[tex]\large\underline{\sf{Solution-}}[/tex]
Let us assume that:
[tex] \sf \longmapsto x = \sqrt{6 + \sqrt{6 + \sqrt{6 + ... \infty } } } [/tex]
We can also write it as:
[tex] \sf \longmapsto x = \sqrt{6 + x } [/tex]
Squaring both sides, we get:
[tex] \sf \longmapsto {x}^{2} =6 + x[/tex]
[tex] \sf \longmapsto {x}^{2} - x - 6 =0[/tex]
By splitting the middle term:
[tex] \sf \longmapsto {x}^{2} - 3x + 2x - 6 =0[/tex]
[tex] \sf \longmapsto x(x - 3) + 2(x - 3 ) =0[/tex]
[tex] \sf \longmapsto (x+ 2)(x - 3 ) =0[/tex]
Therefore:
[tex] \longmapsto\begin{cases} \sf (x+ 2) =0 \\ \sf (x - 3) = 0 \end{cases}[/tex]
[tex] \sf \longmapsto x = - 2,3[/tex]
But x cannot be negative.
[tex] \sf \longmapsto x = 3[/tex]
Therefore, the value of the expression is 3.
[tex]\large\underline{\sf{Verification-}}[/tex]
Given:
[tex]\sf\longmapsto x=3[/tex]
We can also write it as:
[tex]\sf\longmapsto x = \sqrt{9}[/tex]
[tex]\sf\longmapsto x = \sqrt{6+3}[/tex]
[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{9}}[/tex]
[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+3}}[/tex]
[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{9}}}[/tex]
[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+3}}}[/tex]
This pattern will continue.
[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+...\infty}}}[/tex]
Which of the ordered pairs is a solution to
4x - y = 8?
a. (0, -8).
b. (0,8).
c. (8,0).
(-3.0
Answer:
a(0,-8)
Step-by-step explanation:
4x0=0
0--8= 8
at sunrise,the temperature outside was 5 below zero . by noon the temperature dropped 27. what was the temprature at noon
Answer:
-32
Step-by-step explanation:
hope this helps you with the question
PLEASE HELP HELPPPPPPPPP
Answer:
(1,-4)
Step-by-step explanation:
2x+4y=-14
x-2y=9
2x+4y=-14
2(x-2y)=(9)2
2x+4y=-14
2x-4y=18
Add X
4x=4
X=1
Substitute x into any equation
(1)-2y=9
-2y=8
y=-4
Eight identical pens cost $10.80.
a. Write an equation in the given box that represents the total cost, y, in dollars for a pens.
The Wilsons have triplets and another child who is ten years old. The sum of the ages of their children is 37. How old are the triplets
Hope this helps have a nice day!!!!
Y=5x+b
how do i solve for B?
Answer:
Y=5x+b
y-5x=b
B= y-5x
hope this helps
Answer:
b = y-5x
Step-by-step explanation:
y =5x+b
Step 1- Cancelation minus or add the numeric first both side then variable numbers, then variables then exponents ^2 last.
In this case if we were asked to find x we would divide both sides by 5. But we are not asked that and instead asked to find b so we just apply and keep 5x together through add or subtraction.
For exponents we sqrt both sides. But this equation doesnt show any exponents so we stop at -5 each side.
y-5x=b
Step 2 - keep doing to isolate b we have no more to change other than reverse to show b first.
b = y-5x
Plz help me, thx you
Answer:
transversal line is line A. parallel lines are B and C. corresponding to angle A is angle D. and alternate angle to E is G.
Please answer these and find the slope intercept form for each one.
Best answer gets brainliest!
What is the square root of 111.2
Answer:
Well that whole thing is to the power of 2, so whatever the square root is, it gets multiplied by itself again just to get 111.2, so the solution to that question is 111.2.
Show that (√7+i√3/√7-i√3 + √7-i√3/√7+i√3) is real
Answer:
Step-by-step explanation:
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]
On taking LCM, we get
[tex]\rm \: = \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]
and
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]
So, using these Identities, we get
[tex]\rm \: = \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{2(7 - 3)}{7 + 3} [/tex]
[tex]\rm \: = \: \dfrac{2 \times 4}{10} [/tex]
[tex]\rm \: = \: \dfrac{4}{5} [/tex]
Hence,
[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]
simplify the problem 4 . 3 + 1 . 6 + 8 . 4 − 0 . 9
Answer:
13.4
Step-by-step explanation:
4.3+1.6=5.9
5.9+8.4=14.3
14.3-0.9=13.4
Gabriella is building a garden that is 3.6 m long by 7.77 m wide. What is the area of her garden?
30 POINTS, WILL GIVE BRAINLIEST IF ONLY RIGHT
Which of these expressions is equivalent to log 200?
A) 2 + log 2
B) 2 + log 20
C) log 50 + log 150
D) log 250 – log 50
Answer:
ITS A ITS A ITS A
ANSWER = A
Step-by-step explanation:
URGENT PLEASE HELP, respond to c, d, e, and f please !!
Answer:
Step-by-step explanation:
c. (18.5-17)/.9= 1.66666666667= 1.6667
d. .7107
e. .2185
f. 0.675=(x-17)/.9 x= 17.6075
The magnitude of an earthquake measured on the Richter scale is given by:
R(L) = log (l/l0), where l = amplitude.
Find the Richter scale rating of an earthquake with amplitude 1. 80 X 10 l0.
HELP ME PLEASEEEEEEEEEEE
Answer:
1.26
Step-by-step explanation:
R(L)=log((1.8 ×10)=log(18)=1.26
There are 4 times as many dogs as cats if the total number of dogs and cats is 20
how many dogs are there
Answer:5
Step-by-step explanation: 4*5=20
why did lil uzi vert get a diamond in his head
Answer:
Because he thought it would make him stand out.
Solve the problem based on the picture
Step-by-step explanation:
those are the x values in the graph above
now the slope
first, find the derivative = (-2*x)/(9+(6*x^2)+x^4)+(50*Cos(x))/(3+x^2)+((-100*x)*Sin(x))/(9+(6*x^2)+x^4)
then substitute the X values
the slope at first point=0.00214262528
the slope at secondpoint=0.29521512101
the slope at the third point=0.29521512101
Ricardo invests $8650 in an account that earns 3.9% interest compounded weekly. What is the total amount of his investment after 9 years? Round your answer to the nearest dollar.
Based on the amount he invested and the period of his investment, Ricardo's investment worth in 9 years will be $12,286.
The period of compounding is weekly so you first need to convert the interest rate to a weekly rate as well as the period of investment:
= 3.9% / 52 = 3.9/52%
= 9 years x 52 weeks per year = 468
Value of the investment after 9 years is:
= Amount x ( 1 + rate) ^ no. of periods
= 8,650 x (1 + 3.9/52%)⁴⁶⁸
= 12,285.599
= $12,286
In conclusion, the investment would be worth $12,286.
Find out more at https://brainly.com/question/10582389.
a cheetah ran 300ft in 2.92 sec what was the average speed in mph
Answer:
70.05 mph
Step-by-step explanation:
A cheetah ran 300 feet in 2.92 seconds. What is the cheetah's average speed in miles per hour
--------------------------------------
(300 ft/2.92 sec)(1 mi/ 5280 ft)(3600 sec/1 hour)
= {300*1*3600 miles)/(2.92*5280*1 hour)
= 91080000 miles/15417.6 hours
= 70.05 mph
Claire ate dinner at her favorite restaurant. When she received her bill, she wanted to
leave a 15% tip. What is the correct amount for Claire to tip, if the bill was $9.00?
Answer:
$1.35
Step-by-step explanation:
you multiply $9.00 (9) by 15% (.15). Which gives you 1.35.
What is the volume of this rectangular prism
Answer:
Do 7 x 4 = 28 and the bottom is 28
do answer is 56 enjoy brainliest
Can someone help me please ?
Answer:
=
Step-by-step explanation:
1. The square root of 4 is 2 because [tex]2^2[/tex] = 4.
2. The cube root of 8 is 2 because [tex]2^3 = 2* 2 * 2[/tex] = 8.
3. 2 and 2 are equal.
Therefore, the correct symbol is =.
The following relation is a function: {(-1,0), (1,3), (-2,0), (0,4)}.
True
False
Answer:
My answer is true hope this'll help
Can someone help me, please?
Answer:
112
Step-by-step explanation:
|2i+3j| is equal to:
Answer:
Step-by-step explanation:
|2i+3j|=√(2²+3²)=√(4+9)=√13
3.5m/min = how manny miles/hour
Answer:
[tex]\sf\longmapsto0.13 miles/hour[/tex]
Step-by-step explanation:
Firstly we have to use the formula to find the miles/hour
[tex]\sf\longmapsto \: Formula:Divide \: the \: speed \: value \: by \: 26.822.[/tex]
[tex]\sf\longmapsto \: 3.5 \div 26.822[/tex]
[tex]\sf\longmapsto \: 0.13 miles/hour[/tex]
Show 2 + 5 in number line.
Help ASAP I’ll mark you as brainlister
Pablo's father is 4 years older than his mother. Pablo's mother is 42 years old. How old is his father? Pablo's father's age is:
Answer:
46
Step-by-step explanation:
1 sum 42+4