yellow marbles)

y=2x-2

y=2(6)-2

y=12-2

y=10

8 0

3 years ago

Read 2 more answers

Graph the function. Upload a handwritten copy of your graph as your final answer.

Serhud [2]

The function is divided in 2 parts:

For x<0, the function is $y=x$ , which is a linear function, and its graph is a line.

For x≥0, the function is $y=-x^2$ , which is a quadratic function, and its graph is a parabola.

Note that y=x is the line containing the points (0, 0), (1, 1), (5, 5) etc, that is, it is the line passing through the origin, with an inclination of 45° with the positive x-axis.

The parabola $y=-x^2$ is the parabola $y=x^2$ reflected with respect to the x-axis. It contains points like (0, 0), (-1, 1), (2, -4) etc...

The 2 graphs, with domain all real numbers, are shown in the first picture.

The second picture is the graph of the function described in our problem. We use the first picture, but restrict the domains.

That is, we delete the part of the line corresponding to x≥0, and the part of the parabola corresponding to x<0.

7 0

3 years ago