1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Arte-miy333 [17]
2 years ago
7

Write an expression to represent the total cost of paint at a rate of $5.75 per ft.? to paint a triangular-shaped mural where th

e base of the triangle is 22 feet longer than the height
Mathematics
1 answer:
ASHA 777 [7]2 years ago
7 0

Answer:

C($)= (x²/2 +11x)5.75

Step-by-step explanation:

Let's assume the height= x

The base= x+22

Area= 1/2(base*height).

Area= 1/2((x+22)(x))

Area= x²/2 +11x

Cost per ft= $5.75

Cost for painting the triangular mural C

C($)= (x²/2 +11x)5.75

You might be interested in
Question (c)! How do I know that t^5-10t^3+5t=0?<br> Thanks!
astra-53 [7]
(a) By DeMoivre's theorem, we have

(\cos\theta+i\sin\theta)^5=\cos5\theta+i\sin5\theta

On the LHS, expanding yields

\cos^5\theta+5i\cos^4\theta\sin\theta-10\cos^3\theta\sin^2\theta-10i\cos^2\theta\sin^3\theta+5\cos\theta\sin^4\theta+i\sin^4\theta

Matching up real and imaginary parts, we have for (i) and (ii),


\cos5\theta=\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta
\sin5\theta=5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta

(b) By the definition of the tangent function,

\tan5\theta=\dfrac{\sin5\theta}{\cos5\theta}
=\dfrac{5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta}{\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta}

=\dfrac{5\tan\theta-10\tan^3\theta+\tan^5\theta}{1-10\tan^2\theta+5\tan^4\theta}
=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}


(c) Setting \theta=\dfrac\pi5, we have t=\tan\dfrac\pi5 and \tan5\left(\dfrac\pi5\right)=\tan\pi=0. So

0=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}

At the given value of t, the denominator is a non-zero number, so only the numerator can contribute to this reducing to 0.


0=t^5-10t^3+5t\implies0=t^4-10t^2+5

Remember, this is saying that

0=\tan^4\dfrac\pi5-10\tan^2\dfrac\pi5+5

If we replace \tan^2\dfrac\pi5 with a variable x, then the above means \tan^2\dfrac\pi5 is a root to the quadratic equation,

x^2-10x+5=0

Also, if \theta=\dfrac{2\pi}5, then t=\tan\dfrac{2\pi}5 and \tan5\left(\dfrac{2\pi}5\right)=\tan2\pi=0. So by a similar argument as above, we deduce that \tan^2\dfrac{2\pi}5 is also a root to the quadratic equation above.

(d) We know both roots to the quadratic above. The fundamental theorem of algebra lets us write

x^2-10x+5=\left(x-\tan^2\dfrac\pi5\right)\left(x-\tan^2\dfrac{2\pi}5\right)

Expand the RHS and match up terms of the same power. In particular, the constant terms satisfy

5=\tan^2\dfrac\pi5\tan^2\dfrac{2\pi}5\implies\tan\dfrac\pi5\tan\dfrac{2\pi}5=\pm\sqrt5

But \tanx>0 for all 0, as is the case for x=\dfrac\pi5 and x=\dfrac{2\pi}5, so we choose the positive root.
3 0
3 years ago
NEEED HELP FROM BRAINLIEST??????
Leno4ka [110]

Answer:

A

Step-by-step explanation:

5 0
3 years ago
9. What is the solution to this equation? 2x + 10 = 28 help​
abruzzese [7]

Answer: x=9

Step-by-step explanation:

2x+10=28

2x=18

x=9

5 0
2 years ago
Read 2 more answers
What is the circumference of the circle in terms of pi? The radius is 2.2
klemol [59]
We will use formula for circumference of circle:
lets name it as O

O = 2*r * pi

when we express r in this formula we get:

O = 2*2.2*pi
O = 4.4*pi

From this we can see that for given radius, answer is 4.4. The formula only depends on pi and that is what "in terms of pi" means.
6 0
3 years ago
Read 2 more answers
Alex, Toby and Samuel are playing a game together.
Shalnov [3]

Answer:

1/9

Step-by-step explanation:

There are three places and three people.

Times them together for the total outcomes:

1/3 x 1/3= 1/9

8 0
3 years ago
Other questions:
  • How do I write 20,484,163 in expanded form
    10·2 answers
  • The coefficient of the second term in the expansion of the binomial (4x+3y) to the 3rd power
    12·1 answer
  • Help me please and give the right answer
    11·2 answers
  • Which system of inequalities is represented by the graph?
    13·2 answers
  • Every day, Katie looks for seashells on the beach. She has 28 shells in her collection. Katie finds 12 more shells each day. Wri
    13·1 answer
  • There are four students and a lecturer for a photography session. Determine the number of ways the people can be arranged such t
    9·1 answer
  • Please Help! <br> I will give Brainliest!!<br>HELP ANYONE!!!
    5·1 answer
  • The point of ____ makes both equations true?
    11·1 answer
  • What is a solution to (x + 6)(x + 2) = 60?<br><br> x = −6<br> x = −4<br> x = 4<br> x = 12
    7·2 answers
  • What is the solution to the following equation?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!