What is the value of x? [Art not to scale.] Ox=23 Ox=35 Ox=58 Ox=93

General solutions of sin(x-90)+cos(x+270)=-1 {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

Which ordered pair is a solution to the equation y=5x-25?

Trava [24]

Answer:

I'm not sure but i think it is D

7 0

3 years ago

20 POINTS

Nesterboy [21]

Answer:

7.5 meters

Step-by-step explanation:

As with many quadrilaterals, pairs of sides have the same length, so the perimeter is twice the sum of two of the sides.

In a kite, generally, opposite sides have different lengths, so the perimeter is twice the sum of the lengths of opposite sides. That is

51 m = 2(18m + side opposite)

15 m = 2 × (side opposite)

7.5 m = side opposite

_____

Comment on side lengths

In a rectangle or parallelogram, the perimeter is twice the sum of adjacent sides. A kite is different in that adjacent sides may be the same length. If the kite is not a rhombus, opposite sides are always different lengths.

4 0

3 years ago

I need help helphelphelp helphelphelp helphelphelp

Brut [27]

Answer:

234 in^2

Step-by-step explanation:

*look at the pick* 6+60+168=234

7 0

3 years ago

Solve by factoring and list only the positive solution: 2x2 - 5x = 88

Semmy [17]

It has to be noted that there are several ways to factor the item. One of these is shown below.

The general form of a quadratic equation is,
Ax² + Bx + C = 0

where A and B are numerical coefficients and C is the constant. If we are to express the given equation in this form,
2x² - 5x - 88 = 0

The sum of the roots, x₁ and x₂ is -B/A and the product is equal to C/A.

Sum: x₁ + x₂ = -(-5/2) = 5/2
Product: x₁x₂ = -88/2 = -44

The values of x₁ and x₂ are 8 and -11/2.

The factors are (x - 8) and (x + 11/2)

ANSWERS: 8 and -11/2. 

8 0

3 years ago