Give the sum of 1/2 and 8/12 in simplest form

The figure in the picture is made up of 5 congruent squares. If the perimeter of the entire figure is 21.6 cm, find its area.

vovikov84 [41]

Perimeter is length plus width so use that to help you

3 0

3 years ago

Solve y=x+5 and 2x-3y=4

stepan [7]

Answer:

x= -19

y= -14

Step-by-step explanation:

Substitution.

It tells you what y is already. You substitute that into the second equation and then solve. Then you use that answer and substitute it back into the first equation's x, and then you'll get your full answer.

Hope this helps <3

4 0

1 year ago

Read 2 more answers

I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).

Aleksandr-060686 [28]

Answer:

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

Step-by-step explanation:

$\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$

Let's first isolate the trig function.

Add 1 one on both sides:

$\sqrt{3} \tan(x-\frac{\pi}{8})=1$

Divide both sides by $\sqrt{3}$ :

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

Now recall $\tan(u)=\frac{\sin(u)}{\cos(u)}$ .

$\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

or

$\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}$

The first ratio I have can be found using $\frac{\pi}{6}$ in the first rotation of the unit circle.

The second ratio I have can be found using $\frac{7\pi}{6}$ you can see this is on the same line as the $\frac{\pi}{6}$ so you could write $\frac{7\pi}{6}$ as $\frac{\pi}{6}+\pi$ .

So this means the following:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

is true when $x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

where $n$ is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

$x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

Add $\frac{\pi}{8}$ on both sides:

$x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi$

Find common denominator between the first two terms on the right.

That is 24.

$x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi$

$x=\frac{7\pi}{24}+n \pi$ (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval $[0,2\pi)$ .

So if $\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$ and we let $u=x-\frac{\pi}{8}$ , then solving for $x$ gives us:

$u+\frac{\pi}{8}=x$ ( I just added $\frac{\pi}{8}$ on both sides.)

So recall $0\le x$ .

Then $0 \le u+\frac{\pi}{8}$ .

Subtract $\frac{\pi}{8}$ on both sides:

$-\frac{\pi}{8}\le u$

Simplify:

$-\frac{\pi}{8}\le u$

So we want to find solutions to:

$\tan(u)=\frac{1}{\sqrt{3}}$ with the condition:

$-\frac{\pi}{8}\le u$

That's just at $\frac{\pi}{6}$ and $\frac{7\pi}{6}$

So now adding $\frac{\pi}{8}$ to both gives us the solutions to:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$ in the interval:

$0\le x$ .

The solutions we are looking for are:

$\frac{\pi}{6}+\frac{\pi}{8}$ and $\frac{7\pi}{6}+\frac{\pi}{8}$

Let's simplifying:

$(\frac{1}{6}+\frac{1}{8})\pi$ and $(\frac{7}{6}+\frac{1}{8})\pi$

$\frac{7}{24}\pi$ and $\frac{31}{24}\pi$

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

5 0

3 years ago

For all values of x,

Nana76 [90]

Answer:

For f(x) = 2x + 3 and g(x) = -x 2 + 1, find the composite function defined by (f o g)(x)

(f o g)(x) = f(g(x))

= 2 (g(x)) + 3

= 2( -x 2 + 1 ) + 3

= - 2 x 2 + 5 Given f(2) = 3, g(3) = 2, f(3) = 4 and g(2) = 5, evaluate (f o g)(3)

Step-by-step explanation:

6 0

2 years ago

In his first year, a math teacher earned $32,000. Each successive year, he

Ivan

Answer:

Step-by-step explanation:

Each successive year, he

earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence(amount earned in the first year).

r represents the common ratio.

n represents the number of terms(years).

From the information given,

a = $32,000

r = 1 + 5/100 = 1.05

n = 20 years

The amount earned in his 20th year, T20 is

T20 = 32000 × 1.05^(20 - 1)

T20 = 32000 × 1.05^(19)

T20 = $80862.4

To determine the his total

earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as

Sn = (ar^n - 1)/(r - 1)

Therefore, the sum of the first 20 terms, S20 is

S20 = (32000 × 1.05^(20) - 1)/1.05 - 1

S20 = (32000 × 1.653)/0.05

S20 = $1057920

3 0

3 years ago