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2 years ago

Write the equation in general form of a line with a slope of 1 and a y-intercept of -1

Mathematics

1 answer:

UkoKoshka [18]2 years ago

8 0

Start with the facts that m = 1 and b = -1:

y = 1x - 1, or simply y = x - 1. This is the simplest possible equation for this straight line.

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There are 24 students on the math team. If the probability of a new student being drawn at random is 1/3, then how many of the s

andreev551 [17]

Answer:

Step-by-step explanation:

24/3 =8

8=1/3

6 0

3 years ago

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Lines and triangles practices

Marianna [84]

<1 = 123
60 + 63 = 123
180 - 123 = 57
180 n- 57 = 123

Triangle angle-sum theorem
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4 0

3 years ago

The book store is having a sale. Every book is $5 off, regardless of the original price.

jarptica [38.1K]

Answer:

y=x-5

Step-by-step explanation:

sale price (y) is equal to the original (x) minus five dollars

5 0

2 years ago

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4sin²<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D" id="TexFormula1" title="\frac{x}{2}" alt="\frac{x}{2}" align="absm

raketka [301]

Answer:

$\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}$

Step-by-step explanation:

Hi there!

We want to solve for $x$ in:

$4\sin^2(\frac{x}{2})=3$

Since $x$ is in the argument of $\sin^2$ , let's first isolate $\sin^2$ by dividing both sides by 4:

$\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}$

Next, recall that $\sin^2x$ is just shorthand notation for $(\sin x)^2$ . Therefore, take the square root of both sides:

$\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}$

Simplify using $\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ :

$\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}$

Let $\phi = \frac{x}{2}$ .

<h3><u>Case 1 (positive root):</u></h3>

$\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}$

Therefore, we have:

$\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

<h3><u>Case 2 (negative root):</u></h3>

$\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

8 0

2 years ago

Find the area of the triangle ABC given angle A = 60°, b = 2, and c = √2.

Irina18 [472]

<span>If you know 2 sides and an included angle, the area formula is:
</span>
<span>Area = ½ • side 1 • sine (A) • side 2
</span>
<span>Area = ½ • 2 * sine (60) * sq root (2)
</span>
<span>Area =sine (60) * sq root (2)
</span>
<span>The sine of 60 degrees = sq root (3) / 2
</span>
Area = sq root (6) / 2

7 0

3 years ago

Read 2 more answers