[tex]\large\underline{\sf{Solution-}}[/tex]
We have to find out the value of the fraction.
Let us assume that:
[tex] \sf \longmapsto x =2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ... \infty} } } [/tex]
We can also write it as:
[tex] \sf \longmapsto x =2 + \dfrac{1}{x} [/tex]
[tex] \sf \longmapsto x =\dfrac{2x + 1}{x} [/tex]
[tex] \sf \longmapsto {x}^{2} =2x + 1[/tex]
[tex] \sf \longmapsto {x}^{2} - 2x - 1 = 0[/tex]
Comparing the given equation with ax² + bx + c = 0, we get:
[tex] \sf \longmapsto\begin{cases} \sf a =1 \\ \sf b = - 2 \\ \sf c = - 1 \end{cases}[/tex]
By quadratic formula:
[tex] \sf \longmapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1} [/tex]
[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1} [/tex]
[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{8} }{2} [/tex]
[tex] \sf \longmapsto x = \dfrac{2 \pm2 \sqrt{2} }{2} [/tex]
[tex] \sf \longmapsto x = 1 \pm\sqrt{2}[/tex]
[tex] \sf \longmapsto x = \begin{cases} \sf 1 + \sqrt{2} \\ \sf 1 - \sqrt{2} \end{cases}[/tex]
But "x" cannot be negative. Therefore:
[tex] \sf :\implies x = 1 + \sqrt{2}[/tex]
So, the value of the fraction is 1 + √2.
Shawn planned to run 4.2 miles every day, but yesterday he only had time to run 0.2 of that distance. How far did Shawn run yesterday?
Answer:
That would be 4.0
Step-by-step explanation:
if you have 4.2 take away 0.2 that would be 4.0
4.2
0.2
-__
4.0
Hope this helped regards
Which equation is equivalent to 0.3y +0.4(25 - y) = 6.8 ?
Answer
y = 32
Step-by-step explanation:
Let's solve your equation step-by-step.
0.3y+0.4(25−y)=6.8
Step 1: Simplify both sides of the equation.
0.3y+0.4(25−y)=6.8
0.3y+(0.4)(25)+(0.4)(−[tex]\frac{-0.1y}{-0.1} =\frac{-3.2}{-0.1}[/tex]y)=6.8(Distribute)
0.3y+10+−0.4y=6.8
(0.3y+−0.4y)+(10)=6.8(Combine Like Terms)
−0.1y+10=6.8
−0.1y+10=6.8
Step 2: Subtract 10 from both sides.
−0.1y+10−10=6.8−10
−0.1y=−3.2
Step 3: Divide both sides by -0.1.
-0.1y/-0.1=-3.2/-0.1
y=32
I hope this helps?
Factorise; c cubed divided by c cubed?
HELP ASAP
Step-by-step explanation:
c³/c³ =1 .
hope this helps you.
solve for x on both
1. -1-3x+7x=17
2. 4x-5+7x=-10
(please show your work if possible:)
Step-by-step explanation:
1. -3x+7x=18
x(-3+7)=18
x=[tex]\frac{18}{(-3+7)}[/tex]
2. 4x+7x=-5
x(4+7)=-5
x=[tex]\frac{-5}{(4+7)}[/tex]
I hope this helped, may be wrong but ive done it my way
14. A customer's cell phone bill cost $60.50. The company charges a monthly fee of $28 plus
five cents for each minute. Create and solve an equation for the number of minutes the
customer spent talking on the phone. Let m represent the number of minutes.
your work is not complete
A farmer owns a total of 8 acres of land. The land is separated into (3)1/3 equally sized sections. How many acres are in each section?
Write your answer as a mixed number in simplest form.
Answer:
each section is 2 2/3 or 2.66666666
Step-by-step explanation:
What is 3/4+1/4+1/2=
Answer:
3/2
Step-by-step explanation:
Answer:
Exact Form: [tex]\frac{3}{2}[/tex]
Decimal Form: 1.5
Mixed Number Form: [tex]1\frac{1}{2}[/tex]
Step-by-step explanation:
In pic
(Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
The rectangular frame is made from 5 straight pieces of metal.
6 m
8 m
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.
Step-by-step explanation:
the perimeter = 2×(8+6)
= 2(14) = 28m
the diagonal = √8²+6²
= √64+36
=√100 = 10m
the total length of the frame =
28+10 = 38 m
therefore the total Weight =
38× 1.5 kg = 57 kg
The correct answer is 57kg.
the perimeter = 2×(8+6)
= 2(14) = 28m
the diagonal = √8²+6²
= √64+36
100 = 10m
the total length of the frame =
28+10 = 38 m
therefore the total Weight =
38× 1.5 kg = 57 kg
What is the weight formula?The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg.
To obtain the weight of your metal, you will multiply the sectional area, length and density together. Then, to convert the weight to kilograms, you must divide the product by 1,000. You can also determine the weight of your metal product using any number of online metal weight calculators.
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Hi can u help me with this
Answer:
it's D, 27
Anything in the middle would be both so just add only the yellow and red numbers, not orange
What is the value of 2.3+8−12?
1.) 10.8
2.) 10.3
3.) 9.8
4.) 9.5
Answer:
2
Step-by-step explanation:
to answer this algebraic question use BDMAS rule
first solve bracket then division, multiplication,addition then subtraction.
6+8-12
14-12
2
Answer:
9.8
Step-by-step explanation:
convert your decimal into a fraction so 2.3= 23/10
23/10 + 8 - 1/2
then calculate your sum or difference
leaving you with
49/5
meaning your answer is
9.8
Let f(x)=5x^4 and g(x)=e^2x+x. If h is the function defined by h(x)=f(g(x)), which of the following gives a correct expression for h′(x)?
The values of h'(x) is h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 ).
Option C is the correct answer.
Given,
f(x)=5x^4 and g(x)=e^2x+x.
If h is the function defined by h(x)=f(g(x)),
We need to find h′(x).
What is the differentiation formula for the following?We have,
dx/dx = 1
d[tex]x^{n}[/tex]/dx = n[tex]x^{n-1}[/tex]
d[tex]e^{x}[/tex]/dx = [tex]e^{x}[/tex]
d[tex]e^{n}[/tex]/dx = [tex]ne^{n}[/tex]
d(cx)/dx = c(dx/dx) = c
We have,
- f(x)=5[tex]x^{4}[/tex] ______(1)
- g(x)=[tex]e^{2x}[/tex]+x ______(2)
- h(x)=f(g(x)) _______(3)
Now,
h(x) = f ( [tex]e^{2x}[/tex]+x )
From (1)
h(x) = 5[tex](e^{2x} + x) ^{4}[/tex] ______(4)
Now,
Differentiate (4)
h'(x) = 5 d[tex](e^{2x} + x) ^{4}[/tex]/dx
h'(x) = 5 x 4 [tex](e^{2x} + x) ^{3}[/tex] d [tex](e^{2x} + x)[/tex] / dx
h'(x) =20 [tex](e^{2x} + x) ^{3}[/tex] ( d[tex]e^{2x}[/tex]/dx + dx/dx )
h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 )
Thus the values of h'(x) is h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 ).
Option C is the correct answer.
Learn more about differentiation here:
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Inverse operation for 6*8=48
HELP ASAP 100 POINTS!!
Is this graph a function?
This cannot be determined from this graph.
This is a function.
This is not a function.
Answer:
Sorry but.
Step-by-step explanation:
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Evaluate -(2")(2º).
A.1/8
B. -8
C. 8
D.-1/8
Answer:
= -8
(hope this helps) :)
Name two triangles that are congruent by the ASA Postulate.
ATC=DOG
ATC=NFI
PQR=INF
PQR=IFN
Answer:
ATC is congruent to DOG by ASA axiom for congruency
Answer: ATC = DOG
Step-by-step explanation:
30. You can work at most 25 hours next week. You need to earn at least $85 to cover your gas and food
expenses. Your babysitting job pays $7.50 per hour and your math tutoring job pays $6 per hour.
a) Define your variables.
b) Write two inequalities that represent the constraints of the scenario.
In the inequality 4>-4, which number appears farther right on a number
line and why?
O A. -4 appears farther right because -4 is smaller than 4.
O B. -4 appears farther right because - 4 is larger than 4.
C. 4 appears farther right because 4 is larger than -4.
D. 4 appears farther right because 4 is smaller than -4.
PLEASE HELP ASAP!! THIS IS ONE OF MY FINAL TEST… AKA- ITS MOST OF MY GRADE
Answer:
"C" 4 appears farther right because 4 is larger than -4.
plZ help...................
Answer:
B
Step-by-step explanation:
[tex]\frac{x}{5}[/tex] + 4 = 1 ( subtract 4 from both sides )
[tex]\frac{x}{5}[/tex] = - 3 ( multiply both sides by 5 to clear the fraction )
x = 5 × - 3 = - 15 → B
The circumference of a circle is just ?
Answer:
The formula is C = πd
π = pie
d= diameter
C =circumference
Answer:
C = 2πr
Step-by-step explanation:
C = 2πr
where C = circumference,
π = pi = 3.14159...,
and r = radius of the circle.
Which numbers are between -7 and 2 on a number line? Circle all that apply.
A. 2.1
B. -1
C. 0
D. -7.5
E. 3.5
F. -6.4
G. -8
Answer: See below
Step-by-step explanation:
A. 2.1 No (2.1>2)
B. -1 Yes
C. 0 Yes
D. -7.5 No (-7.5<-7)
E. 3.5 No (3.5>2)
F. -6.4 Yes
G. -8 No (-8<-7)
PLEASE HELP
Absolute Value Inequalities
I need help with this
Answer:
Step-by-step explanation:
∠5 = ∠1 {Alternate exterior angles are congruent}
8x - 19 = 7x - 3
Add 19 to both sides
8x = 7x - 3 + 19
8x = 7x + 16
Subtract 7x from both sides
8x - 7x = 16
x = 16
∠5 = 8x - 19
= 8*16 - 19
= 128 - 19
∠5 = 109
∠5 + ∠4 = 180 {linear pair]
109 + ∠4 = 180
∠4 = 180 - 109
∠4 = 71°
v=t+s+u, for the letter u please and thank you
Answer:
u = v - s - tStep-by-step explanation:
V=t+s+u, for the letter u please and thank you
v = t + s + u
u = v - s - t
pythagorean theorem help meeeeee!!
Answer:
25
Step-by-step explanation:
remember that the pythagorean theorem is a²+b²=c²
so this equation would be:
7²+24²=c²
solve the exponents
49 + 576 = c²
combine like terms
625 = c²
take the radical of each number
√625 = √c²
25 = c
have a lovely day <3
1. How has the cost of a movie ticket changed over the last 30 years? What has been the general trend? How can you tell this from the graph? (2 points)
2. What years did the cost of movie ticket decrease compared to the year before? How can you tell from the graph when the price is decreasing? (2 points)
Student Name:
Predicting Movie Ticket Costs Activity
3. There was a time where the cost of a movie ticket stayed relatively the same over several years. For what years did the cost stay relatively the same? How can you tell this from the graph? (2 points)
4. The graph could be divided up into three different periods of relatively consistent ticket price change: The years 1980 – 1988, 1989 – 1993 and 1994 – 2011. Can you find a typical rate of change in the price of a ticket for each of these time periods? In other words, on average, by how much did the price of a ticket increase by each year during each of these time periods? (2 points)
5. Predict the cost of a ticket in 2012 – 2015. Plot your predictions and give your actual predictions for each year below. How did you determine how much a ticket would cost each year? (2 points)
6. What might have been the cost of a ticket during the years 1975 – 1979? Plot your estimates on the grid and give your actual predictions for each year below. How did you determine how much a ticket would cost each year? (2 points)
Student Name:
Predicting Movie Ticket Costs Activity
7. Find a line of best fit to represent the data. Let y = ticket price and x = the number of years since 1980 (1980 is year zero, 1981 is year one). Approximate a line to represent the data, a slope, a y- intercept and equation that models your line of best fit. (2 points)
8. Use your equation (or graph or a table) to predict the cost of a movie ticket in the years 2020 and 2030. Be sure to show how you came to each answer. (2 points)
Answer:
1. For most of the 1990s, tickets sold for an average of less than $5 apiece, and dating back to the 1960s, many Americans could go to the movies for less than a buck. 24/7 Wall St. reviewed data from the National Association of Theatre Owners to determine the cost of a movie ticket the year you were born. A full-price AMC ticket is averages $10.50 nationwide, reflecting a 50-cent increase. Concession prices also increased.
Your asking alot for 50 points so i did 1..
Step-by-step explanation:
ggle is saying the wrong answer, anyone can help??
Answer:
X=2
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
I am pretty good at math.
I WILL GIVE BRAINLESS) Math Journal Write a word problem that involves a proportional relationship and needs more than one step to solve. Show how to solve the problem. 1
Answer:
565.48 sq. in.
Step-by-step explanation:
Given the Slant height and radius, we are asked to find the lateral area of the cone.
Lateral area of the cone is given by
where, 'r' is the radius of the cone.
and 'l' is its slant height.
From the figure, we see that the slant height of the cone, l = 15 in
Also, the radius of the cone, r = 12 in.
Therefore,
= 565. 48 sq. in. which is the required answer.
Answer:
A proportional relationship is written as:
y = k*x
where k is the constant of proportionality.
A general word problem that represents one of these relationships can be:
If each burger costs $1.50, what would be the cost of buying x burgers?
The cost of x burgers will be x times $1.50, so if we define y as the total price, we will have the relation:
y = $1.50*x
Which is a proportional relationship where the constant of proportionality is $1,50
Questions linked below
Answer:
The blur of the photo I do not understand sorry
Step-by-step explanation:
ty for the points
Question 20
Figure A is doubled in size then reflected across the x-axis creating Figure B.
How will the coordinates of Figure B differ from Figure A as a result of this series of transformations?
А
two times the x-value and two times the opposite y-value
B the opposite x-value and two times the y-value
С
two times the x-value and two times y-value
D
two times the opposite x-value and the opposite y-value
Answer:
Two-times the x-value and two-times the opposite y-value.
If a student (represented by initials) was chosen at random, find P(HH|C').
P(HH|C') = 3/5
P(HH|C') = 1/2
P(HH|C') = 2/5
P(HH|C') = 9/16
Answer: the answer is P(HHlC') = 1/2
Step-by-step explanation: