Answers
Answer:
y = [tex]\frac{24}{\sqrt{x} }[/tex]
Step-by-step explanation:
given y varies inversely as [tex]\sqrt{x}[/tex] then th equation relating them is
y = [tex]\frac{k}{\sqrt{x} }[/tex] ← k is the constant of variation
to find k use the condition y = 8 when x = 9 , then
8 = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
24 = k
y = [tex]\frac{24}{\sqrt{x} }[/tex] ← equation of variation
Related Questions
The following formula models the number of automobiles, A,in thousands, that Washington residents purchased
x years after 1980.
A=2x2+24x+300
A) Write an equation that you can use to determine the first year in which residents purchased approximately 566 thousand cars.
B) Now solve your equation and specify the first year (for example, enter 2019 and not 39) in which residents purchased approximately 566 thousand cars.
Answers
Considering the given quadratic equation for the number of automobiles, we have that:
A) The equation to be solved is: x² + 12x - 133 = 0
B) The first year was of 1987.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The number of automobiles, in x years after 1980, is modeled by:
A(x) = 2x² + 24x + 300.
The amount is of 566,000 when A(x) = 566, hence the equation is:
2x² + 24x + 300 = 566
2x² + 24x - 266 = 0
x² + 12x - 133 = 0
The coefficients are a = 1, b = 12, c = -133, hence:
[tex]\Delta = 12^2 - 4(1)(-133) = 676[/tex][tex]x_1 = \frac{-12 + \sqrt{676}}{2} = 7[/tex][tex]x_2 = \frac{-12 - \sqrt{676}}{2} = -19[/tex]Time is a positive measure, hence we take the solution of 7, 1980 + 7 = 1987, which is the year.
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NO LINKS!! Please help me with this problem
Answers
Answer:
y²/324 -x²/36 = 1
Step-by-step explanation:
Where (0, ±b) are the ends of the transverse axis and y = ±(b/a)x describes the asymptotes, the equation of the hyperbola can be written as ...
y²/b² -x²/a² = 1
ApplicationHere, we have transverse axis endpoints of (0, ±18) and asymptotes of y = ±3x, so we can conclude ...
b = 18
b/a = 3 ⇒ a = 18/3 = 6
The equation of the hyperbola in standard form is ...
y²/324 -x²/36 = 1
At the beginning of 2000 Randall's house was worth 234 thousand dollars and Damien's house was worth 110 thousand dollars. At the beginning of 2003, Randall's house was worth 176 thousand dollars and Damien's house was worth 154 thousand dollars. Assume that the values of both houses vary at an exponential rate.
Write a function [tex]f[/tex] ,that determines the value of Randall's house (in thousands of dollars) in terms of the number of years [tex]t[/tex] since the beginning of 2000.
Write a function [tex]g[/tex] that determines the value of Damien's house (in thousands of dollars) in terms of the number of years [tex]t[/tex] since the beginning of 2000.
How many years after the beginning of 2000 will Randall's and Damien's house have the same value?
Answers
Using linear functions, we have that:
Randall's value is: f(t) = -19t + 234.Damien's value is: g(t) = 14.67t + 110They will have the same value in 3.68 years since the start of 2000.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.We consider the initial values as the y-intercepts. Randall's house decayed 58 thousand dollars in 3 years, hence the slope is:
m = -58/3 = -19.
Hence the function for the value, in thousands of dollars, is:
f(t) = -19t + 234.
Damien's initial value was of 110, and it increased 44 thousand in 3 years, hence the slope is:
m = 44/3 = 14.67
Hence the function for the value of Damien's house, in thousands of dollars, in t years after 2003, is:
g(t) = 14.67t + 110
They will have the same value when:
f(t) = g(t)
-19t + 234 = 14.67t + 110
33.67t = 124
t = 124/33.67
t = 3.68
They will have the same value in 3.68 years since the start of 2000.
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Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 20 more adult tickets han student tickets to the fall play. to If the
class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution
Answers
Answer:
80
Step-by-step explanation:
Let the number of adult tickets sold be a and the number of student tickets sold be s.
"The drama class sold 20 more adult tickets han student tickets to the fall play." means that a-20=s."the class collected $880 from ticket sales" means that 8a+4s=880, which is the same as 2a+s=220.Substituting the first equation into the second,
[tex]2a+a-20=220 \\ \\ 3a-20=220 \\ \\ 3a=240 \\ \\ a=80[/tex]
Merger_Model_Evaluation_-_Question.xlsx 19 The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is: $92,165 $30,498 $92,661
$91,669
Answers
The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is $91,669
How to calculate the value?Share Price, P = 44.29
Premium on the acquisition, p = 20%
Therefore, effective share price for acquisition, P* = P x (1 + p) = 44.29 x (1 + 20%) = $ 53.15
Number of shares outstanding, N = 1,734 MM
Equity value, E = P* x N = 53 x 1,734
= $92,158.63 MM
Net Debt, D = - 496
Hence, the implied enterprise value:
= Equity value + net debt
= 92,158.63 + (- 496)
= $$91,669
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Mrs. Oliver drew a box plot to represent her students’ scores on a mid-term test.
Answers
Answer:
About 1/4 scored higher and 3/4 scored lower
Step-by-step explanation:
84 is on the right side line
Each line represents 25 % of the score
It is 75 percent ( 3 lines) of the way
She scored higher than 75% of the students and lower than 25% of the students
About 1/4 scored higher and 3/4 scored lower
how much money would u get from $521 a second in 19 minutes
Answers
We get $593,940
Answer:
Solution Given:
1 second = $ 521
19 minutes=19*60=1140 seconds
1140 seconds =$521*1140 =$593,940
Answer:
$593,940
Step-by-step explanation:
$521 for every second
First, you need to multiply 60 with 19, since there are 60 seconds in a minute.
We get: 60 × 19 = 1140
Now multiply $521 with 1140
We get: 521 × 19 = 593,940
Final result: $593,940
Hope this helps :)
The dialogue of a square is X units what is the area of the square in terms of X
Answers
The area of the square in terms of x unit is x²/ 2
Diagonal of a square
The expression for the diagonal of a square is written as'
d^2=s^2+s^2
Where
s² is the area of the squared² is the diagonal of the same squareBut from the given question we have that the diagonal of the said square is 'x'
Now, let's substitute the values into the expression of the diagonal given above,
d^2=s^2+s^2
d² = s² + s²
We have,
x² = s² + s²
Collect and add like terms
x² = 2s²
But we know that s² represents the area of the square
So,
x² = 2 × area
Make 'area' subject of formula
Area = x²/ 2
Now, we can say that the area of the square in terms of x units is x²/2
Therefore, the area of the square in terms of x unit is x²/ 2
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1.
Find a polynomial f(x) of degree 3 that has the following zeros.
4, 0, -7
Leave your answer in factored form.
Answers
Answer:
x³+3x²-28x
Step-by-step explanation:
(x-4)(x-0)(x+7)
(x-4)(x)(x+7)
(x-4)(x+7)=(x²+3x-28)
(x²+3x-28)(x)=x³+3x²-28x
use yours formula to find the missing number of faces edges 15 vertices 9
Answers
Using Euler's Formula, the number of faces is given by: 8.
What does Euler's Formula states?It states that the number of vertices, edges and faces is related by the following equation:
V - E + F = 2.
In this problem, the parameters are given as follows:
E = 15, V = 9.
Hence the number of faces is given by:
V - E + F = 2.
9 - 15 + F = 2
F - 6 = 2
F = 8.
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Suppose that the base salary of a salesperson is $30,000 per year. The salesperson gets an additional $50 for every sale. Let x represents the number of sales. How can we model the scenario with a linear function? How many items does the salesperson need to sell to earn $50,000
Answers
Answer:
See below
Step-by-step explanation:
Salary (y) = 30 000 + 50 x
y = 30 000 + 50x where x is the number of sales
How many sales for 50 000 ?
50 000 = 30 000 + 50 x
20 000 = 50 x
x = 400 sales
I. Model Problems
A linear model is a linear equation that represents a real-world
scenario. You can write the equation for a linear model in the same way
you would write the slope-intercept equation of a line. The y-intercept
of a linear model is the quantity that does not depend on x. The slope is
the quantity that changes at a constant rate as x changes. The change
must be at a constant rate in order for the equation to be a linear model.
Example 1 A machine salesperson earns a base salary of $40,000 plus
a commission of $300 for every machine he sells. Write an equation
that shows the total amount of income the salesperson earns, if he sells
x machines in a year.
The y-intercept is $40,000; the salesperson earns a $40,000 salary in a
year and that amount does not depend on x.
The slope is $300 because the salesperson’s income increases by $300
for each machine he sells.
Answer: The linear model representing the salesperson’s total income
is y = $300x + $40,000.
Linear models can be used to solve problems.
Example 2 The linear model that shows the total income for the
salesperson in example 1 is y = 300x + 40,000. (a) What would be the
salesperson’s income if he sold 150 machines? (b) How many
machines would the salesperson need to sell to earn a $100,000
income?
(a) If the salesperson were to sell 150 machines, let x = 150 in the linear
model; 300(150) + 40,000 = 85,000.
Answer: His income would be $85,000.
(b) To find the number of machines he needs to sell to earn a $100,000
income, let y = 100,000 and solve for x:
7/3 4/2 as improper fraction
Answers
Answer:
If the question asked mixed fraction:
7/3 = 2 1/3
4/2 = 2
Step-by-step explanation:
I converted it to mixed fraction because it is already improper fraction.
Ian is playing video games. For every 11 enemies he defeats, he gets 6 points. If he has 24 points at the end of the game, how many enemies has Ian defeated?
Answers
Hi
if he has 24 point he scored 24/ 6 = 4 times
As he score points every 11 ennemies,
He had : 4*11= 44 ennemies.
e) 1 cubic centimetres = 1÷1000000 cubic meter. Rewrite in scientific notation
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{1000000} \: \: m {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{10 {}^{6} } \: \: m {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = {}{10 {}^{ - 6} } \: \: m {}^{3} [/tex]
given the quadriatic equation
x² + 6x + 9 = 4kx
find the set values for which k has real roots
Answers
Answer:
⇒ The given quadratic equation is x2−kx+9=0, comparing it with ax2+bx+c=0
∴ We get, a=1b=−k,c=9
⇒ It is given that roots are real and distinct.
∴ b2−4ac>0
⇒ (−k)2−4(1)(9)>0
⇒ k2−36>0
⇒ k2>36
⇒ k>6 or k<−6
∴ We can see values of k given in question are correct.
Coach Kirby is forming dodgeball teams from students in her physical education class.
She wants teams that each have 6 students. There are fewer than 48 students in the class,
so Coach Kirby can't form as many full teams as she wants.
1)) Let x represent how many full teams Coach Kirby can form. Which inequality describes
the problem?
6x < 48
6x > 48
Solve the inequality. Then, complete the sentence to describe the solution.
1) Coach Kirby can form fewer than 8|
full teams.
Please hurry
Answers
Answer:
6x<48
Step-by-step explanation:
ik its this one because theres 48 players and 6 teams both are even numbers so if you did 48÷6x you would get 8 but theres fewer than 48 kids
It takes Natalie's mother 20 minutes to drive to work. She works 6 miles away.
If she drives the same speed to pick up Natalie at a friend's house that is 14 miles
away, about how long will the drive take?
A 8.7 minutes
B 2.4 minutes
C 45.7 minutes
D 705 minutes
Answers
Answer:
B. 45.7
Step-by-step explanation:
20/6=3.33
3.33*14=46.62
46.62 is closest to 45.7
Therefore, 45.7 is the best answer.
A person needs to fill 15 water jugs with a hose. Filling the first 3 jugs has taken 4 minutes. How long to finish filling the remaining jugs?
Answers
3 divided by 4 = 0.75
0.75 times 12(remaining jugs) = 9 :)
hope this helps!
Answer:
20 minutes
Step-by-step explanation:
Rate x Time = jobs
The rate is 3 jugs/ 4 minutes.
The number of jobs is 15
Use T for time
3/4T = 15 Multiply both sides by 4/3 to get the variable T by itself
(4/3) 3/4 T = 15(4/3)
T = 20 minutes
What is the equation of a line that goes through the point (0, -5) and
has a slope of -3?
O -5y = - 3x
O y = 3x - 5
O y=-3x - 5
O y = -5x - 3
Answers
Answer:
Equation of a line has a form as below:
y=ax+b
Given:
b ( the y intercept)= -5
a ( the slope)= -3
so, y= -3x -5 is the equation of the line.
Please give me Brainliest [:)
A sequence starts 1, -1 . Give a different rule the sequence could follow and the next 3 terms.
Answers
Subtract -2 each time!
(a-1) -2
1
-1
-3
-5
-8
You decide that you want to purchase a Tesla SUV. You borrow $95,000 for the purchase. You
agree to repay the loan by paying equal monthly payments of $1,200 until the balance is paid off. If
you're being charged 6% per year, compounded monthly, how long will it take you to pay off the
loan?
Answers
Answer:
8.5 years
Step-by-step explanation:
It will take 102 more payments
8.5 years
Interest will be $26,239
It would take approximately 15 years to pay back the loan of 95000 which is compounding monthly and the rate of interest is 6%.
What is compound interest?Compound interest is basically the interest which is calculated on the primcipal with addition to aggregate interest. The formula of sum after compounding is as under:
S=P[tex](1+r/n)^{nt}[/tex] in which P is principal amount, r is rate per annum, n is number of times of compounding and t is time period.
How to calculate time?We have been given that the amount of loan is $95000, installment is $1200 , rate of interest is 6% and it is compounded monthly.
First of all we have to find the effective rate=6%/12=0.005.
The future value of 95000 at a rate of 6% compunded monthly should be equal to the amount of all installments. So,
95000[tex](1+0.005)^{12n}[/tex]=12*1200*n
95000[tex]1.005^{12n}[/tex]=14400n
[tex]1.005^{12n}[/tex]=14400n/95000
[tex]1.005^{12n}[/tex]=0.1515n
We have to make graph of this to find the value of n which after graphing will come approx 15.
Hence it would take 15 years to pay back loan amount.
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A ship left a port and sailed east at the rate of 30 miles per hour. One hour later, a second ship left the same port at the rate of 40 miles per hour, also traveling east. In how many hours did the second ship overtake the first ship?
Answers
Answer:
3 hours
Step-by-step explanation:
When the ships meet each other, that means the the distance travelled for both ships are the same, that is where the 2nd ship will overtake the ship.
Distance = Speed * Time
So, given information from the question, and letting x be the time in hours (from when the 1st ship departs), we can deduce:
Distance travelled of 1st ship = Distance travelled of 2nd ship
30x = 40(x-1)
30x = 40x - 40
-10x = - 40
x = [tex]\frac{-40}{-10}[/tex]
= 4
Since we are calculating based on the 2nd ship,
Time taken for 2nd ship to overtake first ship = x - 1 = 4 - 1 = 3 hours.
Find the equation of the line that passes through point (6, 1) with the x-intercept of 2.
Answers
[tex]y = \frac{ - 1}{4} x + \frac{1}{2} [/tex]
Of the stamps in a book, 5/12 came from Brian's collection and 24 came from Amy's. Of the rest, 15 were Jo's, 3/10 were Carl's and 27 were purchased. How many stamps are there in the book? HELPPP
Answers
Algebraic expressions are mathematical statements that consist of both number(s) and alphabet(x). Thus the number of stamps in the book is 66[tex]\frac{43}{60}[/tex] (67).
Algebraic expressions are mathematical statements that consist of both number(s) and alphabet(x). Majorly, the alphabet in the expression is referred to as the unknown value which has to be determined.
When the power of any of the alphabets contained in an algebraic expression is more than one, then it can be referred to as a polynomial.
In the given question, let the number of stamps in the book be represented by N.
So that;
N - 5/12 + 24 + 15 + 3/10 + 27 = 0
N - (5/12 + 24 + 15 + 3/10 + 27) = 0
N - [tex]\frac{8006}{120}[/tex] = 0
N - 66[tex]\frac{43}{60}[/tex] = 0
N = 66[tex]\frac{43}{60}[/tex]
= 66.72
N ≅ 67
Therefore the number of stamps in the book is approximately 67.
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PLEASE HELPPPPP PLEASE so confused
Answers
Answer:
105°
Step-by-step explanation:
EFGH is an isosceles trapezoid (a trapezoid with congruent legs is an isosceles trapezoid)
∠G=75° (base angles of an isosceles trapezoid are congruent)
∠F=105° (same-side interior angles theorem)
SOMEBODY PLEASE HELP ASAP
Answers
Answer:
40
Step-by-step explanation:
[tex]\frac{RW}{24}=\frac{30}{18} \\ \\ RW=40[/tex]
A rectangular table is six times as long as it is wide. If the area is 150 ft2, find the length and the width of the table.
The width of the table is
The length of the table is?
Answers
Answer:
Length = 30ft, Width = 5ft
Step-by-step explanation:
Let x be the width.
Area of Rectangle = Length * Width
Given from the information in the question,
Length = 6x ft
Width = x ft
Substitute the values into the formula:
6x * x = 150
[tex]6x^{2}[/tex] = 150
[tex]x^{2} =\frac{150}{6}[/tex]
[tex]x^{2} =25[/tex]
[tex]x=\sqrt{25}[/tex]
x = 5 ft.
Therefore,
Length = 6 * 5 = 30ft
Width = 5 ft.
Please help me solve the problem in the image. I found that a=-65 and b=17 and when I plug it in the equation it’s wrong
Answers
Answer:
-181 - 79x
Step-by-step explanation:
I am not sure your comment fits the given problem.
I get the following approach and solution :
T(1 + 4x) = 1×a + 4x×b = 2 + 2x
a = 2 + 2x - 4xb
T(4 + 15x) = 4×a + 15x×b = -3 + 3x
4×(2 + 2x - 4xb) + 15xb = -3 + 3x
8 + 8x - 16xb + 15xb = -3 + 3x
11 + 5x - xb = 0
11 + 5x = xb
b = (11 + 5x)/x
a = 2 + 2x - 4x(11 + 5x)/x = 2 + 2x - 44 - 20x = -42 - 18x
T(3 - 5x) = 3×a - 5xb = 3(-42 - 18x) - 5x(11 + 5x)/x =
= -126 - 54x - 55 - 25x = -181 - 79x
control :
T(1 + 4x) = a + 4xb = -42 - 18x + 44 + 20x = 2 + 2x
T(4 + 15x) = 4a + 15xb = -168 - 72x + 165 + 75x = -3 + 3x
What number is next 3,8,35,48,99
Answers
Answer: 120
Step-by-step explanation: The pattern is a very weird pattern, but still a pattern.
The pattern starts with number 2 to the power of 2, and then subtract 1. This is 3.
Then we keep using this same pattern, keeping the exponent the same but increasing the numbers. 3^2 is 9, and subtracting 1 gives 8.
Then the pattern skips two numbers 4 and 5. So for every 2 numbers that is squared and subtracted 1, 2 other numbers are not apart of the pattern.
So the next is 6^2, which is 36-1 which is 35.
Then 7^2 is 49 and subtracting 1 is 48.
Then, ignoring the next 2 numbers because of the pattern, we have 10^2 which is 100, and subtracting 1 is 99.
Now the next number is 11^2 which is 121, and subtracting 1 is 120.
Hope this helped! If it did, please mark as Brainliest.
Deion misses 4% of the free throws he attempts in a seaon. How many total free throws did he attempt if he missed 17
Answers
Answer: 425
Step-by-step explanation:
Think of this problem as 4% of a number equals 17
since in math, the word 'of' usually means multiplication, we can think of it that way.
Also, 4% = 0.04
[tex]x*0.04=17[/tex]
[tex]0.04x=17[/tex]
[tex]\frac{0.04x}{0.04} =\frac{17}{0.04}[/tex]
[tex]x=425[/tex]