Answers
Horizontal asymptotes: y = 2 ; vertical asymptotes: x = 2; x- intercept and y- intercept is at (0,0).
Explain about the asymptotes:A value that you approach steadily yet never quite reach is an asymptote. An asymptote is a line in mathematics that a graph reaches but never crosses. It can be horizontal, vertical, or slanted.
A graph's vertical asymptote is a vertical line with the equation x = a, where the graph tends to positive or negative infinity as when the inputs get closer to the value of a. A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph moves closer to the line even as inputs get closer to ∞ or –∞.Given function:
f(x) = 2x² /(x² - 4)
horizontal asymptotes:
As the degree of both numerator and denominator is same that is 2.
The horizontal asymptotes y = a/b
a - leading coefficient of numerator
b - leading coefficient of denominator
y = 2/1 = 2
horizontal asymptotes: y = 2
vertical asymptotes:
Put the denominator = 0 and find the 'x'.
(x² - 4) = 0
x² = 4
x = ± 2
vertical asymptotes: x = 2
x- intercept : Put f(x) = 0 and find 'x'.
f(x) = 2x² /(x² - 4)
0 = 2x² /(x² - 4)
2x² = 0
x = 0
x- intercept : x = 0
y- intercept : Put x = 0 and find 'f(x)'.
f(x) = 2(0)² /((0)² - 4)
f(x) = 0
y- intercept is at 0
Thus, x- intercept and y- intercept is at (0,0).
The graph for the function is drawn using the graphing tool, as shown.
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Related Questions
The graphs below have the same shape. What is the equation of the graph of g(x)?
A. g(x) = (x-2)^2
B. g(x) = (x+2)^2
C. g(x) = x^2 - 2
D. g(x) = x^2 + 2
Answers
Answer:
Step-by-step explanation:
B. Because adding 2 moves you to the left when inside the parentheses.
What are the 4 properties of a rhombus?
Answers
- Opposite angles are equal in a rhombus.
- The diagonals bisect each other at 90 degrees.
- Adjacent angles add up to 180 degrees.
The 4 properties of the rhombus are:
All sides of the rhombus are equalThe opposite sides of a rhombus are parallelOpposite angles of a rhombus are equaldiagonals bisect each other at right angles.What is a rhombus?A quadrilateral in Euclidean geometry is a rhombus. It's a parallelogram with all sides equal and diagonals intersecting at 90 degrees. In addition, opposing sides are parallel, and opposing angles are equal. This is a fundamental property of the rhombus. A rhombus is shaped like a diamond. As a result, it's also known as a diamond.
Some of the important properties of the rhombus are as follows:The rhombus's sides are all equal. A rhombus' opposite sides are parallel. A rhombus' opposite angles are equal. Diagonals in a rhombus bisect each other at right angles. Diagonals cut the angles of a rhombus in half. 180 degrees is the sum of two adjacent angles. When you connect the midpoints of the sides, you will get a rectangle. When you join the midpoints of half the diagonal sides as the axis of rotation, you will get another rhombus.To know more about Rhombus visit the link
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Find the lengths of AC and BC, and find the measure of angle B.
please help :)
Answers
Answer:
I know that the angle is 57
Step-by-step explanation:
The equation y = 20x + 500 models the relationship between the number of video games, x, a company manufactures and the cost in dollars, y, to manufacture that number.
Answers
Kai wants to buy a new surfboard. He earns $12.50 each time he mows a lawn. He keeps track of the total amount of money that he has, y, with the equation y-12.5x+30
. The x represents the number of lawns that Kai mows. What does the y-intercept represent in this equation?
A
The cost of the surfboard
B
The number of lawns that Kai mows
C
The total money that Kai will make
D
The money that Kai started with before he mowed any lawns
Answers
Answer:
D. The money that Kai started with before he mowed any lawns.
Step-by-step explanation:
We Know
The equation is y = mx + b
The x represents the number of lawns that Kai mows.
What does the y-intercept represent in this equation?
The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.
Answer:
The Answer is D
Step-by-step explanation:
у - 2x = 3
Solve for y
Answers
Isolate y by adding 2x to both sides:
y = 3 + 2x
Answer:
y=2x+3
Step-by-step explanation:
y-2x =3
add 2x on both sides
y=2x+3
If your heart rate is 120 beats per minute during strenuous exercise, what is the period of a single heart beat in units of seconds
Answers
I hope this helps (:
Renting a truck for a day costs $75, plus 0.50 for every mile the truck is driven. Function f represents the cost of a day's rental in dollars as a function of the total miles driven x. Which function represents the total miles driven as a function of the daily rental cost?
A-F^-1(x)=2x+150
B-F^-1(x)=2x-150
C-F^-1(x)=0.5x+75
D-F^-1(x)=0.5x-75
Answers
Alinehasaslopeof 1/3 anda y-intercept of –5What isitsequationin slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
\(y = \frac{1}{3}x - 5\)
Step-by-step explanation:
Given
\(slope\ (m) = \frac{1}{3}\)
\(y\ intercept = -5\)
Required
Determine the line equation in slope intercept
The equation of a line in slope intercept is:
\(y = mx + b\)
Where
\(m = slope = \frac{1}{3}\)
\(b = y\ intercept = -5\)
So, \(y = mx + b\) becomes
\(y = \frac{1}{3}x - 5\)
12 / | - 4 | x 3 + |5|
Answers
Answer:
Step-by-step explanation:
Given, 12 / (-4) * 3 + 5
Here we can use the BODMAS rule and solve this problem.
B ⇒ Brackets
O ⇒ Of
D ⇒ Division
M ⇒ Multiplication
A ⇒ Addition
S ⇒ Subtraction
Now, let’s solve this by applying the BODMAS rule.
BracketsIn the given sum we can find the Brackets in (-4).
12 / -4 * 3 + 5
OfThere is no Of in this sum.
Let’s gust ignore it.
12 / -4 * 3 + 5
DivisionIn this sum we can Divide 12 and -4.
-3 * 3 + 5
MultiplicationIn this sum we can Multiply -3 and 3.
-9 + 5
AdditionIn this sum we can Add -9 and 5.
-4
PLZ PLZ HELP ME ILL MARK AS BRAINLIESTT!!
Answers
Answer:
option B would be the closest estimation.
Answer:
B.) 50 * 80 = 4,000 yd^2
Step-by-step explanation:
Estimate meaning round the numbers
A regular pentagon has perimeter 42.5 cm.
What is the length of each side?
Answers
Answer:
8.5 cm
Step-by-step explanation:
A regular pentagon has 5 congruent sides , then
length of each side = perimeter ÷ 5 = 42.5 ÷ 5 = 8.5 cm
The boundary value problem Td^2y/dx^2+ pw^2y = 0, y(0) = 0, y(L) = 0 is a model of the shape of a rotating string. Suppose T and p are constants the non-trivial solutions for y are Select the correct answer. (a) y = sin(wnx) (b) y = cos(wnx) (c) y = sin(w2nx) (d) y=cos(w2nz) (e) none of the above
Answers
The non-trivial solutions for y in the given boundary value problem are of the form y = A sin(pwnx/T) or y = A cos(pwnx/T), where A is a constant determined by the initial conditions and n is a positive integer. Therefore, the correct answer is (a) y = sin(wnx).
To solve the given boundary value problem Td^2y/dx^2 + pw^2y = 0 with boundary conditions y(0) = 0 and y(L) = 0, we first consider the non-trivial solutions for y.
The general solution for this homogeneous differential equation is:
y(x) = A * sin(wx) + B * cos(wx)
Now, we apply the boundary conditions:
1) y(0) = 0:
0 = A * sin(0) + B * cos(0)
0 = A * 0 + B * 1
0 = B
So, B = 0, and our solution becomes:
y(x) = A * sin(wx)
2) y(L) = 0:
0 = A * sin(wL)
Since we are looking for non-trivial solutions, A ≠ 0, which means sin(wL) must be 0. This occurs when wL = nπ, where n is an integer. So, w = (nπ)/L.
Thus, the non-trivial solutions for y are:
y(x) = A * sin((nπx)/L)
Comparing this to the given options, the correct answer is (a) y = sin(wnx).
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a right isosceles triangle has legs 6 meters long each. find the length of the hypotenuse to the nearest tenth of a meter
Answers
Answer:
6√2, or about 8.5 meters
what is the distance along the unit circle between any two successive 8th roots of 1?
a. π/8
b. π/6
c. π/4
d. π/2
Answers
The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.
To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.
Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.
Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.
Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.
Therefore, the correct answer is option c. π/4.
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There is a line through the origin that divides the region bounded by the parabola y=5x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?
Answers
The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.
To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.
Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.
To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.
Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.
Therefore, the slope of the line that divides the region into two equal areas is 5.
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Which of the following represents the dimensions of the room
Answers
Given:
The length of the rectangular room is 6 more than the width.
The area of the room, A = 27 square units.
Required:
We need to find the dimensions of the given rectangular room.
Explanation:
Let w be the width of the rectangle.
6 more than means add 6.
The length of the rectangle, l= w+6.
Consider the area of the rectangle formula.
\(A=lw\)Substitute A = 27, and l=w+6 in the formula.
\(27=(w+6)w\)\(27=w^2+6w\)Subtract 27 from both sides of the equation.
\(27-27=w^2+6w-27\)\(0=w^2+6w-27\)\(w^2+6w-27=0\)\(Use\text{ }6w=9w-3w.\)\(w^2+9w-3w-27=0\)Take out the common multiple.
\(w(w+9)-3(w+9)=0\)\((w+9)(w-3)=0\)\((w+9)=0,(w-3)=0\)\(w=-9,3\)The measure is always positive.
\(w=3\text{ units,}\)Substitute w =3 in the equation l =w+6.
\(l=3+6=9\text{ units.}\)We get l =9 units and w =3 units.
Final answer:
The dimensions of the room are 3 and 9.
PLEASE HELP!! solve for x
Answers
The value x in the secant line using the Intersecting btheorem is 19.
What is the numerical value of x?
Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.
From the image;
External line segement of the first secant line = 8
First sectant line segment = ( x + 8 )
External line segement of the second secant line = 9
First sectant line segment = ( 15 + 9 )
Using the Intersecting secants theorem:
8 × ( x + 8 ) = 9 × ( 15 + 9 )
Solve for x:
8x + 64 = 135 + 81
8x + 64 = 216
8x = 216 - 64
8x = 152
x = 152/8
x = 19
Therefore, the value of x is 19.
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What is the coefficient of y in the expression 2x4+3y
Answers
Answer:
3
Step-by-step explanation:
find the value of X
Answers
Answer:
x = \(\frac{91}{6}\)
Step-by-step explanation:
Given 2 intersecting chords in a circle, then
The product of the parts of 1 chord is equal to the product of the parts of the other chord, that is
6x = 7 × 13 = 91 ( divide both sides by 6 )
x = \(\frac{91}{6}\)
Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 1 + cos cos($) -ISXS*, with n = 3, 4, and 6. Illustrate each case with a sketch similar to the figure shown below. (Round your answers to two decimal places.) n = 3: upper sum ll lower sum n = 4: upper sum II lower sum n = 6: upper sum IO lower sum
Answers
In this Trigonometric Functions F(x) = 1 + cos(1/X): n=3 (12.01, 8.10), n=4 (11.65,8.50), and n=6 (11.24, 9.12), with their upper and lower value
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
F(x) = 1 + cos(1/X)
for n=3
Upper sum = 12.01
Lower sum = 8.10
Δx = (b-a)/n = 2π / 3
for n=4
Upper sum = 11.65
Lower sum = 8.50
Δx = (b-a)/n = π / 2
for n=6
Upper sum = 11.24
Lower sum = 9.12
Δx = (b-a)/n = π / 3
Hence, n=3 (12.01, 8.10), n=4 (11.65,8.50), and n=6 (11.24, 9.12), with their upper and lower value.
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Sheldon picks tomatoes from his garden. He picked 5 3/10 kg, but 1.5 kg were rotten and had to be thrown away. How many kilograms of tomatoes were not rotten?
A. 4 8/10 kg.
B. 3 4/5 kg.
C. 3 5/10 kg.
D. 3 8/10. kg.
Answers
Eric is preparing for a regional swim meet that is a month away. He swims the same distance and clocks his best time on several different days. He plots the best time (in minutes) he swam each day as his y-variable and the day he swam it as his x-variable. When he plots his times and finds a line of best fit, he gets the equation y=−0.03x+3.45.
If Eric continues to practice, on the 15th day his best time for the day should be _[blank]_ minutes.
Enter the value that correctly fills in the blank, like this: 42
Do not round your answer.
Answers
Answer:
On the 15th day his best time for the day is 3 minutes.Step-by-step explanation:
The line that best fits is
\(y=-0.03x+3.45\)
Where \(x\) is days and \(y\) is time in minutes. So, we have \(x=15\), replacing this in the equation and solving for \(y\), we have
\(y=-0.03(15)+3.45=-0.45+3.45=3\)
Therefore, on the 15th day his best time for the day is 3 minutes.
please help really I need help
Answers
Answer:
kkeierikrore
Step-by-step explanation:
46 and big pp no csp
Use the given sets below to find the new set. Write the simplest version of the resulting set. For example (−[infinity],5]∪(−2,6) should be written as (−[infinity],6). Be sure to record your answer using interval notation. If the intersection is empty, type DNE as the answer. A=[−4,1] and B=[−3,0] A∩B=
Answers
The intersection of set A = [-4, 1] and set B = [-3, 0] is [-3, 0]. This means that the resulting set contains the values that are common to both sets A and B.
To determine the intersection of sets A and B, denoted as A ∩ B, we need to identify the values that are common to both sets.
Set A is defined as A = [-4, 1] and set B is defined as B = [-3, 0].
To determine the intersection, we look for the overlapping values between the two sets:
A ∩ B = [-4, 1] ∩ [-3, 0]
By comparing the intervals, we can see that the common interval between A and B is [-3, 0].
Therefore, the simplest version of the resulting set, A ∩ B, is [-3, 0] in interval notation.
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Please I need you to help me and show the steps please so I can understand it better
I will mark brainliest
Answers
Answer:
LM = √34
Step-by-step explanation:
L is at (-7, 4), and M is at (-2, 1).
LM
\( \sqrt{ {( - 7 - ( - 2))}^{2} - {(4 - 1)}^{2} } \)
\( \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} \)
A sector of a circle has central angle 120° and radius of 6 units. what is the area of the sector?
Answers
The area of the sector is 12π square units.
Given data:
To find the area of the sector, use the formula:
\(\text{Area of Sector} = \frac{\text{Central Angle} }{ 360^\circ} * \pi * r^2\)
Given that the central angle is 120° and the radius is 6 units.
Substitute these values into the formula:
\(\text{Area of Sector} = \frac{120^\circ }{ 360^\circ} * \pi * 6^2\)
\(A = \frac{1}{3} * \pi * 36\) square units
A = 12π square units
Hence, the area of the sector is 12π square units.
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A club consists of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve and Samuel).
Find P(S-name U Boy)
Answers
The probability of selecting a person with a name that starts with S or a boy is \(\frac{5}{8}\)
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Given that, a club consists of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve and Samuel)
To find P(S-name U Boy), that is the probability of selecting a person whose name starts with S or boy.
n(S-name U Boy) = 5 {2 girls (Sarah, Suzie), 3 boys( Kevin, Steve and Samuel )}
Number of favourable outcomes=5
Total number of outcomes=5+3=8
P(S-name U Boy) \(=\frac{Number of favourable outcomes}{Total number of outcomes}\)
\(=\frac{5}{8}\)
Therefore, the probability of selecting a person with a name that starts with S or a boy is \(\frac{5}{8}\).
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What is the solution to the equation?
6-ste
e
3
2+52-9
2+53 +53-9-5
a-3
2:53 -9
a+54 +5 - 9+53
a-143
2+53 -9
e
Answers
Answer:
a = 3 \(\frac{1}{3}\)
Step-by-step explanation:
Given
a + 5 \(\frac{2}{3}\) = 9 ← change mixed number to improper fraction
a + \(\frac{17}{3}\) = 9 ( multiply through by 3 to clear the fraction )
3a + 17 = 27 ( subtract 17 from both sides )
3a = 10 ( divide both sides by 3 )
a = \(\frac{10}{3}\) = 3 \(\frac{1}{3}\)
Derivations (20 marks): For each of the questions in this section provide a derivation. Other methods will receive no credit i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks) iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
Answers
¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
Proof:
1. ∃x(Fx & Gx) [Premise]
2. Fx & Gx [∃-Elimination, 1]
3. ∃xFx [∃-Introduction, 2]
4. ∃xGx [∃-Introduction, 2]
5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]
6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)
Proof:
1. ¬ 3x(Px v Qx) [Premise]
2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]
3. Vx ¬ Px [∀-Introduction, 2]
4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]
iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
Proof:
1. ¬ Vx(Fx → Gx) v 3xFx [Premise]
2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]
3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]
4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]
5. Fx → Gx [Resolution, 3, 4]
6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
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