The function that models the inverse variation is: y = 1/2x.
When x = 10, y = 1/20.
What is a Function that Models an Inverse Variation?The function that models an inverse variation between two variables, x and y, can be expressed as:
y = k/x.
Given that y = 1/6 when x = 3, find the value of the constant, k, by substituting the values of x and y into y = k/x:
1/6 = k/3
Multiply both sides by 3
1/6(3) = k/3(3)
1/2 = k
k = 1/2.
The function for the inverse variation would be, y = 1/2/x
y = 1/2x
To find y when x = 10, substitute the value of x = 10 into the equation y = 1/2x:
y = 1/2(10)
y = 1/20
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According to the Rational Root Theorem, which of the following could be a root of p(x)=3x3−5x2+4? Select all that apply.
SOLUTION
The rational root theorem, also called rational root test theorem state that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.
Given the polynomial
[tex]p(x)=3x^3-5x^2+4[/tex][tex]\begin{gathered} \text{Leading co}eficient\text{ =3} \\ \text{Constant term =4} \end{gathered}[/tex]The factor of the constant term is
[tex]\pm1,\pm2,\pm4_{}[/tex]The factors of the Leading coefficient are
[tex]\pm1,\pm3[/tex]The root of the p(x) are
[tex]\begin{gathered} \frac{p}{q} \\ \text{where p=factors of the constant term } \\ q=\text{factor of leading coefficient } \end{gathered}[/tex]hence , the possible root of p(x) are
[tex]\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3},\pm4,\pm\frac{4}{3}[/tex]Hence
root of p(x) are 2/3, -2, and 1
Area of Composite Figures Find the area of each figure. Round to the nearest tenth if necessary.
The Area of the composite shape is the sum of the areas of the triangle and that of the square
Area of square = length x breadth =>
[tex]\begin{gathered} \text{Area of square = 10 m x 6m } \\ \Rightarrow60m^2 \end{gathered}[/tex]Area of Traiangle = 1/2 (base x height)
=>
Factorise2rs-4rt-6t+3s
Given expression:
[tex]2rs\text{ - 4rt - 6t + 3s}[/tex]Collect like terms:
[tex]=\text{ 2rs - 4rt - 6t + 3s}[/tex]Next, we bring the common terms:
[tex]=\text{ 2r(s - 2t) -3(2t - s)}[/tex]Re-writing the expression:
[tex]=\text{ -2r(2t - s) -3(2t -s)}[/tex]Since we have a common term on either side of the negative sign, we can write:
[tex]=\text{ (-2r -3)(2t-s)}[/tex]Answer:
[tex]=\text{ (-2r-3)(2t -s)}[/tex]Let us verify the answer:
[tex]\begin{gathered} (-2r\text{ -3)(2t-s)} \\ =-2r(2t\text{ -s) -3(2t -s)} \\ =\text{ -4rt + 2rs -6t + 3s} \end{gathered}[/tex]Would just like to make sure that my answer is correct.
Answer:
[tex]\text{ -2sin(}\frac{11\pi}{24})\cos (\frac{\pi}{24})[/tex]Explanation:
Here, we want to simplify the given expression
The basic rule we will be using here is:
[tex]\sin (A\text{ + B})\text{ = SinACosB + CosASinB}[/tex]Thus, we have it that:
[tex]\begin{gathered} \text{ sin(}\frac{\pi}{6}+\frac{\pi}{4})\text{ + sin(}\frac{\pi}{8}+\frac{3\pi}{8}) \\ \\ \sin (\frac{5\pi}{12})\text{ + sin(}\frac{\pi}{2}) \end{gathered}[/tex]We use the sine addition formula as follows:
[tex]\sin \text{ A + sin B = 2sin(}\frac{A+B}{2})\cos (\frac{A-B}{2})[/tex]Now, we substitute the last expression into the given addition formula above:
[tex]\begin{gathered} \text{ sin(}\frac{5\pi}{12})\text{ + sin(}\frac{\pi}{2})\text{ =2sin(}\frac{\frac{5\pi}{12}+\frac{\pi}{2}}{2})\cos (\frac{\frac{5\pi}{12}-\frac{\pi}{2}}{2}) \\ \\ =\text{ 2sin(}\frac{11\pi}{24})\cos (\frac{-\pi}{24})\text{ = -2sin(}\frac{11\pi}{24})\cos (\frac{\pi}{24}) \end{gathered}[/tex]Muffins $1.75
Cookies $1.25
Cakes
$1.00
For the bake sale, your principal would like to sell each baked good for $4.00. He also mentions that each baked good that is sold needs
at least a 60% profit. Based on this information, which of the baked goods could be sold at the bake sale? Explain how you know whether
each baked good meets or does not meet the criteria for being sold at the bake sale.
Answer:
rat
Step-by-step explanation:
An airplane flying against the wind travels 280 miles in the same amount of time it would take the same plane to travel
420 miles with the wind. If the wind speed is a constant 70 miles per hour, how fast would the plane travel in still air?
The speed of plane in still air is 150 miles per hour.
What is speed?
Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
speed = distance/time
Let s = speed in still air
then(s-70) = ground speed against the wind
and
(s+70) = ground speed with the wind
Write a time equation; time = distance/speed
time against = time with still air
280/(s-30) = 420/(s+30)
Cross multiply
420(s-70) = 280(s+70)
420s - 29400 = 280s + 19600
420s-280s = 19600+29400
140s=49000
s = 49000/140
s = 350 mph
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Hi there I need help what is 39 dollars plus two rolls of pennies equals
Answer:
41
Step-by-step explanation:
Find the are of the circle below.
To find the area of the circle with diameter = 18 cm
We will use the formula:
[tex]\text{Area of a cirlce = }\pi r^2[/tex]where r= radius of the circle
From the quesion diameter = 18 cm
radius = diameter/2
radius = 18cm/2 = 9 cm
substituting r = 9cm into the formula
[tex]Area\text{ of a circle = }\pi(9)^2[/tex][tex]A\text{rea of the circle }=\text{ 81}\pi cm^2[/tex]The above answer is when we are to leave the answer in terms of π
Otherwise if π is given to be 3.14 or 22/7 , we will simply substitute into the formula
That is given that π= 3.14
[tex]\text{Area of the circle = 81 }\times3.14=254.34cm^2[/tex]
Snow is accumulating at a rate of 0.5 inches per hour. Calculate the amount, in inches of snow that will accumulate in 24 minutes.
Given:
Accumulation rate = 0.5 inches per hour
time = 24 minutes
First, convert minutes into hours:
1 hour = 60 minutes
24 / 60 = 0.4 hours (divide by 60)
Now, simly multiply the rate by the number of hours
0.5 in/h x 0.4 h = 0.2 in
Answer: 0.2 inches
Determine the required value of the missing probability to make
the distribution a discrete probability distribution.
X
3
45
4
5
6
P(x)
0.24
?
0.28
0.26
The value that completes the probability distribution is 0.22
How to determine the missing value?The distribution of the discrete probability distribution is given as
x 3 4 5 6
P(x) 0.24 ? 0.28 0.26
Represent the blank value in the distribution with the variable y
So, we have the following representation:
P(x) 0.24 y 0.28 0.26
The sum of probabilities in a distribution is 1
So, we have
0.24 +y + 0.28 + 0.26 = 1
Evaluate the sum
y + 0.78 = 1
Evaluate the like terms
y = 0.22
Hence, the missing value is 0.22
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Solve for X with intersecting chords
We apply the secant-angle theorem,
[tex]\frac{156+54}{2}=105^0[/tex]Then,
[tex]\begin{gathered} x+105^0=180^0\text{ (angle in a straight line)} \\ x=180^0-105^0 \\ x=7^{}5^o \end{gathered}[/tex]Therefore, x=75 degr
Hey can someone please help me? I would appreciate it.
Answer:
8/3 or 2.67
Step-by-step explanation:
your explanation is in the image below hope this helps sorry if wrong
Let C be the boundary of the square with vertices (0,0),(1,0),(1,1) and (0,1) oriented the in the counter clockwise sense. Then the value of the line integral [tex]\oint_ { \rm C} \rm {x}^{2} {y}^{2} dx + ( {x}^{2} - {y}^{2} )dy \\ [/tex] is ________. (rounded of two decimal places)
By Green's theorem,
[tex]\displaystyle \oint_C x^2y^2 \, dx + (x^2-y^2) \, dy = \iint_{[0,1]^2} \left(\frac{\partial(x^2-y^2)}{\partial x} - \frac{\partial(x^2y^2)}{\partial y}\right) \, dx \, dy \\\\ ~~~~~~~~ = \int_0^1 \int_0^1 (2x - 2x^2y) \, dx \, dy \\\\ ~~~~~~~~ = \int_0^1 \left(1-\frac23 y\right) \, dy \\\\ ~~~~~~~~ = 1 - \frac13 = \frac23 \approx \boxed{0.67}[/tex]
Assume that a triangle ABC has standard labeling. Determine wether SAA, ASA, SSA, SAS or SSS is given. Then decide wether the law of sines or the law of cosines should be used to begin solving the triangle.a, c and B
Answer:
Explanation:
Shelby is searching online for airline tickets. Two weeks ago, the cost to fly from to was $210. Now the cost is $305. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percentage increase of the airline ticket is 45.24%
Percentage IncreaseThe concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original. An increase of 5 percent would indicate that, if you split the original value into 100 parts, that value has increased by an additional 5 parts.
Mathematically, the percentage increase of a quantity can be written as
[tex]\% increase =\frac{change in quantity}{original quantity} * 100[/tex]
Let's substitute the values given into the equation and find the percentage increase.
[tex]\% increase =\frac{change in quantity}{original quantity} * 100\\\% increase = \frac{305 - 210}{210} *100\\\% increase = 45.24\%[/tex]
The increase in percentage of the ticket price is 45.24%
If the airline charges an additional $50 with the new ticket price, the percentage increase will remain the same because assuming the baggage fees is also applicable to the old price, there won't be an change in the percentage increase.
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what is the massive objects the planets of the solar system orbit
The planets orbit around stars. Our solar system is an example of that, all the planets in our system orbit around a star, the Sun.
Hence, the answer is stars.
5 ft12 ftWhat is the length of the hypotenuse?
I think these are the lengths of the legs
hypotenuse^2 = 5^2 + 12^2
hypotenuse^2 = 25 + 144
hypotenuse^2 = 169
hypotenuse = 13
The graph of an arithmetic sequence is shown.What is the value of the 7 th term?Round your answer to the nearest tenth. Add a decimal point and a zero if youranswer is a whole number (for example, 10 would be entered as 10.0)
10.0
Explanation
an arithmetic sequence is given by the expression
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{where} \\ a_{_1}\text{ is the first term} \\ \text{and d is the common diference} \end{gathered}[/tex]in the graph , to know the value of the 7 th terms, we need to take the value that y takes, when x= 7
so
therefore, the answer is
10.0
I hope this helps you
when you multiply by a power of 10 the decimal point moves how many places
If we have a number X and we multiply it by a power of 10, then:
[tex]x\text{ }\ast\text{ }10^{n\text{ }}=\text{ x followed by n zeros}[/tex]Example:
x = 7 and we want to multiply it by 1,000
[tex]7\text{ }\ast\text{ 1,000 = 7 }\ast\text{ }10^{3\text{ }}=\text{ 7, 000 (3 zeros, the same quantity of the power)}[/tex]Another example:
x = 27 and we want to multiply it by 1 million
[tex]27\text{ }\ast\text{ 1,000,000 = 27 }\ast10^{6\text{ }}=\text{ 27,000,000 (6 zeros, the same quantity of power)}[/tex]I need help with this question causey teacher didnt teach this to us.3(5-p) - 2(5 + p) = 3(p+1). Find p
Explanations:
The given equation is:
3(5 - p) - 2(5 + p) = 3(p + 1)
Step 1: Expand all the brackets
15 - 3p - 10 - 2p = 3p + 3
Step 2: Collect like terms ( That is, let everything that has p go together)
15 - 10 - 3 = 3p + 3p + 2p ( Note that the sign changes when anything crosses the equality sign)
2 = 8p
Step 3: Divide both sides by 8
2/8 = 8p/8
1/4 = p
p = 1/4
p = 0.25
Find the y-intercept of the line on the graph.
Answer:
-2
Step-by-step explanation:
The y intercept is where the line crosses the y axis. It crosses at the point (0,-2)
Can you guys please help me on this question ?
Solution
Therefore, the correct option is D.
What is the length of AB? round your answer to the nearest hundred.
In order to calculate the length of the line AB, you use the following formula for the distance between points in the coordinate plane:
d = √((x2-x1)²-(y2-y1)²)
That is, it is only necessary to have a pair of points with coordinates (x1,y1) and (x2,y2). In this case you have two points A=(-5,-4)=(x1,y1) and B=(-3,3)=(x2,y2), then, by replacing these values into the formula for the distance you have:
d = √((3-(-3))²-(-5-4)²)
d = √((3+3)²+(-9)²)
d = √(36+81) = √(117) = 10.8166 ≈ 10.82
Hence, the length of the line AB is 10.82
what are all the possible values of 'a' in -3≤a≤3
We have the next
[tex]-3\le a\le3[/tex]The possible values of 'a' for this are
[tex]\mleft[-3,3\mright][/tex]the value of a could be all the values between -3 and 3 including -3 and 3
ANSWER
[-3,3]
Write an equation in the form y suggested by the pattern in the table. т
I'll pick uo two points from the table.
P1 = (5, 11)
P2 = (7, 13)
1.- Find the slope
slope = (y2 - y1) / (x2 - x1)
Substitution
slope = (13 - 11) / (7 - 5)
Simplification
slope = 2/2
Result
slope = 1
2.- Find the equation of the line
y - y1 = m(x - x1)
Substitution
y - 11 = 1(x - 5)
Simplification
y = x - 5 + 11
Result
y = x + 6
This is the answer to your question
I need help on a problem
Triangle BOX = Triangle DEA by Angle Side Angle
3.Ronald loves to compete in triathlons. At a race a few months ago, hefinished in 290 minutes. At a race yesterday, he took 10% more time tofinish. What was his time at yesterday's race?
Explanation:
First we have to get 10% of 290 minutes:
[tex]290\times\frac{10}{100}=290\times0.1=29[/tex]If yesterday took him 10% MORE time to finish the race, it means that it took him 290min as a few months ago plus another 29 minutes
Answer:
Ronald's time at yesterday's race was 319 minutes
Question 3 of 10How many solutions does the nonlinear system of equations graphed belowhave?10X10
Answer:
B. Zero
Explanation:
The solutions of the system of equation are the points where the graph intersect. In this case, the red function and the blue function doesn't cross each other. So, the system formed by these non linear equations has no solutions.
Therefore, the answer is:
B. Zero
Answer:two
Step-by-step explanation:
can someone help me with this please, I need this by tomorrow pleaseeee
In the given figure,
There are non-parallel lines,
Hence these angles are formed by the non-parallel lines.
This means they do not have any relation, i.e., they are not necessarily congruent to each other.
What are Intersecting lines?They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines. The intersecting lines (two or more) always meet at a single location. Any angle can be used to intersect the intersecting lines. This angle is always larger than zero and less than 180 degrees. Vertical angles are created by two lines intersecting. With a common vertex, the vertical angles are opposite angles (which is the point of intersection). Curved lines, not straight ones, are what intersect at several points.To learn more about Intersecting Lines, refer to:
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8 This graph shows how fast Heidi ran on a track. Heidi says she was
running 1.5 laps per minute because 3/2= 1.5. What mistake did
she make? How fast was Heidi running?
