================================================
Work Shown:
[tex]a \bowtie b = a + \sqrt{b+\sqrt{b+\sqrt{b+...}}}\\\\7 \bowtie g = 7 + \sqrt{g+\sqrt{g+\sqrt{g+...}}} = 9\\\\\sqrt{g+\sqrt{g+\sqrt{g+...}}} = 2[/tex]
After subtracting 7 from both sides.
Note how because we have an infinite sequence of nested radicals, we can let [tex]x = \sqrt{g+\sqrt{g+...}}[/tex] which means x is equal to 2 as well.
This lets us say
[tex]\sqrt{g+\sqrt{g+\sqrt{g+...}}} = \sqrt{g+x} = x[/tex]
Solve the equation [tex]\sqrt{g+x}= x[/tex] for x to get
[tex]\sqrt{g+x} = x\\\\g+x = x^2\\\\x^2-x-g = 0\\\\x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-g)}}{2(1)}\\\\x = \frac{1\pm\sqrt{1+4g}}{2}\\\\x = \frac{1+\sqrt{1+4g}}{2} \ \text{ or } \ x = \frac{1-\sqrt{1+4g}}{2}[/tex]
Since x is positive, this means we only focus on the first equation in the last line above.
Earlier we let x be equal to the infinite nested radicals involving g, but x is also equal to 2. So plug in x = 2 and use that to find g.
[tex]x = \frac{1+\sqrt{1+4g}}{2}\\\\2 = \frac{1+\sqrt{1+4g}}{2}\\\\4 = 1+\sqrt{1+4g}\\\\3 = \sqrt{1+4g}\\\\9 = 1+4g\\\\1+4g = 9\\\\4g = 8\\\\g = 2\\\\[/tex]
As a check, we can do the following
[tex]7 + \sqrt{2+\sqrt{2}} \approx 8.84775906502258\\\\7 + \sqrt{2+\sqrt{2+\sqrt{2}}} \approx 8.96157056080647\\\\7 + \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}} \approx 8.9903694533444\\\\[/tex]
we're slowly approaching 9
Answer: [tex]g = \boxed{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{g+\sqrt{g+\sqrt{g+...}}}=2[/tex]
implies that
[tex]\sqrt{g+\sqrt{g+\sqrt{g+...}}}=\sqrt{g+2}=2[/tex].
Squaring both sides of this new equality, we have [tex]g + 2 = 4 \implies g = \boxed{2}[/tex]
According to the bar graph, how many more pages did the winner of the contest read than the loser? Show your work or explain how you got your answer.
Well look at the question.
It is asking you the total difference between the winners score to their opponents score in the contest.
Going by how the graph looks, approximately:
Javi's scores are 10, 20, 60, 20, and 15.
MeriAnne's scores are approximately 20, 30, 40, 20, and 10.
Add all those numbers up individually for each contestant.
Javi has a total score of 125.
Meri has a total score of 120.
Subtract the total scores from each other, as so:
125 - 120 = 5.
Javi read 5 more pages than Meri.
1+1=?.........................................
Answer:
Its 11
Step-by-step explanation:
put 2 ones together and u get 11
-Big Brain Moment-
IT TOOK SO LONG FOR ME TO GET THE ANSWER TO THIS QUESTION
If x = -2,y=-6 and z=4.Find the value of the following. a) 4z+2y-x. Please help.50 points . ASAP
4(4)+2(6)-(-2)
16+2(6)-(-2)
multiply 2 by 6
16+12-(-2)
multiply -1 by -2
16+12+2
add 16 and 12
28+2
add 28 and 2
30
so your answer is 30
please answer!!! click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Solve each equation. 5x^2 + 500 = 844.45
Answer:
5[tex]x^{2}[/tex] = 344.45
[tex]x^{2}[/tex] = 68.89
x = ± [tex]\sqrt{68.89}[/tex]
x = 8.3, −8.3
An urn contains white and red balls. Four balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all balls drawn from the urn are red
Answer:
[r/(w + r)]^4
Step-by-step explanation:
The numbers of the different balls are not given, but here is the solution.
Let w = number of white balls.
Let r = number of red balls.
The total number of balls is w + r.
All drawings have the same probability since there is replacement.
Each drawing has the following probability of drawing a red ball:
p(red) = r/(w + r)
Since there are 4 drawings, and they are all independent events, the overall probability is the product of the individual probabilities.
p(4 red balls in 4 drawings) = [r/(w + r)]^4
To find an actual number, replace w and r with the correct numbers and evaluate the expression.
find the L.C.M of 154 and 49.
Answer:
LCM=1078
Step-by-step explanation:
49=7×7
154=7×11×2
LCM=7×7×11×2
=1078
Answer:
[tex] \boxed{ \huge{ \bold{ \boxed{ \sf{1078}}}}}[/tex]
Step-by-step explanation:
The L.C.M of any numbers can be obtained by using two methods and they are :
Prime factorization methodDivision methodI am going to find the L.C.M of 154 and 49 by using these two methods :
1. Prime factorization method:
[tex] \sf{154 \: and \: 49}[/tex]
First of all , find the prime factors of each numbers.
[tex] \sf{154 =2 \times 7 \times 11}[/tex]
[tex] \sf{49 \: = \: 7 \times 7}[/tex]
Take out common prime factor i.e 7
Thenafter, also take out the other remaining prime factors : 2 , 11 and 7
L.C.M = Common factors × Remaining factors
= 7 × 2 × 11 × 7
= 1078
------------------------------------------------------------
Next method :
2. Division method
[tex] \sf{154 \: and \: 49}[/tex]
Steps :
⇒ Arranging the given numbers in horizontal position.
⇒Thus, arranged numbers should be divided by a prime number. During this process that prime numbers should divide any two or more given numbers.
⇒Repeat the process till you get prime number as quotient for each number.
⇒The product of all prime factors and last quotients is L.C.M
( see attached picture )
Hope I helped!
Best regards!!
Let ∠BOC=x+3, ∠AOB=4x−7, and ∠AOC=21. Solve for x.
Answer:
5Step-by-step explanation:
Given the following angles ∠BOC=x+3, ∠AOB=4x−7, and ∠AOC=21, the expression is true about the angles;
∠AOC = ∠BOC+∠AOB
Substituting the given values into the expression, we will have;
21 = x+3+4x-7
collect the like terms
21 = x+4x+3-7
21 = 5x-4
Add 4 to both sides
21+4 = 5x-4+4
25 = 5x
Divide both sides by 5
5x/5 = 25/5
x = 5
Hence the value of x is 5
64 + 13 + (-83) Thanks for taking time out of your day your help
if 3 divide a profit of rs 72,000 at end of the year according to the ratio of 2:3:4 of their investment how much did they receive
Step-by-step explanation:
Hey, there!!
See explanation in picture.
They receive 16000, 24000 and 32000 as per the ratios 2:3:4.
let x be a common factor,
Then,
2x+3x+4x =72000
sum them,
9x= 72000
x = 72000/9
=8000
Therefore, x= Rs. 8000.
2x= 8000×2 = Rs.16000
3x= 3×8000= Rs.24000
4x= 4×8000= Rs. 32000
You just need to put common factor on the ratios and then sum up them to get the value.
Hope it helps..
please help me on this
Answer:
reflection across the y- axis
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y )
Thus
The given transformation rule (x, y ) → ( - x, y )
Represents a reflection in the y - axis
For the function p defined by p(m) = 2m2 - 4m +3, find p(-2).
Answer:
p(m) = 2m² - 4m +3
p(-2) = 2(-2)² - 4(-2) + 3
= 2 × 4 - 4 × (-2) + 3
= 8 + 8 + 3
= 16 + 3
= 19
The value of p(-2) of function p(m) = 2m² - 4m +3 is 19.
What is function?The function is defined as mathematics expression defines a relationship between one variable and another variable. When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that value of x determines what value of y will be. This relationship can be expressed as follows: y = f (x)
What is quadratic expression?The quadratic expression is defined as an expression containing the highest power of a variable is two.
For the function p defined by p(m) given as :
p(m) = 2m² - 4m +3,
To determine the value of p(-2).
p(m) = 2m² - 4m +3,
Substitute the value of m = -2 in the function,
p(-2) = 2(-2)² - 4(-2) +3,
p(-2) = 2(4) + 8 +3,
p(-2) = 8 + 11
p(-2) = 19
Hence, the value of p(-2) is 19.
Learn more about function here :
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THIS NEEDS TO GET DONE FAST! I DONT KNOW HOW TO SOLVE IT!
Answer:
8.5
Step-by-step explanation: it might be wrong btw, but i think its right. the question isnt worded very well
A number has the property that its square is equal to 84 more than five times the number. Enter all numbers that have this property.
Answer:
The numbers for which the given property hold true are 12 and -7
Step-by-step explanation:
Let the number be [tex]x[/tex].
As per the given statement:
Square of the number ([tex]x^{2}[/tex]) is 84 more than five times of the number ([tex]5x+84[/tex]).
Writing in the equation form:
[tex]x^{2} =5x+84[/tex]
To find:
All the numbers for which above equation holds true.
Solution:
[tex]x^{2} =5x+84[/tex]
Let us solve the above equation by rearranging the terms and then let us find the roots of the equation.
It is a quadratic equation(i.e. maximum power of [tex]x[/tex] is 2) so it will have 2 solutions i.e. 2 values of [tex]x[/tex] for which the above equation will hold true.
[tex]x^{2} -5x-84=0[/tex]
Let us factorize the equation.
[tex]\Rightarrow x^{2} -12x+7x-84=0\\\Rightarrow x(x -12)+7(x-12)=0\\\Rightarrow (x+7)(x-12)=0\\\Rightarrow \bold{x=12, -7 }[/tex]
So, the numbers for which the given property hold true are 12 and -7.
the sum of n and 7 *
Answer:
n+7
Step-by-step explanation:
Sum means add, so it's just n added to 7:
n+7 :)
Answer:
n+7 is the answer or u can put it in parenthesis (n+7)
Step-by-step explanation:
468−[64÷4×(9÷3−4−2)]
Answer:
the answer is 516
Step-by-step explanation:
Directions: Find the distance between each pair of points
(-4, 6) and (3.-7)
Jika suku pertama suatu barisan geometri = 16 dan suku ketiga = 36, maka besar suku kelima adalah …..
Answer:
Suku yang ke Kelima adalah 56
Kerana anda hanya perlu tambah sepuluh sahaja seperti:
Suku pertama:16
Suku kedua:26
Suku ketiga:36
Suku keempat:46
Suku kelima:56
Harap jawapan tersebut adalah betul and Mark me as BRAINLIEST if the answer is right ✨
A student solves the problem to the left as shown. Which statements describe the solution? Check all of the boxes that apply
Answer:
The stated solution is correct (lengths of 16 feet and 8 feet).
Based on the way the variable is defined, the equation should be x + 2x = 24.
The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.
Step-by-step explanation:
Answer: a, b & d !
Step-by-step explanation:
What is the volume of a certain cube? (1) The sum of the lengths of the edges of the cube is 36. (2) The surface area of the cube is 54.
Answer:
(1) The sum of the lengths of the edges of the cube is 36.
A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3
Volume = 3*3*3 = 27
(2) The surface area of the cube is 54.
A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)
6s^2 = 54
s = 3
Volume = 3*3*3 = 27
Step-by-step explanation:
All you need to uniquely define a cube is any one measurement - length of a side/edge, area of a surface, volume etc. If you have any one of them, you can uniquely determine the others. So each statement alone is sufficient here.
To show how,
(1) The sum of the lengths of the edges of the cube is 36.
A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3
Volume = 3*3*3 = 27
(2) The surface area of the cube is 54.
A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)
6s^2 = 54
s = 3
Volume = 3*3*3 = 27
What statements are true regarding the given statement and diagram? ∠CED is a right angle. ∠CEA is a right angle. m∠CEA = One-half(m∠CEB) m∠CEB = m∠BEA m∠DEB = 135° m∠AEB = 35°
Answer:
A, B, D, and E
Step-by-step explanation: Hope it helps ^w^
Step-by-step explanation: I hope this helps.
Answer:
The Haas Door Co. produces truck dock door seals. Their 9' × 10' seal costs $280 to produce. The mark-up rate is 75% of the cost to produce. What is the retail price?
Answer:
$490 is the retail price
Step-by-step explanation:
75% = [tex]\frac{3}{4}[/tex]
[tex]\frac{280}{4} = 70[/tex]
[tex]70(3)=210[/tex]
[tex]280+210=490[/tex]
The retail price will be; 490 dollar.
What is Markup and Markdown?Markup is the amount that will be increased in the original price of the considered thing.
Markdown is the amount that will be decreased from the original price of the considered thing.
Think of "up" and "down" as increasing and decreasing prices respectively.
We are given that Haas Door Co. produces truck dock door seals. Their 9' × 10' seal costs $280 to produce.
The mark-up rate = 75% of the cost to produce.
Retail price = cost price + 75 % of cost price
Therefore,
Retail price = 280 + 75 % of 280
Retail price = 280 + 0.75 x 280
Retail price = 280 + 210
Retail price = 490
Thus, retail price is $ 490
Learn more about markup and markdown here:
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PLEASE HELP 1kx + 13kx = 6 Solve for x.
Answer:
[tex]\bold{x=\dfrac3{7k}}[/tex]
Step-by-step explanation:
1kx + 13kx = 6
14kx = 6
÷(14k) ÷(14k)
x = 6/(14k)
x = 3/(7k)
HELP ME I GIVE UP PLEASE HELP ASAP
Work Shown:
T = C(3 + AB)
T = 3C + ABC .... distribute
3C + ABC = T
ABC = T - 3C ... subtract 3C from both sides
(AC)*B = T - 3C
B = (T - 3C)/(AC) .... divide both sides by AC
Answer:
T-AB-3=0
Step-by-step explanation:
Momo has $4.05 in dimes and quarters. If she has 5 more quarters than dimes,
how many of each does she have? Show your work and write a complete
sentence answer
Answers:
8 dimes13 quarters==================================================
Work Shown:
$4.05 = 405 cents
d = number of dimes
q = number of quarters
q = d+5 since she has 5 more quarters compared to dimes
10d = value in cents of all the dimes
25q = value in cents of all the quarters
10d+25q = total value in cents = 405
10d+25q = 405
10d+25(d+5) = 405
10d+25d+125 = 405
35d+125 = 405
35d = 405-125
35d = 280
d = 280/35
d = 8
She has 8 dimes
q = d+5 = 8+5 = 13
She also has 13 quarters
-------------------------
1 dime = 10 cents
8 dimes = 80 cents (multiply both sides by 80)
1 quarter = 25 cents
13 quarters = 325 cents (multiply both sides by 13)
8 dimes + 13 quarters = 80 cents + 325 cents = 405 cents
This converts back to $4.05, which confirms our answers.
84 POINTS!!!!!!!! The hands on a clock represents rays. At 6:00, they forn opposite rays. What undefined term do the hands of the clock represents at 6:00?
A. Point
B.Line
C. Plane
D. Space
Answer:
Line of course! So its B
X-2
X + 2
3x + 3
4x + 12
3x + 12
X+4
x+1
Which of the
following
represents
the sum of
three
consecutive
integers?
o
o
Which of the
following
represents
the average
of three
consecutive
integers?
o
О
Answer:
1)3x+3
2)x+1
Step-by-step explanation:
1)consecutive integer = x and x+1 and x+2
x+x+1+x+2= 3x+3
2)average= total sum/number of numbers involved.
average = 3x+3
3
= x+1
Need help solving this equation
Answer:
The answer is 4xStep-by-step explanation:
[tex] ({64 {x}^{3} })^{ \frac{1}{3} } [/tex]
To solve the expression convert 64 to exponential form
That's
64 = 4³
So we have
[tex]( { {4}^{3} {x}^{3} })^{ \frac{1}{3} } [/tex]
Using the rules of indices
That's
[tex]( { {a}^{x} {b}^{y} })^{z} = {a}^{x \times z} . {b}^{y \times z} [/tex]
So for the above expression we have
[tex]( { {4}^{3} {x}^{3} })^{ \frac{1}{3} } = {4}^{3 \times \frac{1}{3} } . {x}^{3 \times \frac{1}{3} } [/tex]
Simplify the expression
We have the final answer as
4xHope this helps you
What is the percentage of change from 50 to 17
Answer:
66%
Step-by-step explanation:
50 - 17 = 33, so that is the difference between the two numbers. Percent change is the change over the original, so 33/50. 33/50 equals 66/100, so the percent change is 66%
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Identify the mapping diagram that represents the relationship and determine whether the relation is a function. {(–2, –4), (–1, –4), (3, –4), (6, –4)}
Answer:
PIC 1: Option 2. this relation is a function
PIC 2. Option 1. this relation is not a function
Step-by-step explanation:
To be a function, the domain (x value) can only have one range (y value). But one range can have multiple domain
PIC 1
Function {(-2, -4) (-1, -4) (3, -4) (6, -4)}
This relation is a function
EXPLANATION: each domain only have one range
PIC 2
Function {(-4, -2) (-4, -1) (-4, 3) (-4, 6)}
This relation is not a function
EXPLANATION: each domain has multiple range.
Hope this helps!! :)
Please let me know if you have any question or need any further explanation
What is the domain of the function shown in the
mapping?
O x x= -5,-3,1,2,6}
O fyy=-9,-6,0, 2, 4)
O(|x=-9,-6.-5.-3, 0, 1, 2, 4, 6)
O fyly = -9,-6, -5,-3,0,1.2, 4, 6)
Answer:
{x | x = -5, -3, 1, 2, 6}
Step-by-step explanation:
In a function, the domain values are all the possible values of input in a function. In order words, they are the x-values in a function, which are also referred to as independent variable.
In the mapping of the function above, all input values make up the domain of the function.
Thus, the domain is:
{x | x = -5, -3, 1, 2, 6}