All categories

3 years ago

Work out the value of 1. 7/2 -a ² 2. 3x-8 = 19

Mathematics

2 answers:

Zanzabum3 years ago

8 0

Answer:

1. -45 1/2.

2. x = 9.

Step-by-step explanation:

a/b - a^b when a = 7 and b = 2

= 7/2 - 7^2

= 7/2 - 49

= -91/2

= -45 1/2.

3x - 8 = 19

3x = 19 + 8 = 27

x = 9.

ratelena [41]3 years ago

3 0

Yes it is very easy, but

You might be interested in

Find the sum of the two matrices: 17 12 −3 −2 + −4 −1 8 14 = w x y z w = x = y = z =

klasskru [66]

Answer:

w =

x =

y =

z =

6 0

3 years ago

There are 12 football teams in a competition. The lions have a probability of 1/12 of winning the competition. How is this true?

MaRussiya [10]

Asuming that all the teams have the same skill levels the game will mostly be chance. The chance of winning will be 1/12 because they are 1 out of 12 teams.

7 0

3 years ago

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

What is the radius and diameter of the circle 14

gizmo_the_mogwai [7]

Answer:

it is

D=14

R=7

Step-by-step explanation:

sorry if it is incorrect

3 0

3 years ago

What’s the slope of y=4x+5

victus00 [196]

Answer:

Step-by-step explanation:

The slope is 4 because in the y=mx+b format m is always the slope while b is your initial value or starting point

3 0

3 years ago