Write an equation for a rational function with: Vertical asymptotes at x = − 3 and x = 4 x intercepts at x = − 2 and x = 1 y intercept at 4
Answers
The equation of the rational function with the given asymptotes is\(y=\frac{\frac{2}{3} (x+3)(x-4)}{(x+2)(x-1)}\).
What is a Function?A function sets the value of one set's elements to the value of another set's specified element.
An asymptote is a straight line that always approaches a given curve but never meets it at any infinite distance. To put it another way, an asymptote is a line that a curve approaches as it approaches infinity.
According to the given information:
To get vertical asymptotes at x=-3 and x=4, the denominator of the rational function has to be (x+3)(x-4). The reason is that when x=-3 or x=4, we would get division by zero, which is undefined, and causes the vertical asymptote.
To get x-intercepts at x=-2 and x=1, the NUMERATOR of the rational function has to be (x+2)(x-1). The reason is that when x=-2 or x=1, it causes the numerator to be 0. This makes y=0, and we have an x-intercept.
so far we have,
\(y=\frac{a(x+3)(x-4)}{(x+2)(x-1)}\)
The y-intercept at 4 gives us the point (0,4) which we can plug in to find a.
\(4=\frac{a(0+3)(0-4)}{(0+2)(0-1)}\)
\(4=\frac{-12a}{-2}\)
\(\frac{8}{12} =a\)
\(a=\frac{2}{3}\)
We will get a=2/3, so the final answer is:
\(y=\frac{\frac{2}{3} (x+3)(x-4)}{(x+2)(x-1)}\)
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Related Questions
show your work” below and solve the given equation for x showing all your steps.
3.5(6 – x) + 14 = 7 – 1.5(5x + 16)
please make the steps as clear as you can for brainliest!
Answers
Answer:
x=-13
Step-by-step explanation:
21-3.5x+14=7-7.5x-24
21+14-3.5x=7-24-7.5x
35-3.5x=-17-7.5x
35+17=3.5x-7.5x
52=-4x
-4. -4
x=-13
Three more than the product of 24 and a number
Answers
Answer:
24n+3
Step-by-step explanation:
More than means it comes after
The product of 24 and a number means multiply
24n
Now three more than
24n+3
Answer:
3 + 24a
Step-by-step explanation:
24a + 3
...
Reuben made a shirt using 7/8yards of red fabric and 1/4yards of yellow fabric. How many more yards of red fabric did Reuben use?
Answers
Answer and Step-by-step explanation:
To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:
7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8
So, Reuben used 5/8 yards more red fabric than yellow fabric.
If you answer I’ll give brainliest and points
(Question in photo!)
Answers
Answer:
c
Step-by-step explanation:
Answer:
KKKK
Step-by-step explanation:
can anyone help me find the area pls ty
Answers
area = length × breadth
area = 5.6 × 4.8
area = 26.88
therefore area = 26.88 sq. ft
hope it helps...!!!
Answer:
722.5344
Step-by-step explanation:
Corrine is purchasing beads to make a new necklace and bracelet set. The two pieces of jewelry each need silver and green beads. The necklace requires 25 silver beads and 15 green beads. The bracelet requires 10 silver beads and 5 green beads. Corrine paid $27.50 for the necklace beads and $10 for the bracelet beads. How much does each silver bead cost? How much does each green bead cost? Be sure to show your work and explain your answer.
Answers
Each silver bead costs $0.50, and each green bead costs $1.
Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.
According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.
The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.
Using this information, we can set up the following system of equations:
25s + 15g = 27.50 (Equation 1)
10s + 5g = 10 (Equation 2)
We can solve this system of equations using any appropriate method, such as substitution or elimination.
Let's use the elimination method to solve the system:
Multiplying Equation 2 by 3, we get:
30s + 15g = 30 (Equation 3)
Subtracting Equation 3 from Equation 1:
25s + 15g - (30s + 15g) = 27.50 - 30
-5s = -2.50
s = 0.50
Now, substituting the value of s into Equation 2:
10(0.50) + 5g = 10
5 + 5g = 10
5g = 5
g = 1
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Someone please help answer !
Choose the number that is closest to the mean of the distribution
Answers
The mean of the distribution is 3
What is arithmetic mean?Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
According to the first graph,
Given the bar of observations as :
0, 5, 6, 3, 1, 1, 3, 6, 4, 1
Here the Sum of Observations = 30
And the total number of observations = 10
The mean of the distribution = 30/10
The mean of the distribution = 3
According to the second graph,
Given the bar of observations as :
0, 1, 3, 3, 9, 0, 9, 4, 4, 1
Here the Sum of Observations = 34
And the total number of observations = 10
The mean of the distribution = 34/10
The mean of the distribution = 3.4
The mean of the distribution = 4 (closest)
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What’s the correct answer for this?
Answers
Answer:
A.
Step-by-step explanation:
We would reflect the point P so that another point would be made of the same length from the line.
Practice using graphs of equivalent ratios. On a coordinate plane, point (2, 3) is plotted.A 2-column table with 3 rows. Column 1 is labeled x with entries 2, blank, blank. Column 2 is labeled y with entries 3, blank, blank. The table shows one point from the given graph. How could you find more ordered pairs to create a graph and table of equivalent fractions? Check all that apply. Include the point (0, 0), which is on every graph of equivalent ratios. Multiply both 2 and 3 by 4. Multiply 2 by 2 and 3 by 3. Start at the point on the grid. Move right 2 and up 3 and plot the point. Multiply 2 by 3 and 3 by 2.
Answers
Answer:
2
Step-by-step explanation:
if you multiply 2 by 3=6
2×2=43×3=9Answer:
B: Using the table,multiply 2 and 1 both by 3
Step-by-step explanation:
Just took the quiz on Edge 2021
find the inverse of each function
Answers
Answer:
c
Step-by-step explanation:
assume base 10
-logy = x
\( \frac{1}{ log(y) } = x\)
log base x y = 5 turns into the format x^ 5 = y
implement that to get c
The sum of 9 and c is less than or
equal to 15.
Answers
Answer:
less than or equal to -26
Answer:
9+c < 15
OR
c < 6
Step-by-step explanation:
"the sum of 9 and c" means: 9+c
"is less than or equal to 15" means: < 15
If you need to simplify it, then subtract 9 from both sides, and you get
c < 6
What is the pow of a
4.5 x 10-3 M OH solution?
Answers
Answer:
p O H = 2.35
Step-by-step explanation:
Suppose you make a purchase for $814.13. You get a 70% discount, and sales tax is 10.4%.
Compute the sales tax. Round your answer to the nearest cent.
S
Compute the final cost of the purchase. Round your answer to the nearest cent
Answers
The sales tax is $25.4, and the final cost of the purchase is $269.64.
The actual price of the item is $814.13. The discount on the item is 70% of the actual price. The discount equals 70% * 814.13.The discount equals 0.7 * 814.13.The discount is $569.89.The discounted price of an item is the actual price minus the discount. The discounted price of this item is $814.13 - $569.89.The discounted price of this item is $244.24.The sales tax is applicable on the discounted price of the item. The sales tax is 10.4% of the discounted price. The sales tax is 10.4% * 244.24.The sales tax is 0.104 * 244.24.The sales tax is $25.4.The final cost of the item is the discounted price plus the sales tax. The final cost of the item = $244.24 + $25.4The final cost of the item is $269.64.To learn more about discount, visit :
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heeeeeeeeeellllllllllppppppppppppp
Answers
Answer:
AB = 28 , BC = 17.5 , X = 13.2
Step-by-step explanation:
since the figures are similar then the ratios of corresponding sides are in proportion, that is
\(\frac{AB}{PQ}\) = \(\frac{AD}{PS}\) ( substitute values )
\(\frac{AB}{8}\) = \(\frac{14}{4}\) ( cross- multiply )
4 AB = 8 × 14 = 112 ( divide both sides by 4 )
AB = 28
and
\(\frac{BC}{QR}\) = \(\frac{AD}{PS}\) ( substitute values )
\(\frac{BC}{5}\) = \(\frac{14}{4}\) ( cross- multiply )
4 BC = 5 × 14 = 70 ( divide both sides by 4 )
BC = 17.5
similarly for the 2 similar figures
\(\frac{x}{6}\) = \(\frac{11}{5}\) ( cross- multiply )
5x = 6 × 11 = 66 ( divide both sides by 5 )
x = 13.2
Answer:
\(\overline{AB}=28\)
\(\overline{BC}=17.5\)
\(x=13.2\)
Step-by-step explanation:
Question 4If quadrilateral PQRS is similar to quadrilateral ABCD, their corresponding sides are in the same ratio:
\(\overline{PQ} : \overline{AB} = \overline{QR} : \overline{BC} = \overline{RS} : \overline{CD} = \overline{SP}:\overline{DA}\)
From inspection of the two quadrilaterals, the given side lengths are:
\(\overline{PQ} = 8\)
\(\overline{QR} = 5\)
\(\overline{RS} = 6\)
\(\overline{SP} = 4\)
\(\overline{DA} = 14\)
Substitute these into the ratio equation:
\(8 : \overline{AB} = 5 : \overline{BC} = 6 : \overline{CD} = 4:14\)
Solve for AB:
\(8 : \overline{AB} = 4:14\)
\(\dfrac{8}{\overline{AB}}= \dfrac{4}{14}\)
\(8 \cdot 14=4 \cdot{\overline{AB}}\)
\(\overline{AB}=\dfrac{8 \cdot 14}{4}\)
\(\boxed{\overline{AB}=28}\)
Solve for BC:
\(5 : \overline{BC} = 4:14\)
\(5 \cdot 14=4 \cdot \overline{BC}\)
\(\overline{BC}=\dfrac{5 \cdot 14}{4}\)
\(\boxed{\overline{BC}=17.5}\)
\(\hrulefill\)
Question 5Assuming the two figures are similar, their corresponding sides are in the same ratio. Therefore:
\(x:6=11:5\)
\(\dfrac{x}{6}=\dfrac{11}{5}\)
\(x=\dfrac{11 \cdot 6}{5}\)
\(x=\dfrac{66}{5}\)
\(\boxed{x=13.2}\)
Write the augmented matrix for the system of linear equations. (Do not perform any row operations.)
x − y + 8z = 8
3x − 9y + z = −1
8x + y = 0
Answers
Answer:
Step-by-step explanation:
To create an augmented matrix, we need to transfer the coefficients of each system of equations into its respective place in the matrix. The first row will be the coefficients of the first equation and so on. The number to the right of the equals sign is the last column of the augmented matrix.
\(\left[\begin{array}{ccc|c}1&-1&8&8\\3&-9&1&-1\\8&1&0&0\end{array}\right]\)
Write a two-column proof for the following information. Upload your proof below.
Given: M is the midpoint of CD; CM = 5x – 2; MD = 3x + 2
Prove: x = 2
Answers
The required two column proof is explained below.
What is a midpoint?A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.
The two column proof for the information is given as:
M is the midpoint of CD (Given)
CD = CM + MD (addition property of a line segment)
CM = MD (definition of a midpoint)
So that;
5x – 2 = 3x + 2 (Definition of midpoint)#
Then,
5x - 3x = 2 + 2 (collecting like terms)
2x = 4
x = 2
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List all the 4-tuples in the relation {(a,b,c,d) | a,b,c,d∈!+ , a+b+c+d = 6}
Answers
We have a total of seven 4-tuples that satisfy the given relation.The given relation is {(a,b,c,d) | a,b,c,d∈!+ , a+b+c+d = 6}. It can be understood as the set of 4-tuples (a, b, c, d) such that a, b, c, and d are positive integers and their sum is equal to 6.
Let's now list all the possible 4-tuples that satisfy the given relation. The possible combinations are as follows: (1, 1, 1, 3), (1, 1, 2, 2), (1, 2, 1, 2), (2, 1, 1, 2), (1, 2, 2, 1), (2, 1, 2, 1), and (2, 2, 1, 1).
Here's a brief explanation on how these 4-tuples were obtained. Let a, b, c, and d be positive integers such that a+b+c+d = 6. The least possible value that each variable can take is 1.
So, we start with a=1 and find all possible values of (b, c, d) that satisfy the given equation. Then, we move to a=2 and repeat the process. Finally, we list all the possible 4-tuples that we obtained.
Thus, we have a total of seven 4-tuples that satisfy the given relation.
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The area of the circle x² + y2 - 6x-4y +9 = 0 is
Answers
Answer:
Your answer is here.Enjoy dude
Answer:
12.56 unit²
Step-by-step explanation:
Given:x² + y² - 6x - 4y + 9 = 0To find:The area of circleSolution:The form of the circle is:
(x- h)² + (y-k)² = r²Let's bring the given to the form of a circle as above:
x² + y² - 6x - 4y + 9 = 0x² - 6x + y²- 4y + 9 = 0 ⇒ combining like terms and completing squarex² - 6x + 9 + y²- 4y + 4 = 4 ⇒ adding 4 to both sides(x-3)² + (y - 2)² = 2² ⇒ got the form of this circleAs per the form, we got r² = 2², so the radius of circle is 2 units.
The area of circle:
A= πr² = 3.14×2² = 12.56 unit²Please help, thanks!
Answers
The change in function values is f(40) - f(10) = 49 - 55 = -6.
The change in x-values is 40 - 10 = 30.
Therefore, the average rate of change is -6/30, which simplifies to -1/5.
The average rate of change of the function over the interval 10 < x ≤ 40 is -1/5.
Triangle SRTs angle R is 59° angle T is 79° what is the length of ST to the nearest 10th of a yard 
Answers
If Triangle SRTs angle R is 59° angle T is 79° the length of ST to the nearest 10th of a yard is 6.1
How do we find the length ST of a triangle?Since we have given that
ΔSRT is a triangle with measures :
SR = 7 yd
∠T = 79°
∠R = 59°
We need to find the side ST .
To find the length of ST, we can use the Law of Sines, which states:
sin(T) / SR = sin(R) / ST
sin(79°) / 7 = sin(59°) / ST
0.14 = sin(59°) / ST
ST = sin(59°)/0.14 ⇒ 0.8572 / 0.14 ≈ 6.1229
Therefore, the length of ST is approximately 6.1 yards to the nearest tenth of a yard
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f(x) = √3x
g(x) = 3x + 2
Find (4) (2). Include any restrictions on the domain.
Answers
Option A is correct. The value of function (f/g)(x) is found to be \(\sqrt[3]{3x}\)/(3x+2) where the condition is that x ≠ -2/3.
What exactly is a function composition?In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
What is the sum of two functions?The new function obtained by performing f first and then g is the combination of two functions g and f.
Given:
f(x) = \(\sqrt[3]{3x}\)
g(x) = 3x + 2
(f/g)(x) = \(\sqrt[3]{3x}\)/(3x+2)
Also, the denominator should not be equal to 0.
So, 3x + 2 ≠ 0
x ≠ -2/3
Therefore, the value of function is found to be \(\sqrt[3]{3x}\)/(3x+2) where the condition is that x ≠ -2/3. So, Option A is correct
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Help The equation 4x − 4 = 2x represents two electric scooters traveling in opposite directions, where x represents the distance in miles between the scooters. What is the distance, in miles, between the scooters?
*
1 point
x = 0.5
x = 2
x = 4
x = 8
Answers
The distance in miles between the two electric scooters travelling in opposite direction is 2 miles.
What is an equation?An equation is a formula that proves the equality of two mathematical expressions in algebra and is the most commonly used formula. For example, in the expression 3x + 5 = 14 the two terms 3x + 5 and 14 are separated by the "equals" symbol.
What is distance?
The length or width in between two objects, points, lines, etc. Distance is the condition or fact that something or someone is physically apart.
Given 4x - 4 = 2x,
so 2x = 4
x = 2
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Can someone help me, please?
Answers
Answer:
16
Step-by-step explanation:
7x+20+2x-5=159
9x+15=159
9x=159-15
9x=144
x=16
PLEASEEEEEE HELPPPPPPPPPP MEEEEEEEEEEEEEEEE
Answers
Answer:
120.2 or in other words, the answer is the last option, D
Britany wants to read a book. In her room, she has 5 mysteries, 15 historical fictions, 12 modern fantasies, and 7 blographies. how many different choices are available ?
a. 78
b. 34
c. 32
d.39
Answers
Answer
I guess
39 different choice are available
100 POINTS PLEASE HELP FAST
Select the correct answer.
The weight of a radioactive isotope was 96 grams at the start of an experiment. After one hour, the weight of the isotope was half of its initial weight. After two hours, the weight of the isotope was half of its weight the previous hour. If this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time?
Answers
The top left graph represents the weight of the radioactive isotope over time.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for the function in this problem are given as follows:
a = 96, b = 0.5.
Hence the function is given as follows:
\(y = 96(0.5)^x\)
Two points on the graph of the function are given as follows:
(1,48) and (2, 24).
Hence the top left graph represents the weight of the radioactive isotope over time.
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Answer:
Graph W
Step-by-step explanation:
The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.
Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).
The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.
Initial weight: 96 grams
After 1 hour: 96 / 2 = 48 grams
After 2 hours: 48 / 2 = 24 grams
After 3 hours: 24 / 2 = 12 grams
After 4 hours: 12 / 2 = 6 grams
After 5 hours: 6 / 2 = 3 grams
So, the points on the graph would be:
(0, 96), (1, 48), (2, 24), (3, 12), (4, 6), (5, 3)Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.
Solve for x.
X - 2 = 3( 2 - X ) divided by 4
Answers
Answer:
x = 7/12
Step-by-step explanation:
We start off by multiplying both sides by 4:
4(x-2) = 3(2-x)
Distribute the 4 and the 3:
4x - 8 = 6 - 3x
Bring all the terms with the x at the first side:
4x + 3x = 6 + 8
7x = 12
x = 7/12
PLEASE HELP!!! WILL GIVE BRAINLIEST!!
Answers
Answer:
I think it would be a
Step-by-step explanation:
im rlly srry if im wrong!
Please help!!!!
Find the surface area of the composite figure below to
the nearest tenth.
Answers
Answer:
16801.2cm²
Step-by-step explanation:
Cone :
SA = πrl
SA = π · 28 · 45 90-45 = 45
SA = 3958.406744
Cylinder :
SA = 2 · π · r · ( r+h)
SA = 2 · π · 28 ( 28 +45 )
SA = 2 · π · 28 (73)
SA = 12842.83077
12842.83077 + 3958.406744 =
16801.2cm²
PLEASE HELPPP ASAP I REALLY NEED MATH HELPPPP
Answers
The graph of the odd-degree polynomial reaches positive and negative infinity.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
The given polynomial is shifted towards the left it reaches negative infinity quicker than positive infinity.
Also, the graph of the polynomial is of odd degree as it is symmetric about the origin shifted towards left.
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