Let
[tex]x = 6 + \dfrac1{2 + \dfrac1{6 + \dfrac1{2 + \cdots}}}[/tex]
Then
[tex]x = 6 + \dfrac1{2 + \dfrac1x}[/tex]
and solving for x gives
[tex]x = 6 + \dfrac x{2x + 1}[/tex]
[tex]x = \dfrac{13x + 6}{2x + 1}[/tex]
[tex]x(2x+1) = 13x + 6[/tex]
[tex]2x^2 + x = 13x + 6[/tex]
[tex]2x^2 - 12x - 6 = 0[/tex]
[tex]x^2 - 6x - 3 = 0[/tex]
By the quadratic formula,
[tex]x = 3 \pm 2\sqrt{3}[/tex]
but x must be a positive number, so only the positive square root solution is valid.
[tex]x = 3 + 2\sqrt{3}[/tex]
We identify a = c = 3 and b = 2, so a + b + c = 8.
no link no bot please right fast but right
Answer:
12 in
Step-by-step explanation:
3in + 3in + 3in + 3in = 12
Ophira’s insurance company has notified her that her premiums will increase due to a poor insurance score and a recent claim she filed. The recent claim has increased her premiums by 41%, and her poor insurance score will cost her an additional $25 per month. Ophira currently pays $815 per year for insurance. How much will she pay next year?
$1149.15
$1672.15
$1449.00
$1449.15
Answer:
$1449.15
Step-by-step explanation:
currently paying 815
to pay next year: 41% increase + 25 extra per month
⇒ 141%·815 + 12·25
= 1149.15 + 300
= 1449.15
Extra Points and Brainliest Award if answered!!!!
Gerald is testing to see if a possible rational root is an actual rational root of a polynomial. He uses synthetic division to determine the value of the remainder.
Which theorem is he using to test the value?
A. Linear Factorization Theorem
B. The Fundamental Theorem of Algebra
C. The Factor Theorem
D. The Remainder Theorem
Answer:
its C.
Step-by-step explanation:
please mark me brainlists
Gerald used the factor theorem to test the value. Therefore, option C is the correct answer.
Given that, Gerald is testing to see if a possible rational root is an actual rational root of a polynomial.
What is Synthetic Division?Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.
The factor theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then (x - a) is a factor of f(x) if f(a) = 0. In other words, we can say that (x - a) is a factor of f(x) if f(a) = 0.
Therefore, option C is the correct answer.
To learn more about the factor theorem visit:
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Need some help with these 2 math questions, They are related so best to finish one then work on the bisect. Thank you.
Answer:
∠RQT = 23.5
∠PQR = 133°
Step-by-step explanation:
Question 1Step 1 - Add angles together:
As all angles on a straight line must add up to 180°:
3x - 5 + x + 1 = 180
Add like terms together
3x + x - 5 + 1
4x - 4 = 180
Step 2 - Add 4 to both sides of the equation:
4x - 4 + 4 = 180 + 4
4x = 184
Step 3 - Divide both sides by 4:
[tex]\frac{4x}{4} = \frac{184}{4}[/tex]
x = 46
∠RQS = x + 1
∠RQS = 46 + 1
∠RQS = 47
Given the ray QT bisects ∠RQS, the angles must be the same on either side so:
47 ÷ 2 = ∠RQT
∠RQT = 23.5
Question 2As we know the value of x:
∠PQR = 3x - 5
Plug known values in:
3x - 5
3(46) - 5
138 - 5
∠PQR = 133°
This can also be calculated by subtracting known angle ∠RQS from 180:
180 - 47 = 133.
Hope this helps!
The perimeter of a rectangle is 21+ 2where is the
length of the rectangle and wis the width find the
Perimeter of the rectangle if the length is 12 inches and the width is 9 inches
Answer:19 - 20
Step-by-step explanation:
Yo
help ! ✬
due tomorrow, i font understand this at all :(
Answer:
41 litters to gallons is 10.8311
3.5 gallons to litters is 13.2489
A = 10.8311 Gallons
B = 13.2489 Literes
As an estimation we are told 5 miles is 8 km.
Convert 52.5 miles to km.
PLEASE HELP NO TIME FOR LINK!!!
Answer:
Step-by-step explanation:
52.5 mi(8 km/5mi) = 84 km
What is Two-thirds divided by one-sixth?
An area model with 4 shaded parts and 2 unshaded parts. The shaded parts are labeled two-thirds.
2
3
4
6
Answer: 4
Step-by-step explanation:
So, what I do to divide fractions is to turn them into reciprocals, which means changing it into a multiplication problem and turning the second fraction upside down. So, [tex]\frac{2}{3}[/tex] x [tex]\frac{6}{1}[/tex]. We multiply across, so 2 x 6 is 12, and 3 x 1 is 3, which gets us to [tex]\frac{12}{3}[/tex]. Since this is an improper fraction, we can simplify by dividing 12 by 3 to get 4. Hope this helps! :)
Answer:
4 (C) hope this helps!!
BYEEEEEEEEE!
debbie used 40% of her flour for
cookies she started with 24 cups how many cups did debbie use?
Answer:
24 x 40% = 9.6
Step-by-step explanation:
the answer is Lil Debbie™ 9.6 cup used.
Find the angles of a triangle which are in the ratio 4:3:2.
Answer:
80o, 60o, 40o
Step-by-step explanation:
The sum has to add up to 180 degrees because of the three sides and this is what matches.
Answer:
Let the given angles of the triangle be 4x, 3x and 2x.
We know that the sum of all interior angles of a triangle is 180°.
Therefore,
4x+3x+2x = 1809x = 180x = 180/9x = 20Hence, the angles of the triangle are -
4x = 4×20 = 80°3x = 3×20 = 60°2x = 2×20 = 40°which is the first question in brainly
Answer:
this question
Step-by-step explanation:
Answer:
The first question was this: https://brainly.com/question/420 ur welcome :)
Step-by-step explanation:
The diameter of Pilar's bike wheel is 24 inches.
How far does Pilar's bike travel when the wheel makes
10 complete rotations?
The distance Pilar's bike travel when the wheel makes 10 complete rotations is 753.6 inches
Since the wheel is circular in nature, we will take the circumference to determine the distance travelled for 1 revolution
Circumference of a circle = πr²
r is the radius of the wheel.
Given that d = 24 in, r = 24/2 = 12in
C = 2(3.14)(12)
C = 75.36 in
Hence the distance completed by 1 revolution is 75.36. If Pilar's bike makes 10 revolutions, hence the required distance will be:
D = 10 * 75.36
D = 753.6in
Hence the distance Pilar's bike travel when the wheel makes 10 complete rotations is 753.6 inches
Learn more here: https://brainly.com/question/23242098
A car salesman earns a 3% commission on sales. If he sells a car for AED 75,990, how much the commission amount will he earn if he sells 4 cars?
Answer:
AED 9118.80
Step-by-step explanation:
to find out how much he earns for 1 car, multiply 75990 by 0.03 (3%). so the salesman earns 2279.70 per car sold. next, multiply this number by 4 to get the amount he earned for 4 cars: 9118.80
On Saturday, 150 people at a movie theater purchased popcorn, and 350 people did not purchase popcorn. What percentage of people did not order popcorn at the movie theater on Saturday?
Answer:
70% of people did not order popcorn at the movie theater on Saturday.
Step-by-step explanation:
first, add to get the total amount of people
150 + 350 = 500
now that we have the total, divide the people that did not buy popcorn by the total amount of people
350/500 = 0.7
then, multiply that by 100
0.7 x 100 = 70
your final answer would be 70%
I need help I can’t find the anwer please help
Answer:
You: 3, 6, 9, 12
Friend:4, 8, 12, 16
Step-by-step explanation:
You/Friend ratio is 3/4
Missing numbers:
8 / (4/3) = 612 * (4/3) = 16Numbers:
You 3, 6, 9, 12
Friend 4, 8, 12, 16
Please Help!
what is the resultant of the two vectors shown above?
A. (9,1)
B. (1,-9)
C. (-1,9)
D. (5,5)
Answer:
D 5 5 it has to be the answer
Jacob saw a model of a building that will be built in his city. The model has a height of 40 centimeters and will be built to a scale of 1:50. What is the actual height of the building? (1 m = 100 cm)
Answer:
20 m
Step-by-step explanation:
1/50 = 40/x
Cross multiply.
1 × x = 50 × 40
x = 2000
2000 cm × (1 m)/(100 cm) = 20 m
Answer: 20 m
In a school of 1,000 students, 600 study physics, 300 study Calculus, and 100 study both. What is the probability that someone who does not study calculus studies physics? Give your answer as a decimal to one decimal place.
The probability that someone who does not study calculus studies physics is 0.5
Since there are 1000 students in the school and 600 study physics, 300 study Calculus, and 100 study both, we need to find the number of students that study only physics to find the probability that someone who does not study calculus studies physics.
Let x = number of students who study both = 100, y = number of students who studies only physics and z = number of students who studies only calculus.
Given that the number of students who study physics are 600, we have
x + y = 600 (1)
Also, given that the number of students who study calculus are 300, we have
x + z = 300 (2)
From (1)
y = 600 - x
y = 600 - 100
y = 500
So, the probability of students that study only physics = probability that someone who does not study calculus studies physics is
P(physics) = number of students studying only physics/total number of students
= 500/1000
= 5/10
= 0.5
So, probability that someone who does not study calculus studies physics is 0.5
Learn more about probability here:
https://brainly.com/question/19916581
how many times does 32 go into 7500
Answer:
yy
Step-by-step explanation:
Answer:
234.375
Step-by-step explanation:
divide 7500 by 32, and you'll get the number of times 32 goes into 7500.
7500 ÷ 32 = 234.375
and if the question is asking for whole numbers it would be just 234 times (and a 3/8)
What is rhe relationship between a centimeter and a meter?
Answer:
A meter is 100x bigger than a centimeter.
Step-by-step explanation:
1 meter = 100 centimeters
Answer:
1metre=100 centimeter
Step-by-step explanation:
that is the relationship between centimeter and metre
PLEASE NO LINKS DONT WASTE YOUR TIME IM NOT GONNA CLICK. Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
Answer:
B.
Step-by-step explanation:
factored form actually contains the x intercepts right in it. Basically whatever sets the whole equation equal to zero.
On the graph you can see that it passes through both positive and negative 4. so (x+4)(x-4) is the answer because plugging in 4 for x will make it zero. Same for plugging in negative 4
Hope this helps!
Find c
[tex]a+a=10\\a+b=35\\b-z=5\\z+a+b+c= 10[/tex]
Answer= -50
a= 5
b= 30
z= 25
c= -50
Ernie deposits $9,800 into a pension fund. The fund pays a simple interest rate of 7%. What will the balance be after four years?
Answer:
$12,845.80
Step-by-step explanation:
take the first number and go +7%. repeat four times
hope this helps :-)
Two teams are going on a trip to play a game. There will be
2 buses to take the students. On each bus, there are 60
seats. Teachers and parents will sit in 10 of the seats on
each bus
How many seats are available for students on the buses?
No links
I’ll make you to Brainlius if you answer the question no links I’ll take a folder but no links or power point As long as you know the question and you didn’t the quiz at least send either PowerPoint or a folder please I need help immediately ASAP
Answer:
1) Is 9 2)x-3 3) 12 ,106,42 4)1/12 5) one ,three half ,three 6)32 7) 1,4,5 8) 1 z-9 2 9+z 3 9/3 4 9z 9) 3/n 10 10) 1 2
Step-by-step explanation: Cuz I'm In The Test Now And Jest Got Done With It And All The Answers are Right here
PLEASE ASAP HELPPPP PICK THEM ALL!!
Answer:
B
Step-by-step explanation:
Suppose that a risk-free investment will make three future payments of $250 in 1 year, $250 in 2 years, and $250 in 3 years. Instructions: Round your answers to 2 decimal places. a. If the Federal Reserve has set the risk-free interest rate at 4 percent, what is the proper current price of this investment? $ b. What is the price of this investment if the Federal Reserve raises the risk-free interest rate to 6 percent? $
Answer:
la théorie des plaques est
The total present value will be $693.75
The total present value will be $668.23
What is Future Value?Future value is the value of an asset or investment as of some future date. In other words, the future value is the sum of money that an investment will be worth, assuming a certain rate of return, after a specific amount of time (interest rate).
First, i= 4/100 = 0.04
n= 1, 2, 3
Amount= $250
So, Present Value = 250/ (1 + 0.04) + 250/ (1 + 0.04)² + 250/ (1 + 0.04)³
= 250/ 1.04 + 250/ 1.04² + 250/ 1.04³
= 240. 38 + 231.13 + 222.24
= $693.75
So, The total present value will be $693.75
Second, i= 6/100 = 0.06
n= 1, 2, 3
Amount= $250
So, Present Value = 250/ (1 + 0.06) + 250/ (1 + 0.06)² + 250/ (1 + 0.06)³
= 250/ 1.06 + 250/ 1.06² + 250/ 1.06³
= 235. 84 + 222.49 + 209.90
= $668.23
So, The total present value will be $668.23
Learn more about Future Value here:
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Could I get help with this?
Answer:
you would pay $1000 because insurance would cover the 1500 for medical, and it would pay 5000 of the 6000 for damage to the car
Step-by-step explanation:
A new cell phone costs $108.99 in the store. What would your total cost be if the sales tax is 4.5%? Round your answer to the nearest cent, if necessary.
Answer: $113.89
Step-by-step explanation:
108.99 * 0.045
= 4.90455
108.99 + 4.90455
= 113.89455
$113.89
Answer:
Total Cost = $113.89
Step-by-step explanation:
Total Cost = Cell phone cost + sale Tax % ( cell phone cost)
Total Cost = $108. 99 + .045 × $108.99
Total Cost = $108.99 + $4.90455
Total Cost = $108.99 + $4.90
Total Cost = $113.89
Fill in the missing
numbers?
?•(-10) = 90
Answer:
?=-9
Step-by-step explanation:
A negative x negative is positive. 90/10=9 and mutiply both by -1. -10x-9=-90