y is inversely proportional to the square of x find an equation for y in terms of x
Answers
hmmm from the table, let's just pick one point since we know "y" is inversely proportional, so hmmm let's say hmm the point when x = 4 and y = 9/16
a)
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" inversely proportional to }x^2}{ {\LARGE \begin{array}{llll} y = \cfrac{k}{x^2} \end{array}}}\qquad \textit{we also know that} \begin{cases} x=4\\ y=\frac{9}{16} \end{cases} \\\\\\ \cfrac{9}{16}=\cfrac{k}{(4)^2}\implies \cfrac{9}{16}=\cfrac{k}{(16)}\implies \cfrac{9(16)}{16}=k\implies 9=k~\hfill \boxed{y=\cfrac{9}{x^2}}[/tex]
b)
when y = 16, what's "x"?
[tex]16=\cfrac{9}{x^2}\implies x^2=\cfrac{9}{16}\implies x=\pm\sqrt{\cfrac{9}{16}}\implies x=\pm \cfrac{\sqrt{9}}{\sqrt{16}}\implies \stackrel{positive~value}{x=+\cfrac{3}{4}}[/tex]
Related Questions
Find a number such that one-half of the number is three more than one-fourth of the number.
Answers
The number such that one-half of the number is three more than one-fourth of the number is 12.
It is given in the question that a number is such that one-half of the number is three more than one-fourth of the number.
We have to find the number.
Let the number be x.
According to the question, we can write,
x/2 = x/4 + 3
Solving the linear equation, we get,
x/2 - x/4 = 3
(2x - x)/4 = 3
x/4 = 3
x = 4*3
x = 12
Hence, the number such that one-half of the number is three more than one-fourth of the number is 12.
To learn more about linear equation, here:-
https://brainly.com/question/13738061
#SPJ4
Which set of values contains no integers?
A. {-5, 9/3, 7.2}
B. {2.2361, 4, 7.8}
C. {-12, -3.33, 2.6458}
D. {-23/5, 2.4495, 5.1}
Answers
Answer:
D
Step-by-step explanation:
Integers found in:
A: -5, 9/3 = 3
B: 4
C: -12
Hope this helped! ^^
Which of the following options are examples of how you can name the angle?
Answers
Answer:
<STP
Step-by-step explanation:
please help me with this problem
Answers
Answer:
The equivalent fraction of 6/9 is 4/6
Explanation:
9 divided by 6 = 1.5
6 x 1.5 = 9
please help thank youuuu
Answers
Answer: 87/100
Step-by-step explanation:
Is the following statement true or false?
The intersection of three planes can be a point
Answers
Answer: Sometimes true
Step-by-step explanation:
This statement is sometimes true. If three planes intersect, then their intersection can be a line or a point.
Shaneya purchased a membership to play basketball at her local gym. The membership costs $150 for the year, plus she pays $2 to rent equipment each time she goes. If Shaneya doesn't want to spend any more than $300 on basketball for the year, what is the maximum amount of times can she go to the gym to play?
Answers
Answer: maximum amount: 75 times a year
Step-by-step explanation:
#12: m∠GKH = ____
need the answer
Answers
Check out the attached photo
The equation of line j is y+5=8(x+4). Perpendicular to line j is line k, which passes through the point (4, – 1). What is the equation of line k?
Answers
8x+y=31
perpendicular means the slopes are opposite reciprocals of each other. perpendicular to: y +5= 8(x +4) → m = 8 m⊥ = -8
Input the slope (m⊥ = -8) and the point (x₁, y₁) = (4, -1) into the Point-Slope formula: y - y₁ = m(x - x₁)
y - (-1) = -8(x -4)
y + 1 = -8 x + 32 simplified
8x+y =31
learn more of perpendicular line here
https://brainly.com/question/11917669
#SPJ9
Five sections of fencing around a garden are 7 yards long, 8 3/4 yards long, 12 1/2 yards long, 15 1/3 yards long, and 7 3/4 yards long. What is the total length of the fencing?
Answers
Answer: 51.33
Step-by-step explanation:
7+8.75+12.5+15.33+7.75 = 51.33
y=-1/14x+33/14 in standard form
Answers
Answer:
Step-by-step explanation:
1) Find the LCD and multiply what is missing: LCD (x)(14)
-1x/14x + 33/14x
2) Get rid of the denominators
-1x+33
-x+33
That should be right! Sorry if it isn't!
What is 7[2.5 + 3(12 - 7)] and can you please show me how to do it
Answers
Answer: 122.5
Step-by-step explanation:
First, you have to do the distributive property for all numbers. In order to do that, you must first combine like terms.
Combining like terms are numbers that are in the parenthesis that don't have an exponent, variable, etc. In this case, you would combine 12 and -7 since they are in the same parenthesis case. 12-7 would be 5. Now, you have 7[2.5] + 3(5)]
Next, you use PEMDAS which means multiplication (parenthesis) is next which means you multiply 3 and 5. 3x5 - 15.
After that, you combine like terms again with the 2.5 and the 15 since the 15 is now out of the parenthesis. 2.5 + 15 = 17.5
Finally, you take the 7 and multiply that by 17.5 now that you have those 2 numbers left and they are in the brackets. 17.5x7 is 122.5!
However, if there is a variable to solve for, then the answer would be none/no solution because both sides are not equal.
Help, Theres a time limit!
Answers
Answer:
The answer is 2.72 * 10^8 sec.
Step-by-step explanation:
Distance between Earth and Sirius is 5.062 * 10^13 miles.
Time taken = Distance travelled/speed
5.062*10^13 miles/sec/1.86*10^5 miles.
=2.72 * 10^8 sec.
So this means that the time taken to travel light from Sirius to Earth is 2.72*10^8.
A teacher surveys a random group of students about their preference for doing classwork
online or on paper. The results are shown in the table below.
STUDENT CLASSWORK
PREFERENCE
Preference
Online
Paper
Number of
Students
17
8
Based on the results, how many students out of 350 will most likely have a preference to
do their classwork online?
Show your work.
Answers
The number of students those who will most likely have their preference to do their classwork online is 238 out of 350
According to the question statement, A teacher surveys a random group of students about their preference for doing classwork online or on paper.
17 Preferred Online and 8 Preferred on paper.
We are supposed to find the number of students who will most likely have their preference to do their classwork online.
We will be using the concept of Probability for solving this.
[tex]Probability(Event)=\frac{Favourable Outcomes}{Total Outcomes}[/tex]
Probability(Event) = Favorable Outcomes/Total Outcomes
For the survey probability of students preferring online mode of classwork is = [tex]\frac{17}{17+8} =\frac{17}{25}[/tex]
= [tex]0.68[/tex]
Now if we consider a group of 350 students and probability of students preferring online mode of classwork as 0.68
Let the number students preferring online mode of classwork be "x"
so [tex]\frac{x}{350} =0.68[/tex]
or [tex]x=0.68*350\\x =238[/tex]
Therefore, the number of students those who will most likely have their preference to do their classwork online is 238 out of 350
Probability: P(A) = n(A)/n(S)where P(A) is the probability of an event “A”, n(A) is the number of favorable outcomes and n(S) is the total number of events in the sample space.
If you want to learn more about probability, click on the link given below:
https://brainly.com/question/11234923
#SPJ9
Colton looks around at an assembly. he notices his younger sister to his right and his older brother 7 feet ahead of him. if colton's brother and sister are 8 feet apart, how far apart are colton and his younger sister? if necessary, round to the nearest tenth.
Answers
Colton is approximately 3.9 feet apart from his younger sister.
Pythagoras Theorem:
The statement o the Pythagoras theorem is, "if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. "
Then it can be written as,
BC² = AB² + AC².
Where,
AB is the base,
AC is the altitude (height), and
BC is the hypotenuse.
Given,
Colton looks around at an assembly. he notices his younger sister to his right and his older brother 7 feet ahead of him.
And Colton's brother and sister are 8 feet apart.
Now, we need to find the distance between Colton and his younger sister.
Based on the given statement, we can draw their position like the following figure.
Here B represents the position of Colton, A represents the position of his older brother and C represents the position of his younger sister.
Now, we have to use the Pythagoras Theorem in order to solve it,
=> 8² = BC² + 7².
=> 64 = BC² + 49
=> 64 - 49 = BC²
=> BC² = 15
=> BC = √15
Therefore,
=> BC ≈ 3.9 feet
Therefore, the distance between Colden and his younger sister is approximately 3.9 feet.
To know more about Pythagoras Theorem here.
https://brainly.com/question/343682
#SPJ4
4.51X3=
SHOWN WORK 13.53
Answers
Multiplication is the opposite of division. When we multiply 4.15*3 we get 13.53.
What do you mean by multiplication?Multiplication is one of the four basic arithmetic operations, alongside the addition, subtraction, and division. In math, multiply means the repeated addition of groups of the equal sizes.
The symbols for multiplication are cross (x), asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).
Commutative Property: According to this property, when we multiply two numbers, the result will not change depending on the order.
Associative property: It states that if we multiply three or more numbers consecutively, the order is irrelevant.
4.51
X 3
-----------
13.53
-----------
To know more about division visit: https://brainly.com/question/25921802
#SPJ9
Using the protractor tool on the right, choose the image that represents an angle that is 100°.
Answers
Answer:
If I'm right it should be B.
Step-by-step explanation:
I looked it up
Evaluate the expression for X=6 y= -1 4x + 5y
Answers
We know the value of x and y,
x = 6 and y = -1 [Given]
Substitute the value,
4x + 5y4(6) + 5(-1)24 + (-5)24 - 519 Ans.The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 60 feet. If w is the width of the rectangle, which expression represents the length? w+5 w-5 5w 1/5w
Answers
The length expression is 6 + w
How to determine the length expression?The given parameters are:
Length =6 more than the width
Width = w
Perimeter = 60
Subsitute Width = w in Length =6 more than the width
This gives
Length =6 more than the w
More than mean +
So, we have
Length = 6 + w
Hence, the length expression is 6 + w
Read more about perimeter at:
https://brainly.com/question/24571594
#SPJ1
A yard has a perimeter of 190 feet. If four times the length of the yard equals 15 times the width, what are its dimensions
Answers
We get the dimensions of the park as length = 75 feet and width = 20 feet.
We are given that:
A yard has a perimeter of 190 feet.
Also, four times the length of the yard equals 15 times the width.
Now,
Let the length of the yard be x.
ATQ, we get the width of the yard as:
15 width = 4 x
Width = 4 / 15 x
Perimeter = 2 ( l + b )
190 = 2( x + 4 / 15 x )
95 = 19 x / 15
19 x = 95 × 15
19 x = 1425
x = 1425 / 19
x = 75 feet.
Length = 75 feet
Width = 4 / 15 x = 20 feet.
Therefore, we get the dimensions of the park as length = 75 feet and width = 20 feet.
Learn more about perimeter here:
https://brainly.com/question/24571594
#SPJ9
M
80.7°
Solve x
29°
N
Answers
Answer:
So what's M and N?
Step-by-step explanation:
PLEASE AM BEGGINNN YOUUUUU
Answers
Answer:
Step-by-step explanation:
A)
A - the population after its decrease
x - the number of years in which there has been a decrease in population
Hence,
[tex]\displaystyle\\A=30000-475x\\A+475x=30000-475x+475x\\A+475x=30000\\A+475x-A=30000-A\\475x=30000-A[/tex]
Divide both parts of the equation by 475:
[tex]\displaystyle\\x=\frac{30000-A}{475}[/tex]
B)
[tex]\displaystyle\\x=\frac{30000-24300}{475} \\\\x=\frac{5700}{475}\\\\x=\frac{12*475}{475} \\\\x=12\ years[/tex]
Say you are given the graph of a line y=-x. Write an equation that intersects the given line but is not perpendicular to it. PLEASE ANSWER!!! NEED EXTREME HELP!!!
Answers
Answer:
fdsjfgdndgnxhñgjxgjxgjx
f(x) = 12x + 10 is a function which can used to to calculate a person's daily paycheck.
Which would be a reasonable domain for this function?
A : all real numbers
B : 0
C : 0
D : 0
Answers
A : all real numbers
Answer:
A. All real numbers.
Step-by-step explanation:
Is height discrete or continuous data? Give a reason for your answer.
please help
Answers
Answer: Continuous data
Step-by-step explanation:
The graph of the function f(x) = -(x + 3)(x - 1) is shown
below.
-6 -4-2
6
A
2
-2
-4
-6-
y
2
4
6
→
X
What is true about the domain and range of the function?
The domain is all real numbers less than or equal to
4, and the range is all real numbers such that -3 ≤x≤
1.
The domain is all real numbers such that -3 ≤ x ≤ 1,
and the range is all real numbers less than or equal to
4.
The domain is all real numbers, and the range is all
real numbers less than or equal to 4.
The domain is all real numbers less than or equal to
4, and the range is all real numbers.
Answers
The cheerleaders want to raise money to go to camp, so they decide to sell spirit ribbons. They will earn 50¢ for each ribbon that they sell. However, they have to purchase the ribbons first for a total cost of $75. Use the table below to figure their total profit from selling ribbons.
What is the total profit after selling 0 ribbons?
Answers
Using a linear function, we have that:
The rule is P(x) = 0.5x - 75.The total profit after selling 0 ribbons is of -$0.75.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, when x increases by 10, the profit increases by 5, hence the slope is:
m = 5/10 = 0.5.
Then:
P(x) = 0.5x + b.
When x = 10, P(x) = -70, hence:
-70 = 0.5(10) + b
b = -75.
Hence:
The rule is P(x) = 0.5x - 75.The total profit after selling 0 ribbons is of -$0.75.More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Please help I have no idea
Answers
Answer: a=5
Step-by-step explanation:
-4(7a+5)=-160
-28a-20=-160
-28a-20+20=-160+20
-28a=-140
a=5
What is the solution to this equation?
5(x-6) + 3 = -7
OA. x=4
OB. x=2
OC. x=3
OD. x = 5
SUBM
Answers
Answer:
the is X=4
Step-by-step explanation:
Distribute
5(x-6)+3= -7
5x-30+3= -7
add numbers
5x-30+3= -7
5x-27= -7
add 27 to both sides
5x-27= -7
5x-27+27= -7 + 27
simplfly
5x=20
divide both sides by 5
5x = 20
-- ----
5. 5
5 and 5 are off
divide 20 by 5
20/5= 4
therefore x= 4
hope this help if it does help I'd be happy if you follow and give me the brainliest answer
2(6-9)-31 helpppppppppppppppp
Answers
Answer: -37
Step-by-step explanation:
Use order of operations
2(6-9)-31
2(-3)-31
-6-31
= -37
