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2 years ago

13

Hannah and Anthony are siblings who have ages that are consecutive odd integers . The sum of their ages is 92 . Which equations

can be used to d=find Hannah's age, h,if she is the older sibling?

1 answer:

Sliva [168]2 years ago

4 0

Is there any options to pick out of?

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Find the area of a triangle with legs that are 9mm 6mm and 12mm

Sidana [21]

Here we are given the three sides of the triangle.

So we have Heron's formula to find its area.

Heron's formula is given by :

$A= \sqrt{S(S-A)(S-B)(S-C)}$

where A, B and C are sides of triangle and S is semi perimeter which is given by,

$S= \frac{A+B+C}{2}$

plugging values of A, B and C to find S

$S= \frac{9+6+12}{2}$

S=13.5

Now plugging values of A, B , C and S in Heron's formula

$A= \sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}$

A=26.14 mm²

Answer: Area of triangle is 26.14 mm².

6 0

2 years ago

What is the range of f(x)=(3/4)^x - 4 a.{y|y > -4} b.{y|y>3/4} c.{y|y<- 4} d.{y|y/4}

Vanyuwa [196]

3/4 *x-4
3/4 x 3/4 x 3/4 x 3/4
3 13/81

8 0

2 years ago

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:

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

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

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

42. The diagram represents a ramp in the shape of a right triangle and the lengths

oee [108]

The length of the ramp is 61 feet.

<h3>What is the length of the ramp?</h3>

In order to determine the length of the ramp, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

√11² + 60²

√121 + 3600

√3721

= 61 feet

Please find attached the image of the ramp. To learn more about Pythagoras theorem, please check: brainly.com/question/14580675

5 0

2 years ago

Evaluate the function f(x)=3x-7if x=6

notka56 [123]

Answer:

if x=6, then f(6)=11

8 0

3 years ago

Read 2 more answers