[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]
Manuel is thinking about ordering some graphic T-shirts online. They cost $9 each, and shipping costs $8 regardless of order size. Write an equation that shows the relationship between the number of T-shirts Manuel buys, x, and the total amount he will pay, y. Do not include dollar signs in the equation.
Answer:
y = T(x) = 8 + (9/shirt)x
Step-by-step explanation:
Represent "total amount" by T(x). Then:
y = T(x) = 8 + (9/shirt)x
Here the shipping cost ($8) is a fixed cost and the cost of the x shirts is ($9/shirt)(x), where x is the number of shirts bought.
Note that this is a linear equation, and that 8 represents the vertical intercept and (9/shirt) the slope of the line representing the total cost.
The equation that shows the relationship between the number of T-shirts Manuel buys, x, and the total amount he will pay, y is y = 9x + 8.
The total amount Manuel will pay consists of the cost of the T-shirts and the shipping cost.
The cost of the T-shirts is $9 each, and the shipping cost is a flat $8.
The equation that shows the relationship between the number of T-shirts Manuel buys (x) and the total amount he will pay (y) can be written as y = 9x + 8.
Hence, y = 9x + 8 is the equation that shows the relationship between the number of T-shirts Manuel buys, x, and the total amount he will pay, y.
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please help with solving systtems of equation by graphing I'm lost
Answer:
Solution is (3, -3)
Step-by-step explanation:
To solve by graphing, you literally have to graph both lines to see where they intersect. That point of intersection is the solution to the given system.
Given the following linear equations:
y = - x where the slope (m) = -1, and the y-intercept (b) = 0.
y = x - 6 where the slope (m) = 1, and the y-intercept (b) = -6.
Plot the intercepts (0, 0) for the first line, and (0, -6) for the second line, as a starting point, then use the given slopes (rise over run) of each line to plot the next points. Repeat the process until you have enough points to connect with and create a line.
Attached is a screenshot of the graphed systems of linear equations. It shows that the solution is (3, -3).
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What is the slope of this graph?
^-4
^1/4
^4
^-1/4
Answer:
It’s -4
Step-by-step explanation:
Your equation is y=-4x -3
The radius of a sphere is increasing at a rate of 0.5 centimeters per minute. At a certain instant, the radius is 17 centimeters.
What is the rate of change of the volume of the sphere at that instant (in cubic centimeters per minute)?
Using implicit differentiation, it is found that the rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is of:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
In this problem, we have that [tex]\frac{dr}{dt} = 0.5, r = 17[/tex], thus:
[tex]\frac{dV}{dt} = 4\pi (17)^2(0.5) = 1815.84[/tex]
The rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.
A similar problem is given at https://brainly.com/question/11496075
Find the missing angle measure.
Can someone tell me the answer to this please
Answer:
sum of all angles of a triangle= 180°
Let angle A be x,
then 63°+90°+x=180°
x=17°
[tex]f(x)=\frac{2x}{x-1}[/tex]
[tex]f(a); f(a+h); \frac{f(a+h)-f(a)}{h}[/tex]
Please answer this it’s very hard for me
Answer:
C, D, E, F
Step-by-step explanation:
Remember y=mxb?
m is slope and b is y-intercept
so y=2/7x-9
Remember that slope is RISE/RUN so for every 2 squares that you go up, you go 7 squares to the right.
Also remember that since your graph is going thru your Cartiesian Plane in quadrent 4, your y value in your ordered pairs will most probably be a negative.
Please see the image to help you viualize this.
if kathy had 1700 apples and split with her 4 friends. and then one friend give her back 15 apples. and she gives then 1 apple back. how. much does she have.
Answer:
439
Step-by-step explanation:
1700/4=425
15-1=14
425+14=439
Can someone answer this really quick
NOT CONGREUNT!! There is no axiom to prove congruent.
Rosalyn is a teacher who plays a review game with her class. The name involves writing each student's name on
an identical slip of paper and selecting students at random Here's the makeup of her class
10th 11th 19
Number of students
18
Suppose that Rosalyn wants 2 different students, so she ples 2 names without replacing names between picks
What is the probability that both students selected are 11th graders!
Round your answer to two decimal places.
Using the principle of probability, probability of selecting 2 students without replacement and being 11th graders is 0.230
The distribution of students :
11th graders = 1810th graders = 19Total number of students = 18 + 19 = 37Recall :
Probability = required outcome / Total possible outcomesSince, selection is done without replacement :
P(both are 11th graders) = (18/37) + (17/36) = 0.230
Therefore, the probability that the two selected students are 11th graders is 0.230
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Which is the correct simplified version of the expression 32x+8-34x? *
1 point
66x+8
74x
-2x+8
6x
Evaluate -5x+8 when x=3 The value of the expression is
Answer:
-7
Step-by-step explanation:
replace x by 3
-5^3+8
-15+8
=-7
Ray GI bisects ∠DGH so that m∠DGI is 3x-9 and m∠IGH is 2x + 21. Find the m< DGI.
Answer:
[tex]3x - 9 = 2x + 21 \\ 3x - 2x - 9 = 2x - 2x + 21 \\ x - 9 = 21 \\ x - 9 + 9 = 21 + 9 \\ x = 30[/tex]
m<DGI = 80°
[tex]3x - 9 = \\ 3(30) - 9 = \\ 90 - 9 = 81[/tex]
The measure of angle ∠DGI can be obtained by finding the solution of the equation as 81°.
What is a linear equation?A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.
It can be represented as a straight line on a graph.
The ray GI bisects ∠DGH.
It implies that the new angles are equal in measurement.
⇒ m∠DGI = m∠IGH
⇒ 3x - 9 = 2x + 21
⇒ x = 30
Then, in order to calculate m∠DGI, plug x = 30 in 3x - 9 as,
3 × 30 - 9 = 81
Hence, the measure of angle ∠DGI is given as 81°.
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Can someone please help
Answer:
<ABC = 70 degrees
<AMC = 60 degrees
< AMB = 60 degrees
Step-by-step explanation:
<ABC = 180-110 = 70 degrees
<AMC = 2x + 60 = 180
2x = 180 - 60
x = 120/2
x = 60
<AMB = 180/3 = 60
If the line t is a transversal of lines I and m, NAME THE SPECIAL ANGLE PAIR RELATIONSHIP of the given angle pairs.
Answer:
a. <1 and <3
Step-by-step explanation:
Which of the following equations listed below has a radius of 3?
O A) x^2 + y^2 + 12x - 20y+ 132 = 0
-
O B) x^2 + y^2 + 12x - 20y + 55 = 0
-
O C) x^2 + y^2 - 12x+ 20y + 127 = 0
-
O D) x^2 + y^2 – 20x – 16y + 155 = 0
Answer:
C.
Step-by-step explanation:
WE need to convert the given equations into the standard form
(x - a)^2 + (y - b)^2 = r^2 where r = the radius.
x^2 + y^2 + 12x - 20y+ 132 = 0
(x + 6)^2 - 36 + (y - 10)^2 - 100 = -132
(x + 6)^2 + (y - 10)^2 = -132 + 36 + 100 = 4
giving a radius of 2
x^2 + y^2 + 12x - 20y + 55 = 0
will give a right hand side of -55 + 36 + 100 = 81 giving radius 9.
x^2 + y^2 - 12x+ 20y + 127 = 0
- gives right hand side of -127 + 36 + 100 = 9 giving a radius of 3.
Answer:
The answer is C I hope this helps
Given the definition of rational numbers, are decimals like 0.5 and 0.3 rational numbers? Why or why not?
Answer:
Yes they are rational numbers
Step-by-step explanation:
Given decimals like 0.5 and 0.3 are rational numbers because they are terminating decimals and can be written as p/q
What are rational numbers?Rational numbers are numbers which can be written in the form p/q , where p and q are integers ,q≠0, highest common factor of p and q is 1.
The decimal expansion of rational number are terminating decimal expansion or non terminating and recurring decimal expansions.
Examples of rational number: 1/2 , 3/4, 13/2, 0.125,0.5, 0.55555....,
0.1212121212.....
As the given decimals 0.5 and 0.3 have terminating decimal expansion therefore they are rational numbers.
The rational form of 0.5 and 0.3 are
0.5 = 5/10 = 1/2
∴ 0.5 is written as p/q with p= 1 and q =2≠0 , p and q are coprime
0.3 = 3/10
∴ 0.3 is written as p/q with p= 3 and q =10≠0 , p and q are coprime
Therefore, 0.5 and 0.3 are rational numbers.
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PLEASE HELP IF YOU KNOW THE ANSWER!!!
I NEED THE DOMAIN AND RANGE
oh yeah i know the answer. thats cool you need it
pls help!!!!!!! i will give brainliest!!!!!
Answer:
There is a strong positive correlation
Step-by-step explanation:
The graph shows as more students study the higher the test score is.
There has been a person on here posting the same link to many answers, can you please delete their account? Thanks.
Yeah... they should.
C(t)=55t+175 represent the total cost for a quilter to make t quilts.
Answer:
what is this question asking for
Hi I am so stuck on this question pls help
Answer:
4500 cm²
Step-by-step explanation:
10 mm = 1 cm
So 450 × 10
= 4500 cm²
1.
What is misleading about the graph?
"MASSIVE INCREASE IN
HOUSE PRICES THIS YEAR!”
HELP PLSSS THIS IS HARD SOMEONEEE
Answer:
Chase is correct. the first one
Step-by-step explanation:
13) What are the solutions to y2 = 81?
Step-by-step explanation:
y²=81
y²=9²
:. bases same powers equal,
y=9.
hope this helps you.
The produce of 2 and the difference of a number and 1
Answer:
2*(n-1) represent the product of 2 and the difference of number and 1.
mark me brainlist plz.
An election is over and a new city council member has been elected. The new councilman received 3 votes for every vote received by his opponent. The new councilman received 2763 votes. How many votes did his opponent receive?
Answer:
921
Step-by-step explanation:
If he recives 3x amount than his oppenent
than we would divided by 3 from his score to find oppponets score
so....
2763 divided by 3=921
it takes 2/3 of an hour to paint 2/5 of a room
Answer:
1 and 2/3 hours or 5/3 hours
Step-by-step explanation
1/3 of an hour would be 1/5 of the room so you would just make it 5/3 hours and it'd be the whole room
how do you do this 1
2
3
−
6
7
=
Answer:
4/21
Step-by-step explanation:
Hope this helps
If it takes 5.5 hours to fill a 4.675 gallon swimming pool, how many gallons can be filled in one hour?
Answer:
0.85 gallons
Step-by-step explanation:
4.675(gallons) dived by 5.5(hours). Hope it helps