Write an equation to describe the variation. Use k for the constant of proportionality.h varies inversely as √pThe equation is___
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For any two values x and y, if x varies inversely as y, the equation of the relationship can be expressed as follows:
[tex]y=\frac{k}{x}[/tex]Where k is a constant of proportionality. From the problem, we identify:
[tex]\begin{gathered} x=h \\ y=\sqrt{p} \end{gathered}[/tex]Finally:
[tex]\begin{gathered} \sqrt{p}=\frac{k}{h} \\ \\ \text{ or} \\ \\ k=h\cdot\sqrt{p} \end{gathered}[/tex]Related Questions
In the figure below, m
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how much more money did the team raise selling sun hats than tumblers
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We are given the following information
Cost of tumblers = $10
Cost of sun hats = $5
Total tumblers and sun hats sold = 30
Total amount raised = $190
Let t represent the number of tumblers and h represents the number of sun hats.
Then we can set up the following two equations
[tex]\begin{gathered} t+h=30\quad eq.1 \\ 10t+5h=190\quad eq.2 \end{gathered}[/tex]Let us solve the above system of equations to find the number of tumblers and sun hats sold.
Separate out one of the variables from eq.1
[tex]t=30-h\quad eq.1[/tex]Now, substitute eq.1 into eq.2 and simplify
[tex]\begin{gathered} 10t+5h=190 \\ 10(30-h)+5h=190 \\ 300-10h+5h=190 \\ 300-5h=190 \\ 300-190=5h \\ 110=5h \\ h=\frac{110}{5} \\ h=22 \end{gathered}[/tex]So, 22 sun hats were sold.
Now, substitute the value of h into eq.1 to find the value of t.
[tex]\begin{gathered} t=30-h \\ t=30-22 \\ t=8 \end{gathered}[/tex]So, 8 tumblers were sold.
Finally, let us find out how much money did the team make selling tumblers and sun hats.
[tex]\begin{gathered} 22\times\$5=\$110 \\ 8\times\$10=\$80 \end{gathered}[/tex]The team made $110 selling sun hats and $80 selling tumblers.
$110 - $80 = $30
This means that the team made $30 more money selling sun hats than tumblers.
Therefore, the correct answer is $30
Where can I find the circumference of a circle in this diagram?
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To find the circumference of a circle with a radius of 7cm, we need to use the next formula:
[tex]C=2\pi r[/tex]We know that the value of π is approximately equal to 3.14159265359, and we also have that the radius is equal to 7cm. Then, we have that the circumference is:
[tex]C=2\cdot3.14159265359\cdot7\operatorname{cm}\Rightarrow C=43.9822971503\operatorname{cm}[/tex]If we round this value to the nearest hundredth, we can conclude that the circumference of the circle is equal to 43.98cm.
In summary, we can say that the circumference of a circle with a radius of 7cm, and using π = 3.14159265359, and then rounding the value to the nearest hundredth is 43.98cm.
the square has a base and height of 10 cm what is the area of the Shaded region?
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Shaded region S= ?
Diameter D= 10cm
Circle area= π•D^2/4
S= Square - Circle
S= D^2 - π• D^2/4
S= 10^2 - π• 25
S= 100 - 78.5= 21.5
Then answer is
Shaded area S= 21.5 cm2
1Figure A and Figure B are scaled copies of each other.HO27220Figure AFigure B35What is the value of x?
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To solve this, we will follow the steps below:
Since the two triangles are scaled copies of each
Answer:
Step-by-step explanation: 5-4+90=91
What is the reduced fraction form of 1.64?
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Given:
1.64
Let's find the reduced fraction form of 1.64
To find the reduced fraction form of 1.64, we have:
[tex]1.64=\frac{164}{100}[/tex]Now, simplify the fraction:
Divide bthe the Greatest Common Factor of 164 and 100.
GCF of 164 and 100 = 4
Hence, we have:
[tex]\frac{164\div4}{100\div4}=\frac{41}{25}[/tex]Therefore, the reduced fraction form of 1.64 is:
[tex]\frac{41}{25}[/tex]Determine the shaded area.The shaded area is(Round to two decimal places as needed.)
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Given Data:
The radius of the circle is r=9 ft.
The side of the square will be twice the radius of the circle, i.e.a=18 ft.
The area of the shaded region can be determined by substracting the area of circle from the area of square,
[tex]\begin{gathered} A=A_s-A_c \\ =(18ft)^2-(\pi(9ft)^2) \\ =69.53ft^2 \end{gathered}[/tex]Thus, the requried shade area is 69.53 square foot.
please help me match the line described on the left with the slope of the line on the right. thankyou!!
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We have:
* y = 3, Horizontal straight lines have zero slope, since the "rise" is zero.
Answer: 0
* 9x - 3y = 18, We rearrange to the slope form equation, which is: y = mx + b, so:
[tex]\begin{gathered} 9x-3y-9x=18-9x \\ -3y=18-9x \\ \frac{-3y}{-3}=\frac{18}{-3}-\frac{9x}{-3} \\ y=3x+6 \end{gathered}[/tex]So the slope is 3.
Answer: 3
* (5,7) and (5, -8) the slope is given by the formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-8-7}{5-5}=\frac{-15}{0}[/tex]So, the "run" is zero, and division by zero is not allowed.
Answer: undefined
* (-4, -1) and (-1, -7)
[tex]m=\frac{-7-(-1)}{-1-(-4)}=\frac{-7+1}{-1+4}=-\frac{6}{3}=-2[/tex]Answer: - 2
at what rate is his distance increasing from home plate when he is 20 feet from second base
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Let's take a look at our situation:
Notice that we can construct a right triangle from this situation!
The key concept here is that the distance bewteen the runner and second base will be a function of x. More specifically, 21x.
Now, we use the Pythagorean Theorem, to conclude that:
[tex]d^2=90^2+\mleft(21x\mright)^2[/tex]If we solve for d, we would have a function for the distance between the runner and home plate in terms of x :
[tex]\begin{gathered} d=\sqrt[]{90^2+\mleft(21x\mright)^2} \\ \\ \Rightarrow d(x)=\sqrt[]{8100+441x^2} \end{gathered}[/tex]Now, to calculate the rate of change for this function, we calculate the derivative. Using the chain rule and simplifying, we can conclude that:
[tex]d^{\prime}(x)=\frac{147}{\sqrt[]{49x+900}}[/tex]Now, we're being asked for the instant of time where the runner is 20 feet from second base. The time when this happens is:
[tex]\begin{gathered} 21x=20 \\ \\ \Rightarrow x=\frac{20}{21} \end{gathered}[/tex]Now, let's evaluate the derivative for this value of x:
[tex]\begin{gathered} d^{\prime}(\frac{20}{21})=\frac{147}{\sqrt[]{49(\frac{20}{21})+900}} \\ \\ \Rightarrow4.78\text{ ft per second} \end{gathered}[/tex]Therefore, the rate at which the distance from the runner to home plate increases when he's 20 feet from second base is 4.78 feet per second.
What is the rate (k) at which the water is leaking per hour?
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is a division betwen the water and the hours
we can take any point (1,1) or (5,5)
because have the same value of bucket and hour
so
[tex]\frac{1}{1}=1[/tex]tha rate is 1 bucket per hour
Take the answer: 8^2/9 . Create an expression using each of the specified properties below that will result in this answer once it is simplifieda. Product of Powersb. Power of a Powerc. Quotient of Powers
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For the value given
[tex]8^{\frac{2}{9}}[/tex]To create the expressions required in the question, we will follow the steps below
Part A: Product of powers
[tex]a^m\times a^n=a^{m+n}[/tex]hence
[tex]8^{\frac{2}{9}}=8^{\frac{1}{9}}\times8^{\frac{1}{9}}[/tex]Part B: Power of power
[tex](a^m)^n=a^{m\times n}[/tex]Thus
[tex]8^{\frac{2}{9}}=(8^{\frac{1}{9}})^2[/tex]Part C: Quotient of powers
[tex]8^{\frac{2}{9}}=\frac{8^1}{8^{\frac{7}{9}}}[/tex]If Zach buys a footstool during the sale for 75% off but the original price is 36$ How much does Zach pay?
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Amount Zach pays = $9
Explanation:original price = $36
75% off = discount of 75%
Amount he pays = original price - discount
discount = 75% of original price = 75/100 × 36
discount = $27
Amount he pays = $36 - $27
Amount Zach pays = $9
the diagram shows two parallel lines cut by a transversal. If the measure <2 = 3y - 8, what is the measure <7
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Notice that due to the fact that two parallel lines are itersected by a transversal, it generales congruent angles <2 , <3 , <6 and <7
Then the measure of angle <7 must equal the measure of <2, That is:
<7 = <2 = 3 y - 8
<7 = 3 y - 8
The SAME measure of that for angle <2 because they are "corresponding angles between parallel lines".
If they give you an answer option that reads 3 y - 8, please select it.
A certain tiger shark is 55 cm long at birth and grows 2.5 cm / year. A certain hammerhead shark is 25 cm long at birth and grows 5 cm/year. When will the sharks be equal in length? Let x = time in yearsLet y = length of the sea creaturesThe equation for the length of the tiger shark is ___. The equation for the length of the spiny dogfish hammerhead shark is ___. Solving with elimination, the sharks will be equal in length when ___ years have passed.
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Let x = time in years;
Let y = length of the sea creatures;
For both sharks, we can describe their growth with a linear equation since they grown in a constant rate. A line equation written in slope-intercept form is
[tex]y=mx+b[/tex]Where m represents the slope(or the rate of growth) and b represents the y-intercept(in our problem, the initial length).
A certain tiger shark is 55 cm long at birth and grows 2.5 cm/year, therefore, its growth can be represented by the following equation:
[tex]y_t=2.5x+55[/tex]A certain hammerhead shark is 25 cm long at birth and grows 5 cm/year, therefore, its growth can be represented by the following equation:
[tex]y_h=5x+25[/tex]The length of the sharks will be equal when the value of those functions are the same. The solution for the following equation is the corresponding time in years
[tex]\begin{gathered} y_t=y_h \\ 2.5x+55=5x+25 \\ 5x-2.5x=55-25 \\ 2.5x=30 \\ x=\frac{30}{2.5} \\ x=12 \end{gathered}[/tex]Their length will be the same after 12 years.
Use in the equation and the ordered pairs fond previously plot the points on the graph that would best satisfy the equation.
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EXPLANATION
Plotting the points in the graph calculator, will give us the following representation:
At the beginning of a basketball season, the Panthers won 20 games out of 60 games. At this rate, how many games will they win in a normal 120-game season?Round answer to the nearest whole number.
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Since we want to calculate for the same rate, we can use the same ratio of won games to total games.
The given ratio is:
[tex]r=\frac{20}{60}=\frac{1}{3}[/tex]For the whole 120-game season, the total is 120 and let's call the number of won games by n, so:
[tex]\begin{gathered} r=\frac{n}{120} \\ r=\frac{1}{3} \\ \frac{1}{3}=\frac{n}{120} \\ \frac{120}{3}=n \\ 40=n \\ n=40 \end{gathered}[/tex]So, at this rate, they will win 40 games.
Write the equationThe line through (1, 7) and (-6, 7) in point-slope form
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ANSWER:
[tex]y-7=0\cdot(x-1)[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation of line in its point-slope form is the following:
[tex]y-y_1=m\cdot(x-x_1)[/tex]We must calculate the slope, we can do it using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We replace the points (1, 7) and (-6, 7) and calculate the value of the slope, like this:
[tex]m=\frac{7-7}{-6-1}=\frac{0}{7}=0[/tex]Since the slope is equal to 0, it would not be an equation of a line, since it is a constant, the line through both points would be:
[tex]\begin{gathered} y-7=0\cdot(x-1) \\ y=7 \end{gathered}[/tex]A painter mixed 5 pints of white paint 3 pints of Lupe 4 pints of yellow paint he wrote the ratio 3:12 Which statement best describes ratio
Answers
D)the ratio of the number of pints of blue paint to the total number of pints of pain
Explanation
Divide data A by data B to find your ratio
Step 1
Let
[tex]\begin{gathered} white\text{ paint= 5 pints} \\ blue\text{ paint =3 pints} \\ yellow\text{ paint =4 pints } \end{gathered}[/tex]Step 2
now, to find the correct choice we need to try one per one
a)
[tex]\begin{gathered} ratio_1=\frac{white+\text{ yellow}}{blue\text{ }} \\ rat\imaginaryI o=\frac{9}{3}=\frac{3}{1}=3:1 \end{gathered}[/tex]so, False
b)
[tex]\begin{gathered} ratio_2=\frac{\text{ yellow}}{4*blue\text{ }} \\ rat\imaginaryI o=\frac{4}{4*3}=\frac{1}{3}=1:3 \end{gathered}[/tex]False
c)
[tex]\begin{gathered} ratio3=\frac{\text{ blue}}{blue+yellow\text{ }} \\ rat\imaginaryI o=\frac{3}{3+4}=\frac{3}{7}=3:7 \end{gathered}[/tex]d)
[tex]\begin{gathered} ratio_4\text{ =}\frac{blue\text{ }}{total}=\frac{blue}{white+blue+yellow} \\ ratio_4=\frac{3}{5+3+4}=\frac{3}{12}=3:12 \end{gathered}[/tex]therefore, the answer is
D)the ratio of the number of pints of blue paint to the total number of pints of pain
I hope this helps you
(x-5)(2x+1)=0in mathmathicso
Answers
(x-5)(2x+1)=0
To solve this equation solve these equations:
Equation 1
x - 5 = 0
x= 5 ( Transposing 5 to the other side of the equation)
Equation 2
2x + 1 = 0
2x = -1 ( Transposing 1 to the other side of the equation)
x= -1/2 (Dividing by 2 on both sides of the equation)
The answers are:
x1= 5 and x2=-1/2
✓13 + 34 + 25. 2((2• 3)2 - 2 • 45) 9
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SOLUTION
Given the expression
[tex]\frac{\sqrt[]{13+3^4+25\times2}}{((2\times3)^2-2\times45)\div9}[/tex]We can find the solution by simplifying the question.
[tex]\begin{gathered} \frac{\sqrt[]{13+3^4+25\times2}}{((2\times3)^2-2\times45)\div9} \\ =\frac{\sqrt[]{13+81^{}+50}}{((2\times3)^2-2\times45)\div9} \\ =\frac{\sqrt[]{13+81^{}+50}}{(6)^2-90)\div9} \\ =\frac{\sqrt[]{144}}{(36-90)\div9} \\ =\frac{12}{-54\div9} \\ =\frac{12}{-6} \\ =-2 \end{gathered}[/tex]Answer: -2
Add and simplify: (2 – 7i) + (14 + 2i)
Answers
Given:
[tex](2-\text{ 7i\rparen + \lparen14 + 2i\rparen}[/tex]To find:
To add and simplify
First, we need to remove the parenthesis:
[tex]\begin{gathered} 2\text{ - 7i + \lparen14\rparen + \lparen+2i\rparen} \\ $$mu\text{ltiplication of same signs give positive sign}$$ \\ \\ 2\text{ - 7i + 14 + 2i} \\ \\ collect\text{ like terms:} \\ 2\text{ + 14 - 7i + 2i} \end{gathered}[/tex][tex]\begin{gathered} 2\text{ + 14 = 16} \\ -7i\text{ + 2i = -5i} \\ \\ =\text{ 16 - 5i} \end{gathered}[/tex]An architect designed a rectangle or flower garden such that the width is exactly two-thirds of the length. If 300 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden
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Step 1:
Given data
[tex]undefined[/tex]The first box is to type in the base. The second bulks is where you feel in the simplified exponent and using the multiplication Property rule of exponents. Multiply. Write the product as one combine power
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Answer: 16m⁹
Explanation
Given
[tex](-2m^4)*(-8m^5)[/tex]In order to multiply, we can divide them into two, the coefficients and the exponents of the variable. Using the Product rule of the exponents we can get that:
[tex]a^x*a^y=a^{x+y}[/tex]Then, based on the latter we can get the following multiplication:
[tex]=-2\cdot-8\cdot m^{4+5}[/tex]Multiplying the signs and the numbers we get:
[tex]=16\cdot m^{4+5}[/tex]Adding the exponents :
[tex]=16m^9[/tex]Look at this table.Hours ofTraining10203040506070MonthlyPay1220142016201820202022202420osAccording to the table, what is the increase in monthly pay for each hour oftraining?A. $10B. $200C. $100D. $20
Answers
From the table,
When hour of training is 10 the pay is $1220
When hour of training is 20 the pay is $1420
Thus for increase in 10 hr the pay increases by $200.
So for 1 hour increase, the pay increases by
[tex]\frac{200}{10}=20[/tex]Thus the answer is D $20
It takes Diego 1/4 of an hour to complete a circular bike track. The track is 1/3 mile longWhat is Diego's bike speed?
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ok
speed = distance / time
speed = 1/3 / 1/24
speed = 24/3
speed = 8 miles per hour the third choice is the right answer
the height of a triangle is 3 yards less than twice the base.the area of the triange is 27 square yards.find the base and height of the triange
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let h be height and b the base. So we get that
[tex]\begin{gathered} \frac{h\cdot b}{2}=27\rightarrow h\cdot b=54 \\ h=2b-3 \end{gathered}[/tex]so we get that
[tex]\begin{gathered} (2b-3)b=54 \\ 2b^2-3b-54=0 \\ (b-6)(2b+9)=0 \end{gathered}[/tex]as b must be positive, we get that b=6, and therefore h=12-3=9
Zelda figures out that her backyard is 56 steps long and 43 steps wide. If she wants to build a 15-foot- tall garage that covers the whole yard and if each of her steps is 2.5 feet, what will the volume of her new garage be?
Answers
Answer:
225,750 cubic feet.
Explanation:
• Her backyard is ,56 steps long, and ,43 steps wide,.
,• Each of her steps is 2.5 feet.
Therefore:
[tex]\begin{gathered} \text{Length of the backyard}=56\times2.5=140\text{ feet} \\ \text{Width of the backyard}=43\times2.5=107.5\text{ feet} \\ \text{Proposed Height of the garage }=15\text{ feet} \end{gathered}[/tex]Therefore, the volume of the new garage:
[tex]\begin{gathered} V=Length\times Width\times Height \\ =140\times107.5\times15 \\ =225,750\text{ cubic feet} \end{gathered}[/tex]The volume of her new garage is 225,750 cubic feet.
Can I find a tutor to help me with this question?
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The initial position of the toy is 96 feet, so for t = 0 we have h = 96.
After 2 seconds, the toy reaches the maximum height of 100 feet, so for t = 2 we have h = 100.
The object hits the ground after 12 seconds, so for t = 12 we have h = 0.
Looking for the graph that has the ordered pairs (0, 96), (2, 100) and (12, 0), the correct graph is graph Z.
Therefore the correct option is D.
use the arithmetic sequence 12 15 18 21 which is an equation for the nth term of the sequence
Answers
use the arithmetic sequence 12 15 18 21 which is an equation for the nth term of the sequence
step 1
Find the common difference d
we have
a1=12 ------> first term
a2=15
a3=18
a4=21
so
a2-a1=15-12=3
a3-a2-18-15=3
a4-a3=21-18=3
therefore
the value of d=3
step 2
The general equation for the arithmetic sequence is
an=a1+d(n-1)
we have
a1=12
d=3
substitute
an=12+3(n-1)
an=12+3n-3
an=3n+9Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form m= -7/2, point (-8,-4)
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Given:-
[tex]undefined[/tex]