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2 years ago

Graph the two equations in the system; y = 2x + 1 y=-3x +6

Mathematics

2 answers:

WINSTONCH [101]2 years ago

7 0

Answer: Hope this helps?

Step-by-step explanation:

NeTakaya2 years ago

4 0

Answer:

Hello!

Step-by-step explanation:

The ordered pair answer is (1, 3) And I have attached a picture of the graph!

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Find all solutions of each equation on the interval 0 ≤ x < 2π.

Korvikt [17]

Answer:

$x = 0$ or $x = \pi$ .

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$ .

$\displaystyle \sec{x} = \frac{1}{\cos{x}}$ .

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, $\sin^{2}{x} = 1 - \cos^{2}{x}$ . Therefore, for the square of tangents,

$\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}$ .

This equation will thus become:

$\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2$ .

To simplify the calculations, replace all $\cos^{2}{x}$ with another variable. For example, let $u = \cos^{2}{x}$ . Keep in mind that $0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1$ .

$\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2$ .

$\displaystyle \frac{(1 - u) + u - u \cdot (1- u)}{u^{2}} = 2$ .

Solve this equation for $u$ :

$\displaystyle \frac{u^{2} + 1}{u^{2}} = 2$ .

$u^{2} + 1 = 2 u^{2}$ .

$u^{2} = 1$ .

Given that $0 \le u \le 1$ , $u = 1$ is the only possible solution.

$\cos^{2}{x} = 1$ ,

$x = k \pi$ , where $k\in \mathbb{Z}$ (i.e., $k$ is an integer.)

Given that $0 \le x < 2\pi$ ,

$0 \le k$ .

$k = 0$ or $k = 1$ . Accordingly,

$x = 0$ or $x = \pi$ .

8 0

3 years ago

Read 2 more answers

Give the center and radius of the circle. (x - 5)2 + y2 = 16

olasank [31]

Answer:

Centre: (5,0)

Radius: 4

Step-by-step explanation:

r² = 16

r = 4

7 0

3 years ago

Can someone help please, will give brainiest if correct!!!!

Bond [772]

Answer:

AB = 9/2 cm

AB = 4.5 cm

Step-by-step explanation:

The area of small rectangle

x * (x-4) = x^2 -4x

The area of the big rectangle

The height is 2x +x and the width is x-2

(2x+x) * (x-2)

(3x) * (x-2)

3x^2 -6x

Add the areas together

x^2 -4x + 3x^2 -6x

4x^2 -10x

This is equal to 36

4x^2 -10x=36

Subtract 36 from each side

4x^2 -10x -36=36-36

4x^2 -10x-36=0

Divide each side by 2

2x^2 -5x -18=0

Factor

(x + 2) (2 x - 9) = 0

Using the zero product property

x+2=0 2x-9=0

x = -2 2x =9

x = -2 x = 9/2

Since we cant have a negative length

x = 9/2

AB = 9/2 cm

5 0

3 years ago

Read 2 more answers

A phone company charges a flat rate of $15 to make phone calls for a month.they charge $0.10 per minute for each call made.if th

Ne4ueva [31]

Answer:

450 minutes

Step-by-step explanation:

15 + 0.1x = 60

15 - 15 + 0.1x = 60 - 15

0.1x = 45

$\frac{0.1x}{0.1} = \frac{45}{0.1}$

x = 450

5 0

3 years ago

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Determine the area and perimeter or circumference of the following figures. What do A and p =

pogonyaev

The perimeter is 34 cm

The area is 48 cm ²

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I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

8 0

3 years ago

Read 2 more answers

Graph the two equations in the system; y = 2x + 1 y=-3x +6​

Graph the two equations in the system; y = 2x + 1 y=-3x +6