Answers
The equation that represents the represents the rational function in the graph, based on the asymptotes and the intercepts is; y = ((3/4)·x - 3)/(x + 3)
What is an asymptote of a function?An asymptote is a line that approaches a curve but at any infinite distance, is still at some distance from the curve.
The asymptotes of the functions are;
Horizontal asymptote; x = -3
Vertical asymptote; y = 1
The points on the graph are;
y-intercept = (0, -1)
x-intercept = (4, 0)
The function is a rational function of the form f(x) = P(x)/Q(x)
The horizontal asymptote of x = -3 indicates that the denominator has a factor of (x + 3)
The vertical asymptote of y = 1 indicates that the degree of the numerator and the denominator are the same and the leading coefficients are the same
The function is therefore in the form; f(x) = (a·x + c)/(x + 3)
a = 1, therefore;
f(x) = (x + c)/(x + 3)
The y-intercept (0, -1) indicates that when x = 0, y = -1, therefore;
-1 = (0 + c)/(0 + 3)
-3 = c
c = -3
The function is therefore;
f(x) = y = (a·x - 3)/(x + 3)
The x-intercept (4, 0), indicates that when y = 0, x = 4, therefore;
0 = (a·4 - 3)/(4 + 3)
a·4 - 3 = 0
a = 3/4 = 0.75
The function is therefore;
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Related Questions
Which equation represents f(x)?
O f(x) = 3√x+6+1
Of(x) = 3√x-6 +1.
O f(x)=3√x+6-1
O f(x)=3√x-6-1
Answers
The equation of the straight line would be -
y = 2x.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a straight line passes through the points (2, 4) and (3, 6).
Refer to the graph of the function attached. We can see that the function that represents the graph is -
\($y=\sqrt[3]{x+6} \;+1\)
Therefore, the function representing the graph is -
\($y=\sqrt[3]{x+6} \;+1\)
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Complete the table. Answer should be T or F.
P Q
T F P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
F T P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
Answers
P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
T T T T T F F F F F T T
F T T F F T T T T T F F
P F T F F T T T T T F F
-P T T F F T T T T T F F
-Q T T T T F T F F F T T
-P V -Q T T F F T T T T T F
-P -> Q T T F F T T T T T F
-P -> -Q T T F F T T T T T F
P <-> Q T T T T F T T T T F
Here is a more detailed explanation of how I filled out the table:
P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.
P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.
P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.
P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.
-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.
-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.
-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.
-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.
-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.
P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.
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A piggy bank contains dimes and nickels that are worth a total of $42.45. If there are 197 nickels, how
many dimes are there?
Answers
Answer:
326 dimes.
Step-by-step explanation:
total value = 197 * value of one nickel
total value = 197 * 0.05
total value = 9.85
Value of dimes = 42.45 - 9.85
Value of dimes = 32.60
1 dollar contains 10 dimes
32.60 dollars contain x dimes
1/32.60 = 10/x Cross multiply
x = 32.60 * 10
x = 326 Dimes
Answer: 326 dimes
Step-by-step explanation:
q + 0.05(197) = 42.45
q + 9.85 = 42.45
q = 42.45 - 9.85
q = $32.6
32.6 / 0.10 = 326
The graph below represents the function f(x) and the translated function g(x) .
If f(x) = x ^ 2 , which of the following functions could be an algebraic representation of g(x) ?
Answers
Answer: D. \(g(x) = (x-b)^2\)
Explanation:
If we want to shift the curve some distance b to the right, then we'll need to replace x with x-b. What this effectively does is shift the xy axis itself b units to the left while the curve is fixed in place. This gives the illusion of the curve moving b units to the right.
Put another way: the old input x is updated to the new input x-b which is smaller by b units. This helps explain why the xy axis is shifted to the left this amount.
So that's how we go from \(f(x) = x^2\) to \(g(x) = (x-b)^2\). You can think of it as \(g(x) = f(x-b) = (x-b)^2\)
Reuben is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Reuben has been adding money. Suppose that x and y are related by the equation 750=40x.
Answers
Based on equation 750=40x, the value of x is 18.75 weeks.
What is an equation?An equation is a mathematical statement that two or more algebraic expressions are equal or equivalent.
Equations must have the equation symbol (=) to show the equality of the mathematical expressions.
Equations are started with let statements, defining the variables.
Let the total amount of money in the account = y (in dollars)
Let the number of weeks Reuben has been adding money = x
Equation:750 = 40x
40x = 750
x = 18.75 (750/40)
Thus, based on the solution to the equation, we know that Reuben has added money into the account for 18.75 weeks.
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Question Completion:Compute the number of weeks Reuben has been putting money into the account.
Higher Order Thinking Morgan read
a thermometer at 7:00 P.M. The
temperature was 16°C. This temperature
was 9°C less than the temperature at
2:00 P.M. The temperature at 2:00 P.M.
was 10°C higher than the temperature at
8:00 A.M. What was the temperature at
8:00 A.M.?
Answers
The temperature at 8:00 A.M. was 15°C.
Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.
We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C
3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.
Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C
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Miranda takes a piece of wood that is 1/2 of an inch thick and glues it to a piece of wood thatis 7/10 of an inch thick. Together, what is the thickness of the two pieces of wood? Write your answer as a fraction or as a whole or mixed number.
Answers
Miranda takes a piece of wood that is 1/2 of an inch thick and glues it to a piece of wood that
is 7/10 of an inch thick. Together, what is the thickness of the two pieces of wood?
Write your answer as a fraction or as a whole or mixed number.
step 1
Adds 1/2 and 7/10
Multiply 1/2 by (5/5)
1/2(5/5)=5/10
therefore
5/10+7/10=12/10
convert to mixed number
12/10=10/10+2/10=1+1/5=1 1/5 in
answer is
1 1/5 inFind the average value of the functions on the given interval.
Average value of
f\left(x\right)=x [4,9]
Answers
The average rate of change of the function over the interval is 1
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
f(x) = x
The interval is given as
From x = 4 to x = 9
The function is a linear function
This means that it has a constant average rate of change
So, we have
f(4) = 4
f(9) = 9
Next, we have
Rate = (9 - 4)/(9 - 4)
Evaluate
Rate = 1
Hence, the rate is 12
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Two buckets of paint have the same mass and temperature. They are combined into one larger bucket. The larger bucket starts at the same temperature as the paint. The larger bucket of paint has the same temperature as the original buckets of paint.
The amount of thermal energy in the larger bucket of paint is about ________ the amount of thermal energy in each of the smaller buckets of paint.
Is the space the same as, twice, or one-half?
Answers
The larger bucket paint contains roughly the same amount of thermal energy as each of the smaller buckets of paint.
What is defined as the thermal energy?Thermal energy is the energy possessed by a substance or system as a result of particle movement within the object or system.
Thermal energy is one of several types of energy, with 'energy' characterized as 'the capacity to do work.'Thermal energy is a form of kinetic energy, that is energy due to motion, because it is caused by particle movement. Thermal energy causes something to have an internal temperature, which can be measured.As, the thermal energy is due to the kinetic energy.
Thus, the kinetic energy of an object is directly proportional to its mass; thus, doubling the mass doubles the kinetic energy.
In, the given case, the paint contained in the two buckets are combined.
Thus, the mass is remained constant.
The larger bucket also have the the same temperature. thus, the thermal energy will not change.
Therefore, the amount of thermal energy with in larger bucket of paint is roughly equal to the amount of thermal energy in all of the smaller buckets of paint.
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After adding the two equations to eliminate x you are left with 4y=-8. Solve for y: y =
Answers
Answer: -2
Step-by-step explanation:
4y/4 = -8/4
y = -2
Answer:
Step-by-step explanation:
Answer is -2
The stem-and-leaf plot shows the test scores for a chemistry class.
How many students had a score greater than 90 points?
5 2
6
7
8
4 6
0 1 4 6 8 8 8
0 1 2 3 4 6 8 8
1 2 3 4 67
9
10 0
Key: 74 74
Answers
7 students had a score greater than 90 points. The solution has been obtained by the stem-and-leaf plot.
What is a stem-and-leaf plot?
The arrangement and representation of data in a stem and leaf plot, sometimes referred to as a stem and leaf diagram, makes it easy to see how frequently different data values occur. It is a graph that shows sequential numerical data.
In a stem and leaf plot, a data value's digits are separated into a stem (the first few digits) and a leaf in a particular table (usually the last digit). The stem and leaf values are divided and represented by the symbol "|".
At the left of the vertical bar, we are given tens places.
Since, we need to find the scores greater than 90, therefore, we will start at the row in the stem and leaf plot with a 9 to the left.
In that row, to the right there are 6 values which are 1, 2, 3, 4, 6, and 7.
So, this means that there are six scores here which are higher than 90. The scores are 91, 92, 93, 94, 96, and 97.
Also, there is one score in the row with 10 at tens place which is 100.
Thus, total 6 scores in the 9 row and 1 score in the 10 row makes 7 students score greater than 90.
Hence, 7 students had a score greater than 90 points.
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8. If floor boards are 2 inches wide, how many will be required to cover a floor 17 feet wide?
Answers
Answer:
Step-by-step explanation:
12 inches per foot
17 (12) = 204 inches
204 inches/ 2 inches/board = 102 boards
What is the solution to -4(8x-3x) greater than or equal to 6x -8
Answers
Step-by-step explanation:
Answer:
x <= 4/13
Step-by-step explanation:
-4(8x - 3x) >= 6x - 8
-4(5x) >= 6x - 8
-20x >= 6x - 8
-26x >= -8
x <= 8/26
x <= 4/13
Find the volume of a cube with the given side length 5a²
Answers
We know
\(\boxed{\sf Volume_{(cube)}=(side)^3}\)
\(\\ \sf\longmapsto Volume=(5a^2)^3\)
\(\\ \sf\longmapsto Volume=5^3a^6\)
\(\\ \sf\longmapsto Volume=125a^6\)
The required volume of the given length 5a² is 125a⁶ units.
Given that,
To determine the volume of a cube with the given side length 5a².
Volume is defined as the ratio of the mass of an object to its density.
Here,
The volume of the cube is given by the cube of its one side because all the sides are identical in the cube and have an angle of 90° with any of the adjacent sides.
So,
The volume of the cube = (side)³
The volume of the cube = (5a²)³
The volume of the cube = 125a⁶
Thus, the required volume of the given length 5a² is 125a⁶ units.
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the elevator can accommodate at most 1500 lbs.Carl is transporting boxes that weigh 15lbs each. If carl weighs 170 lbs.Write an equation that can be used to determine the most number of boxes Carl can transport using the elevator
Answers
Answer:
15x+170≤1500
Step-by-step explanation:
it is at most 1500, so less than or equal to 1500, and the 15 lbs relies on the number of boxes so 15x and carl weighs 170 so that must be added, equaling to
15x+170≤1500
Last year, the City of Greenpoint experienced a budget deficit of $ 838,880. By comparison, the expected deficit for this year is 50% lower. What is the expected deficit for this year?
Answers
Here I will help you
Step-by-step explanation:
We have to divide 838,880 in to the 50% Like this
838,880/50%=1676
Sarah rides her bike with a
constant speed of 15 km/h. How
far can she travel in 6.8 hours?
Answers
Multiply 15 and 6.8. So speed * time = distance
So the answer is 102
NO LINKS!!!
For questions 1-3, decide whether each transformation will result in congruent or similar figures.
1. Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis.
2. ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin.
3. Line segment XY is rotated 90° about the origin , dilated by a scale factor of -1/2, and then reflected in the line x = 5.
Answers
Answer:
1) Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis. This will result in congruent figures. Translation only moves the figure without changing the size or shape, and reflection in the y-axis will mirror the figure across the y-axis without altering its size or shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.
2) ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin. This will result in congruent figures. Dilation by a scale factor of 2 will double the size of the triangle while maintaining its shape, and rotation by 180° about the origin will flip the triangle over the origin while maintaining its shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.
3) Line segment XY is rotated 90° about the origin, dilated by a scale factor of -1/2, and then reflected in the line x = 5. This will result in similar figures. Rotation by 90° about the origin will rotate the line segment by 90 degrees, dilated by a scale factor of -1/2 will shrink the size by half but with a change in direction and reflection in the line x = 5 will mirror the figure across the x=5 line without altering its size or shape. Since all the operations maintain the shape of the figure but the size changes, the resulting figure will be similar to the original one.
Translation and reflection doesn't change the shape or size of the figure, therefore the resulting figure is congruent to the initial one.
Question 2Rotation doesn't change the shape of the figure, but dilation changes the size, therefore the resulting figure is similar to the initial one.
Question 3Rotation and reflection don't change, but dilation changes the size, therefore the resulting segment is similar to the initial one.
The human body is made up of about 9.3% hydrogen. What is the amount of hydrogen contained in a person who weighs 140 pounds? Round you answer to the hundredths place
Answers
Answer:
We know that for a human body 9.3% of its total mass is hydrogen.
Now we have a person with a mass of 140 lb.
Then we have that the 100% of the mass is 140lb, the 9.3% of this is hydrogen.
We can write:
9.3% = X
100% = 140lb
We want to find the value of X (mass of hydrogen)
Then we can take the quotient of these two equations to get:
(9.3%/100%) = X/140lb
Now we can isolate the variable X to get:
(9.3%/100%)*140lb = X = 13.02 lb
So this person has about 13.02 lb of hydrogen in his/hers body.
11. Which one of the following is unique? b. mode a. Mean c. Median d. A and B
Answers
Among the mean, mode, and median, the unique one is the b. mode.
What is the mode?The mode is the data value that occurs many times more than other data values.
Unlike the mean that shows the average value of all the data values, the mode occurs more. While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.
Similarly, the median can be computed when two values occur as the middle values.
Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.
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find the height of a cylindrical water vessel of diameter 1.4m if it holds 770L of water?
Answers
Answer:
0.5 meter
Step-by-step explanation:
Calculate the height of the vessel. = 0.77 m³ So, Volume of the cylinder, V = 0.77 m³. Hence, the height of the cylinder is 0.5 meter
Find the value of y. log 4 64 = y A. 3 B. 4 C. 8 D. 16
Answers
Answer:
A. 3
Step-by-step explanation:
\( log_{4}(64) = y \\ 64 = {4}^{y}(\because if \: log_a b = x \implies b = a^x) \\ {4}^{3} = {4}^{y} \\3 = y..(equal \: bases \: have \: equal \: exponents ) \\ \huge \purple { \boxed{y = 3}}\)
PLEASE HELP ASAP THANK YOU!
Answers
Answer:
D
Step-by-step explanation:
8.42×1000=8420 which is between 8400 and 8500
Answer:
the answer would be D
Step-by-step explanation:
8.42 x 10^3 = 8420
What is 12% of 50?
ОА.
6
ОВ.
7
Ос.
10
OD.
12
Answers
Answer:
a 6
Step-by-step explanation:
can i have brainlest
Is 18.18 rational or irrational
Answers
Answer:
Rational
Step-by-step explanation:
You are able to put 18.18 in a fraction.
Hope this helped, Have an AMAZING day/night!
5. Determine the value of t4 in an arithmetic sequence given that t₁ = 11 and S9 = 243.
Answers
The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).
We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.
From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:
243 = (9/2)(2(11) + (9-1)d)
243 = 9(22 + 8d)
243 = 198 + 72d
45 = 72d
d = 45/72 = 5/8
Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:
tₙ = a + (n-1)d
t₄ = 11 + (4-1)(5/8)
t₄ = 11 + 3(5/8)
t₄ = 11 + 15/8
t₄ = 88/8 + 15/8
t₄ = 103/8
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A researcher needs to split 20 plants into two treatment groups of 10 plants each. How many different groupings can be formed?
Answers
2
If there are only 20 plants and they have to be broken up into groups of 10 then the answer would be 2.
-Ɽ3₮Ɽ0 Ⱬ3Ɽ0
(x-3) + (2x-1) + (3x-2) + (2x-3) + x = 360°
Find the value of x,
Answers
Answer:
41
Step-by-step explanation:
simplify the left side:
\(9x - 9 = 360\\9x = 369\\x = 41\)
Answer:
\(x=41\)
Step-by-step explanation:
1. Simplify the expression
\(x-3+2x-1+3x-2+2x-3+x=360\)
Group like terms:
\(\left(x+2x+3x+2x+x\right)+\left(-3-1-2-3\right)=360\)
Simplify the arithmetic:
\(9x+\left(-3-1-2-3\right)=360\)
Simplify the arithmetic:
\(9x-9=360\)
2. Group all constants on the right side of the equation
\(9x-9=360\)
Add 9 to both sides:
\(9x-9+9=360+9\)
Simplify the arithmetic:
\(9x=360+9\)
Simplify the arithmetic:
\(9x=369\)
3. Isolate the x
\(9x=369\)
Divide both sides by 9:
\(\frac{9x}{9}=\frac{369}{9}\)
Simplify the fraction:
\(x=\frac{369}{9}\)
Find the greatest common factor of the numerator and denominator:
\(x=\frac{41\cdot 9}{1\cdot 9}\)
Factor out and cancel the greatest common factor:
\(x=41\)
Terms and topics
Linear equations with one unknownCheers,
ROR
What is the length of CD to the nearest 10th?
Answers
Answer:
\(\huge \boxed{\mathrm{10.3 \ units}}\)
Step-by-step explanation:
To solve for CD, we can create a right triangle.
Where CD becomes the hypotenuse.
The length of the base of the triangle is 9 units.
The length of the height of the triangle is 5 units.
Apply Pythagorean theorem to solve for the hypotenuse.
\(\sf hypotenuse = \sqrt{(base )^2 +(height )^2 }\)
\(c=\sqrt{9^2 +5^2 }\)
\(c=\sqrt{106}\)
\(c \approx 10.29\)
all the faces of the prism meet at right angles. the volume the prism is 490m cube. what is the surface area of the prism?
Answers
The required surface area of the prism is 378 square meters.
How to find the area of Prism?To find the surface area of the prism, we need to know the dimensions of the prism. Let's call the length, width, and height of the prism l, w, and h, respectively.
Since the prism has right angles between its faces, we know that it is a right rectangular prism.
The formula for the volume of a right rectangular prism is V = lwh, and we know that the volume of the prism is 490m^3. Therefore,
lwh = 490
We are not given any specific values for l, w, or h, so we need to use another piece of information to solve for one of these variables.
The surface area of a right rectangular prism is given by the formula
SA = 2lw + 2lh + 2wh
If we can find the value of one of these dimensions, we can use it to calculate the surface area of the prism
lwh = 490
Since we know that the prism has right angles between its faces, we can assume that its dimensions are integers. We can start by testing integer values for l and w, and see if we can find an integer value for h that satisfies the equation.
For example, if we let l = 7 and w = 10, we get
7 * 10 * h = 490
Simplifying, we get
70h = 490
Dividing both sides by 70, we get
h = 7
Therefore, the dimensions of the prism are l = 7, w = 10, and h = 7.
To find the surface area, we can substitute these values into the formula for SA:
SA = 2lw + 2lh + 2wh
= 2(7)(10) + 2(7)(7) + 2(10)(7)
= 140 + 98 + 140
= 378
Therefore, the surface area of the prism is 378 square meters.
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