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
Nadusha1986 [10]
3 years ago
8

Using the quadratic formula to solve x^2=5-x what are the values of x?

Mathematics
2 answers:
kenny6666 [7]3 years ago
3 0
A
you have to solve x^2+x-5=0
So x=(-1 +/- sqrt(1^2+4*1*5))/2
x=(-1 +/- sqrt(21))/2
Law Incorporation [45]3 years ago
3 0

Answer:

Option a - x=\frac{-1\pm\sqrt{21}}{2}

Step-by-step explanation:

Given : Expression x^2=5-x

To find : What are the values of x?

Solution :

The quadratic formula of the quadratic equation ax^2+bx+c=0 is

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Comparing with general equation, x^2+x-5=0

where, a=1 ,b=1, c=-5

Substitute in the formula,

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\frac{-1\pm\sqrt{1^2-4(1)(-5)}}{2(1)}

x=\frac{-1\pm\sqrt{1+20}}{2}

x=\frac{-1\pm\sqrt{21}}{2}

Therefore, The value of x is x=\frac{-1\pm\sqrt{21}}{2}

So, Option a is correct.

You might be interested in
a model rocket is launched from the ground with an initial velocity of 60 feet per second. the function g(t)= -16t^2 + 60t repre
Lemur [1.5K]
If we use our trusty ti's this will be a breeze
domain is the numbers we can use
obviously we can't have negative time so therefor the domain is all positive integers (0,1,2,2.3, 3/2,3,pi...) 

zeroes is when you set absolute max using ti is
remember vertex form which is
max height of something in
ax^2+bx+c form is -b/2a
-16t^2+60t+0
a=-16
b=60
-60/(2 times -16)
-60/-32=30/16=15/8=1 and 7/8 so subsitute for t
g(15/8)=-16(15/8)^2+60(15/8)=225/4=56.25=max height


zeroes is when the equation equals 0
so set it to zero
0=-16t^2+60t
factor
0=(-4t)(4x-15)
set each to zero
-4x=0
x=0
4x-15=0
add 15
4x=15
divid 4
x=15/4
so the zeros are t=0 and t=15/4

domain is all the nuumbers that can be used logically for time
logically, we cannot have negative time, so all real positive
[0,∞)
(that means from 0 to infinity includng 0 so 0<span><</span>t<∞))


range is the output
output=height
we find the min height and max height
min=0
max=56.25
so range=0 to 56.25 or
[0,56.25]






max height=56.25 ft (15/8 seconds)
zeroes=0 sec and 15/4 sec
domain=all real positive numbers including zero or [0, ∞)
range=[0,56.25]
3 0
3 years ago
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
Help asap!!!!!!!!!! Thank u
Tema [17]

Answer:

The answer is: m\angle 5=34^\circ

Step-by-step explanation:

angles 1 and 5 are equal to each other since a\parallel b

so m\angle 5=m\angle 1=34^\circ

7 0
3 years ago
What is the slope of the line that passes through (-2, 5) and (3, 9)?
Naya [18.7K]

Answer: 4/5

Step-by-step explanation:

1. you need to know the formula which is m = y2-y1/x2-x1

2. you plug in the numbers which would be 9-5/3-(-2)

3. you get your answer as 4/5

4. the answer is 4/5

3 0
3 years ago
Read 2 more answers
How do you us the distributive property to work out (4+5)6
777dan777 [17]
During Distributive property, the number on the outside of the parenthesis basically gets multiplied by the numbers inside the parenthesis. In this case, you would multiply 6 by 5 and 4. When you get the products, then follow the sign that comes next. In this case, you would add the products to get a total sum. I attached a photo for further reference.
Hope this helps!

7 0
3 years ago
Read 2 more answers
Other questions:
  • Factor completely<br> 2n^2+ 5n + 2
    11·1 answer
  • If sin (x+20°)=cos x. Find the value of x.
    6·1 answer
  • Which of the following statements are true for using proportions to solve for missing measures? Select three options.
    15·2 answers
  • If 1 yard = 3 feet and 1 mile = 5,280 feet, how many yards are there in 4 miles?
    15·1 answer
  • Who is a Florida gators football fan​
    7·2 answers
  • Hey I really need your help
    10·1 answer
  • Oscar bought 15 gallons of water at $1.98 per gallon. He wants to divide this water in bottles of 1/8 gallon each. What is the c
    12·1 answer
  • Which expression is equivalent to (x+2)(3x-3)?
    9·1 answer
  • ogether Brianna and Hushley saved $336 for their trip to France. Hushley saved $120 more than Brianna. How much money did Briann
    11·1 answer
  • Determine if the following ration form proportion <br>a)20cm:1m and 10cm:100cm​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!