Could someplease explain the whole problem? For the first part my the answer I got was x= .618, -.618, and [tex]\frac{\sqrt[1+-]{5} }{2}[/tex]
Answers
9514 1404 393
Answer:
a) x = (√5 -1)/2 ≈ 0.618034
b) 1/x = (√5 +1)/2 ≈ 1.618034
Step-by-step explanation:
Given:
x/(1 -x) = 1/x
Find:
Exactly, and as a decimal approximation, ...
a) x, using the quadratic formula
b) 1/x
Solution:
a) We can multiply the given equation by x(1 -x) to obtain ...
x² = 1 -x
x² +x -1 = 0 . . . . . . add x-1
The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{-1\pm\sqrt{5}}{2}[/tex]
We are only interested in the positive solution, which is ...
[tex]\boxed{x=\dfrac{\sqrt{5}-1}{2}\approx0.618034}[/tex]
__
b) The quadratic we developed in the first part can be rearranged like this:
x² +x = 1 . . . . . . add 1 to both sides
x(x +1) = 1 . . . . . factor out x
x +1 = 1/x . . . . . .divide by x
Then to find the value of 1/x, we simply need to add 1 to the value of x we have:
[tex]\dfrac{1}{x}=\dfrac{\sqrt{5}-1}{2}+1=\dfrac{\sqrt{5}-1}{2}+\dfrac{2}{2}=\dfrac{\sqrt{5}-1+2}{2}\\\\\boxed{\dfrac{1}{x}=\dfrac{\sqrt{5}+1}{2}\approx1.618034}[/tex]
Related Questions
. for fraction having same numerator, the fraction with the __________ denominator is the greater number
Answers
Answer:
883773737383838837373737
MATH WEEK 5 HOMEWORK
Answers
Answer:
y=3/5x-1 or y=0.6x-1
Step-by-step explanation:
Answer:
y=3/5x-1 or y=0.6x-1
Step-by-step explanation:
You have just purchased a car and, to fund the purchase, you borrowed $32,000. If your monthly payments are $615.13 for the next 5 years, what is the APR of the loan?
Answers
9514 1404 393
Answer:
5.76%
Step-by-step explanation:
There is no formula for APR. It must be found using an iterative calculation, as from a spreadsheet or financial calculator.
__
The value can also be found graphically from the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where A is the monthly payment, P is the principal amount of the loan, r is the annual rate, and t is the number of years.
This can be put into a form that can be solved easily by a graphing calculator. We want it to find the x-intercept of f(x) = 0, so we define ...
f(x) = A(P, x/100, t) -615.13
where A(P, r, t) is defined above, and we let r = x/100 so x is the APR. The graph shows us the APR is 5.763%.
A full tin of paint has a mass of 22 kg.When the same tin is 3/4 filled with paint,it has a mass of 17 kg.What is the mass of the empty tin
Answers
Answer: 2 kg
Step-by-step explanation:
3/4(22-x)=17-x
66/4-3/4x=34/2-x
33/2-3/4x=34/2-x
1/4x=1/2
x=2
Answer:
that's 2kg because 22*.75 is 17 the difference is -5 each time. 17- another 5 is 12 or 2/4 the original amount. you keep going and at the end you are left with 2kg
Subtracting Unlike denominators 1/3 - 1/6
Answers
Answer:
1/6
Step-by-step explanation:
1/3 - 1/6
1×2/3×2 - 1×1 / 6×1 ( LCM of 3 and 6 )
2/6 - 1/6
2-1/6
1/6 answer
Solve: 3,204 ÷ 119
Show the remainder as a fraction.
Answers
3204:119=
=26,92
=27/10
what is 5/8x+4=3/8x+12
Answers
Answer: It equals 32!
Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
1. In the adjoining figure, p||q .Find the unknown angles.
Answers
Answer:
Step-by-step explanation:
d = 125 {corresponding angles are equal}
e + 125 = 180 {linear pair}
e = 180 - 125
e = 55
f = e {Vertically opposite angles}
f = 55
c = f {corresponding angles are equal}
c = 55
a = c {Vertically opposite angles}
a = 55
b =d {Vertically opposite angles}
b = 125
Answer:
a = 55°
b = 125°
c = 55°
d = 125°
e = 55°
f = 55°
Step-by-step explanation:
125 + e = 180
e = 180 - 125
e= 55°
e = f = 55°
f = a (being alternate angles)
a = c( being vertically opposite angles)
d = 125°(being corresponding angles)
d = b (being vertically opposite angles)
Analyze the diagram below and complete the instructions that follow. find sin angle C
Answers
the answer is A ;
sin = opposite/ hypotenuse
= 24/ 26 ( we need to simplify it)
= 12/13
Answer:
A or 12/13
Step-by-step explanation:
how do you check 2(3x - 3) + 2 = 26
Answers
on a number line, where would 4/10 be located? choose all answers that make a true statement.
Answers
Answer:
A and B only
Step-by-step explanation:
Number lines have smaller numbers on the left and larger numbers on the right. To determine the position of 4/10 on the number line, we just need to compare the value to the values in the answer choices.
a. 4/10 is equivalent to 2/5 (2/5 is just a simplified version of 4/10). If you multiple both the numerator and denominator of 2/5 by 2, you will get 4/10. If you do 4 divided by 10 and 2 divided by 5, you'll also see that they are both equivalent to 0.4. Hence, they have the same value and will be in the same place.
b. 3/10 is smaller than 4/10. In a case where the denominators of two fractions are the same, a smaller numerator would mean a smaller value. In addition, 3/10 is equivalent to 0.3 and 4/10 is equivalent to 4/10 so 0.3 is less than 0.4. That means 4/10 will be on the right of 0.3 because it's a larger number.
c. Using the same logic as part b, 2 is less than 4. That means 2/10 is less than 4/10, so 4/10 would be on the right of 2/10, not the left.
d. Same logic as parts b and c. 7 is greater than 4, so 4/10 should be on the left of 7/10 not right.
5. Aisha is older than Favour Zainab is older than Aisha Favour is older than Jessica Aisha is younger than Michael Who is the youngest?
Answers
Answer:
Denote by A, F, Z, J, and M
A > F A is out
Z > A so Z is out
M > A so M is out
F > J so F is out
That leaves only J, Jessica
Also from above one can write:
(M, Z) > A > F
that only leaves J
please please help me
Answers
Answer:
a) Angle(A+B+C) = 180°
3x - 2° + x - 2° + 2x + 4° = 180°
6x = 180°
x = 30°
<A = 3(30°) - 2° = 88°
<B = 30° - 2° = 28°
<C = 2(30°) + 4° = 64°
b) at point Q
3y + 6y = 180°
y = 20°
<Q = 3(20°) = 60°
<S = 20°
x = 180° - (<S + <Q)
x = 180° - (80°)
x = 100°
<R = 100°
Let f(x)=7x−4, g(x)=x2+4, and h(x)= x+4 7.
Evaluate the expression (f◦g◦h)(3).
Answers
Step-by-step explanation:
(x/z)=3 (7/5)= x'2
tis is the right answer
plz mark me branlists
is it weird to be listening to Christmas songs right now
Answers
Answer:
Yes and No
Step-by-step explanation:
Yes, it is weird because Halloween comes first.
No, it's not weird because it is your choice.
bye.
someone plz help plz
Answers
Answer: -1/7
I hope this helps I would appreciate brainliest if possible :)
Express 15 3/5 as a fraction in simplest form
Answers
Answer: 78/5
Step-by-step explanation:
To simplify this fraction, we should get rid of 15 in order to only have a numerator and a denominator. We would first multiply 15 with 5.
15 * 5 = 75
Then we would add 75 to 3.
75 + 3 = 78
We now have our numerator for our simplified fraction.
78/5
In the diagram, mcd=128º and mpA=76º. What is McABC?
Answers
Answer:
D. 102°Step-by-step explanation:
m∠ABC = m∠ABD + m∠CBD = Angle addition postulate1/2mCD + 1/2mAD = Angle measure is the half the intercepted arc1/2(128) + 1/2(76°) = 102°What is 240.50 x 19.54? Give your answer to 2 significant
Show your work
Answers
Answer:
4700
Step-by-step explanation:
240.50 x 19.54
= 4699.37
2 significant = 4700
Answer:
4,699.37
Step-by-step explanation:
240.50 x 19.54 = 4,699.37
On the following unit circle, θ θtheta is in radians and tan ( θ ) = − 0.99 0.1 = − 9.9 tan(θ)= 0.1 −0.99 =−9.9tangent, left parenthesis, theta, right parenthesis, equals, start fraction, minus, 0, point, 99, divided by, 0, point, 1, end fraction, equals, minus, 9, point, 9. y y x x 1 1 − 1 −1 1 1 − 1 −1 θ θ ( 0.1 , − 0.99 ) (0.1,−0.99) A unit circle with an angle from the positive x-axis to a ray labeled theta. The point where the ray intersects the circle is labeled 0.1, negative 0.99 and is in the fourth quadrant. Without a calculator, evaluate the following expressions to the nearest
Answers
Answer: tan(pi+theta)=-9.9
Tan(2pi+theta)=-9.9
Step-by-step explanation:
By trigonometric expressions we conclude that the values of the tangent functions of the angles π + θ and 2π + θ radians are both equal to - 9.9.
How to calculate trigonometric functions from unit circle
A unit circle is a circle with a radius of a unit used to calculate the value of trigonometric functions associated to a right triangle. In this case, the tangent function for a point (x, y) is:
tan θ = y/x (1)
The trigonometric expression for the tangent of the sum of two angles:
[tex]\tan (\alpha + \theta) = \frac{\tan \alpha + \tan \theta}{1 - \tan \alpha \cdot \tan \theta}[/tex] (2)
Now we proceed to calculate the trigonometric expressions:
[tex]\tan (\pi + \theta) = \frac{\frac{-0.99}{0.1}+0}{1-\left(\frac{-0.99}{0.1}\right)\cdot (0)}[/tex]
[tex]\tan (\pi + \theta) = -9.9[/tex]
[tex]\tan (2\pi + \theta) = \frac{\frac{-0.99}{0.1}+0}{1-\left(\frac{-0.99}{0.1}\right)\cdot (0)}[/tex]
[tex]\tan (2\pi + \theta) = -9.9[/tex]
By trigonometric expressions we conclude that the values of the tangent functions of the angles π + θ and 2π + θ radians are both equal to - 9.9.
To learn more on trigonometric expressions: https://brainly.com/question/6904750
#SPJ2
y=-4x^2-8x-5 find the axis of symmetry and the vertex for the parabola
Answers
Answer:
x= -1 a x i s of s ym m et ry
(-1, -1) v e r t e x
Step-by-step explanation:
M a t h w a y step by step
The person above me is wrong!
Use the properties of equality to complete each proof.
Given: 6x-2y =14; Prove: y = 3x - 7
Answers
Answer:
below
Step-by-step explanation:
[tex]6x-2y=14[/tex]
[tex]-2y=14-6x[/tex]
[tex]y=-7+3x[/tex]
but has in slope-intercept form, y = 3x - 7
both lines are equal
Simplify the expression.
2+2 4+3
O 6
o 7
o 21
067
Yall help this is worth 30 points
Answers
Use properties of operations to write an expression equivalent to the expression below.
(MUST SHOW WORK!)
Answers
Answer:
third option
Step-by-step explanation:
the only difference between the original problem and the third option is where the parentheses are placed
since the operations are all addition it does not matter which pair of values gets added first because of the associate property of addition
PLEASE HELP!!!!!
will mark brainliest!!!!!
Answers
Answer:
(4,7),(5,-1),(6,-10)
Step-by-step explanation:
mark me brainliest
Simplify 6days to 4weeks to it lowest term in ratio
Answers
ratio = 6:28,
simplified ratio = 3:14
z ÷ 12 = 10 please help im giving 60 points for the awnser i realy need this
Answers
Answer:
120
Step-by-step explanation:
10x12=120 z=120
Answer:
120
Step-by-step explanation:
12 times 10 is 120
good luck!
real answers only pls help
Answers
Answer:
the 4th
Step-by-step explanation:
52 teratons
tons
Equals
How many tons
Answers
I will give brainliest.
4 (2x - 3) -6 (3x + 4)
Answers
Answer:
-2x .(5x+18)
Step-by-step explanation: