Rational functions are functions that can be written as the ratio of two polynomial functions, while inverse variations are a type of rational function where the product of two varying quantities is a constant.
Explanation:A rational function is any function that can be written as the ratio of two polynomial functions. Both the numerator and the denominator are polynomials. For example, f(x) = (2x^2 + 3)/(x - 5) is a rational function where 2x^2 + 3 and x - 5 are polynomial functions.
On the other hand, an inverse variation, or inverse proportion, is a specific type of rational function where the product of two varying quantities is a constant. It is in the form of y = k/x, where k is a nonzero constant. For example, if y varies inversely as x, then the product of x and y is constant, which means xy = k.
To summarize, all inverse variations are rational functions since they can be expressed as a ratio of two polynomials. However, not all rational functions are inverse variations since not all can be written in the form y = k/x.
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You are helping a partner in your group with their problem. What mistake did they make solving the system?
3x+y-9
-2x+y=4
Students work when solving the second equation for y:
Y=2x+4
-2x+(2x+4)=4
-2x+2x+4=4
4=4
The students response is there are indefinitely many solutions and this is not correct. Explain the mistake.
The proof that ΔQPT ≅ ΔQRT is shown. Given: SP ≅ SR Prove: ΔQPT ≅ ΔQRT What is the missing reason in the proof? Statements Reasons 1. SP ≅ SR 1. given 2. ST ⊥ PR 2. converse of the perpendicular bisector theorem 3. PT ≅ RT 3. ? 4. QT ⊥ PR 4. ST and QT name the same line. 5. QP ≅ QR 5. perpendicular bisector theorem 6. ΔQPT ≅ ΔQRT 6. HL theorem definition of perpendicular bisector definition of congruence reflexive property substitution property
Answer:
A. definition of perpendicular bisector
Step-by-step explanation:
I JUST TOOK THE TEST!!!!!!
Answer:
The correct option is a) perpendicular bisector definition.
Step-by-step explanation:
Given :
Triangle QPT is similar to triangle QRT.
[tex]\rm SP \cong SR[/tex]
To find : Why [tex]\rm PT \cong RT[/tex]
Solution :
According to perpendicular bisector definition -
Perpendicular Bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment. Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.
Therefore, [tex]\rm PT \cong RT[/tex]
Hence option a) is correct.
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Find the length of arc xpy with a radius of 12m. leave in terms of pi./Users/alymcclellan/Desktop/Screen Shot 2017-07-31 at 10.25.17 PM.png
How many permutations are possible for 11 objects taken 7 at a time?
Help on this please show my work ?
Use the information about the bakery to explain how a manager can use a system of equations to plan employee time. Include a demonstration of how to solve the system of equations given in the problem and an explanation of how a restaurant manager would schedule oven and employee time.
angie andKenny play online video games angie buys 1 software package and 3 months of game play. Kenny buys 1 software package and 4 months of game play. each software package costs $20. if there total cost is $117 what is the cost of one month game play
Pablo plans to both run and swim. let r be the number of laps he runs and let s be the number of laps he swims. each lap he runs takes him 5 minutes, and each lap he swims takes him 2 minutes. he wants to exercise for at least 45 minutes today write an inequality
The function y=-2+5sin(pi/12(x-2)), what is the minimum value?
Answer:
-7
Step-by-step explanation:
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Answer:
-7
Step-by-step explanation:
We are given that a function
[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]
We have to find the minimum value of y.
We know that range of sin x is [-1,1].
[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]
[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]
[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]
[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]
[tex]-7\leq y\leq 3[/tex]
Maximum value of y=3
Minimum value of y=-7
Hence, the minimum value of given function =-7
The following set of coordinates most specifically represents which figure?
(−5, 6), (−1, 8), (3, 6), (−1, 4)
The correct answer is C: Rhombus. This is how you find your answer: desmos.com because you just plant in the ordered pair into the program and it plots out the shape for you. The only thing you need to know is your shapes and you should be set.
What is the value of x 20 35 60 70
Rewrite the equation in vertex form and then give the vertex of the quadratic equation
A=1/2(a+b)h solve for h
What is the solution to the system that is created by the equation y=-x+6 and the graph shown below?
if you roll a normal dice 120 times. How many odd numbers would you expect to get
Answer:
60 odd numbers
Step-by-step explanation:
A normal dice has 6 different sides numbered from 1 to 6, each side has the same probability of appearing when you roll the dice, i.e., in the long run each number will appear 1/6 of the times. We have three different odd numbers in a normal dice each will appear 1/6 of the times in the long run. Therefore, in the long run we hope to get 3/6 = 1/2 of the times an odd number and rolling the dice 120 times will produce about 120(1/2) = 60 odd numbers.
explain why the diagram displqyed on the right cannot represents a real object
Implify the expression. write your answer using decimals. 22.5 + 7(n−3.4
Will give brainliest to correct and best explained answer.
(08.06)The following data show the height, in inches, of 11 different garden gnomes:
2 9 1 23 3 7 10 2 10 9 7
After removing the outlier, what does the mean absolute deviation of this data set represent?
On average, the height of a garden gnome varies 3.2 inches from the mean of 7 inches.
On average, the height of a garden gnome varies 3.6 inches from the mean of 6 inches.
On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
On average, the height of a garden gnome varies 3.6 inches from the mean of 7 inches.
Answer:
The correct statement is:
On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
Step-by-step explanation:
We are given a data of 11 gardens as:
2 9 1 23 3 7 10 2 10 9 7
Now on removing the outlier i.e. 23 (since it is the very large value as compared to other data points) the entries are as follows:
x |x-x'|
2 4
9 3
1 5
3 3
7 1
10 4
2 4
10 4
9 3
7 1
Now mean of the data is denoted by x' and is calculated as:
[tex]x'=\dfrac{2+9+1+3+7+10+2+10+9+7}{10}\\\\x'=\dfrac{60}{10}\\\\x'=6[/tex]
Hence, Mean(x')=6
Now,
∑ |x-x'|=32
Now mean of the absolute deviation is:
[tex]\dfrac{32}{10}=3.2[/tex]
This means that , On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
Find the possible value or values of n in the quadratic equation 2n^2-7n+6=0
A cab ride from your home to the airport cost $23.47. If you want to tip the cab driver close to 10 percent of the fare, how much should you tip?
$0.24
$1
$3
$8
Answer:
Step-by-step explanation:
For all Plato users.
What is the solution to the following system of equations? X-2y=2, x-2y=-2
The given system of equations, x - 2y = 2 and x - 2y = -2, are parallel lines and do not intersect, thus there is no common solution to the system.
Explanation:In mathematics, to find the solution to a system of equations, we generally try to find the values of variables that satisfy all the equations in the system. When looking at the given equations: x - 2y = 2 and x - 2y = -2, we can see that there is something strange. These two equations are equivalent to each other, meaning they represent the same line. This is due to the fact that both equations have the same coefficients for the x and y variables (1 and -2 respectively). So, if two lines are equivalent, they are essentially the same line. This means there are infinitely many solutions which satisfy this system of equations, since all points on the line satisfy both equations. However, if two lines have the same coefficients but different constants (the numbers without the variables), as in our case, then they are parallel and do not intersect, indicating that there's no solution for the system of equations. Therefore, this system of equations has no solution.
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Find f'(x) for f(x) = −7x2 + 4x − 10.
BC is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth? Look at image attached.
Answer:
1. 19.2
Step-by-step explanation:
Please find the attachment.
Since we know that radius is perpendicular to tangent of a circle. So AB will be perpendicular to BC at c and DC is perpendicular to CB at C.
Now we will construct a perpendicular line to radius AB at point E from the center of our small circle. Since we have two right angles at point B and C so we will also have right angles at point E and D as well.
Length of CD is is 7 so length of BE will be 7 as well and length of EA will be 10-7=3. Length of DE will be equal to length BC that is 19.
Now we have formed a right triangle and now we will use Pythagoras theorem to find the length of AD.
[tex](AD)^{2}=(DE)^{2}+(EA)^{2}[/tex]
Upon substituting our values in above formula we will get,
[tex](AD)^{2}=(19)^{2}+(3)^{2}[/tex]
[tex](AD)^{2}=361+9[/tex]
[tex](AD)^{2}=370[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]AD=\sqrt{370}[/tex]
[tex]AD=19.2353840616713448\approx 19.2[/tex]
Therefore, the length of AD will be 19.2 and 1st option is the correct choice.
The box plot shows the number of years during which 24 colleges have participated in a local college fair
At least how many schools have participated for 2 years or fewer?
A.2 kids
B.4 kids
C.6 kids
D.7 kid
For the ordered pair, give three other ordered pairs with θ between −360° and 360° that name the same point. (3, 135°)
Three other ordered pairs with θ between −360° and 360° that name the same point as (3, 135°) are (−243, −45°), (−177, −15°), and (315, 495°).
Explanation:The ordered pairs (−243, −45°), (−177, −15°) and (315, 495°) all name the same point as (3, 135°) with θ between −360° and 360°.
To find these ordered pairs, you can add or subtract 360° to the given angle of 135° while keeping the x-coordinate constant at 3.
For example, you could subtract 360° from 135° to get −225° and combine it with the x-coordinate of 3 to get the ordered pair (3, −225°).
A traffic light is needed at each intersection. How many traffic lights are needed if there are 6 streets in the town.
To calculate the number of traffic lights needed for a town with 6 streets intersecting each other, you can use the formula Number of traffic lights = Number of intersections. In this case, 15 traffic lights are needed.
Explanation:A traffic light is needed at each intersection. How many traffic lights are needed if there are 6 streets in the town?
To determine the number of traffic lights needed for 6 streets, we use the formula: Number of traffic lights = Number of intersections. In a town with 6 streets, each street intersects with every other street, resulting in 15 intersections. Therefore, 15 traffic lights are needed for the 6 streets.
What number must you add to complete the square x^2+12x=-5
A 12
B 36
C 144
D 6
Answer: B. 36
Step-by-step explanation: Trust me!
Which of the following are pairs of congruent segments?
Check all that apply.
Find the midpoint of C and E. Simplify completely.
1. (–4,–3)
2. (0,–3)
3. (–4,–1)
4. (0,–1)
5. none of these
C=(-4,-4)
E = (4,-2)
-4 +4 = 0/2 =0
-4+-2 = -6/2 = -3
(0,-3)