The solution to the given functions are:
a) f(x) is an even function because f(−x) = f(x)
b) f(x) is an odd function because f(-x) = -f(x)
c) f(x) is neither even nor odd because f(-x) ≠ f(x) nor f(-x) ≠ -f(x)
How to find the even or odd function?A function f is said to be an even function if f(−x) = f(x), for all x in the domain of f. A function f is said to be an odd function if f(−x) = −f(x), for all x in the domain of f.
a) The function is given as:
f(x) = 2x⁴ - x² - 4
f(-x) = 2(-x)⁴ - (-x)² - 4
= 2x⁴ - x² - 4
Thus, it is an even function because f(−x) = f(x)
b) The function is given as:
f(x) = 2x³ + ¹/₋ₓ
f(-x) = 2(-x)³ + ¹/₍₋ₓ₎
= -2x - ¹/ₓ
Thus, it is an odd function because f(-x) = -f(x)
c) The function is given as:
f(x) = 2x² - 7x + 10
f(-x) = 2(-x)² - 7(-x) + 10
f(-x) = 2x² + 7x + 10
Thus, it is neither even nor odd because f(-x) ≠ f(x) nor f(-x) ≠ -f(x)
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During practice, the players on a softball team warm up by running the bases. This graph shows the relationship between the number of hours, x, of practice the players attend and the number of minutes, y, the players spend running the bases.
How many minutes do the players spend running the bases during each hour of practice?
The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
In the context of this problem, the variables x and y are given as follows:
Variable x: number of hours.Variable y: time spent running the bases.The equation for the constant is given as follows:
k = y/x.
Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.
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The graph below shows the solutions to which inequality?
A. x^2-3x+3 ≥0
B. x² + 3x-3 <0
C. x²-3x+3<0
D. x² + 3x-3>0
The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.
option B.
What is the solution of the inequality?The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;
The solution of the graph,
x > -4 and x < 1
The first equation with "≥" is ruled out because the graph doesn't have a thick dot.
Let's simplify the second expression;
x² + 3x - 3 < 0
solve using quadratic formula;
x > -3.79 or x < 0.79
The third expression is ruled out since its solution will be complex.
For the last expression;
x² + 3x - 3 > 0
x < -3.79 or x > 0.79
Thus, the correct inequality expression is x² + 3x - 3 < 0.
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Are the graphs of the pair of equations parallel, perpendicular, or neither?
y = 2x + 1
2x - y = 3
Answer:
See below
Step-by-step explanation:
y = 2x+1 <==== is in form y = mx + b where 'm' is the slope
....arrange the other into this form
y = 2x-3 <===== this has the same slope as the other line
so the two lines are PARALLEL
I’LL GIVE BRAINLIEST, A HEART, AND 5 STARS TO WHOEVER ANSWERS FIRST
(Please answer ALL questions and show how you got the answer!)
Group B has lower range.
Group A shows variability.
Mean is the best to make concussion about age of Salsa students.
Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.
This inference is supported by the observation that the majority of data points in Group B are concentrated around younger ages.
In contrast, Group A exhibits a more dispersed distribution of data points across a wider range of ages, including higher.
So, Group B has lower range.
and, Group A shows variability.
Lastly, Mean is the best to make concussion about age of Salsa students.
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Transversal angles
Find x.
Answer: 79
Step-by-step explanation:
Assuming lines k and l are parallel, x=79 by the alternate exterior angles theorem.
solve the PDE using separation of variables method Uxx = 1/2 Ut 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
The general solution of the partial differential equation is:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
How to solve Partial Differential Equations?The partial differential equation (PDE) is given as:
Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Assume that the solution can be written as a product of two functions:
U(x, t) = X(x)T(t)
Substituting this into the PDE, we have:
X''(x)T(t) = (1/2)X(x)T'(t)
Dividing both sides by X(x)T(t), we get:
(X''(x))/X(x) = (1/2)(T'(t))/T(t)
Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:
(X''(x))/X(x) = -λ²
(1/2)(T'(t))/T(t) = -λ²
Simplifying the second equation, we have:
T'(t)/T(t) = -2λ²
Solving the second equation, we find:
T(t) = Ce^(-2λ²t)
Applying the boundary condition U(0, t) = 0, we have:
U(0, t) = X(0)T(t) = 0
Since T(t) ≠ 0, we must have X(0) = 0.
Applying the boundary condition U(3, t) = 0, we have:
U(3, t) = X(3)T(t) = 0
Again, since T(t) ≠ 0, we must have X(3) = 0.
Therefore, we can conclude that X(x) must satisfy the following boundary value problem:
X''(x)/X(x) = -λ²
X(0) = 0
X(3) = 0
The general solution to this ordinary differential equation is given by:
X(x) = Asin(λx) + Bcos(λx)
Applying the initial condition U(x, 0) = 5*sin(4πx), we have:
U(x, 0) = X(x)T(0) = X(x)C
Comparing this with the given initial condition, we can conclude that T(0) = C = 5.
Therefore, the complete solution for U(x, t) is given by:
U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)
where:
Σ represents the summation over all values of n
λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).
To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):
X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0
X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0
From the first equation, we have Bₙ = 0.
From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.
This implies that 3λₙ = nπ, where n is an integer.
Therefore, λₙ = (nπ)/3.
Substituting the eigenvalues into the general solution, we have:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
where Aₙ are the coefficients that can be determined from the initial condition.
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Hosting a dinner party for 38 people, you plan to serve peach pie for desert.
Each pie has 8 slices.
How many slices are in each pie?
Answer:
40 slices
Step-by-step explanation:
I rounded 38 to 40 and divided by 8
1.
(03.03 MC)
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answer:
sept one
Step-by-step explanation:
the perimeter of a triangle is 32 feet. One side of the triangle is 11 feet longer than the second side. The third side is 9 feet longer than the second side. Find the length of each side.
Answer:
One side - 15 feet
Second side - 4 feet
Third side - 13 feet
Step-by-step explanation:
Let's call the sides A B and C, respectively.
We know that:
A = B + 11
C = B + 9
and that
A + B + C = 32
Please note that we have 3 equations and 3 unknowns. We can solve this, we'll use substitution.
A + B + C = (B + 11) + B + (B + 9) = 32
3B + 20 = 32
3B = 12
B = 4
The sides have lengths of 4+11 = 15, 4 and 4+9 = 13. This is in fact a proper triangle (because the shorter sides add up to more than the longer side).
Can y’all please help me answer this, this My last question
Answer:
x ft is the answer since X = 10
so it means 10 ft
Select the correct answer.
Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14?
68% of the data points lie between 10 and 14.
68% of the data points lie between 8 and 12.
68% of the data points lie between 10 and 18.
68% of the data points lie between 10 and 16.
Answer:
68% of the data points lie between 10 and 18.
Step-by-step explanation:
one standard deviation to left of mean = 14 - 4 =10
one standard deviation to right of mean = 14 + 4 = 18
68% of data is in this region.
so the answer is 68% of the data points lie between 10 and 18.
The square prism has a base length of 2 ft. Which describes the cross section of the prism that iS perpendicular to the
base?
12 ft
O a rectangle with two 12-ft sides and two 2-ft sides
O a rectangle with two 12-ft sides and two sides that are shorter than 2 ft
a nonrectangular parallelogram with two 12-ft sides and two 2-ft sides
Answer:
A-a rectangle with two 12-ft sides and two 2-ft sides
Step-by-step explanation:
Got it right on edge
Give a recursive definition for the following set of ordered pairs of positive integers (\(a|b\) means that a is a factor of b): \(S=\){\((a,b)|a \in Z^+, b \in Z^+, a|b\)}
A recursive definition for the set S can be given as follows:
What is recursion?
Recursion is a programming technique where a function calls itself to solve a problem.
Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.
Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.
In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.
The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.
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what is the slope of the line -3y=12x+6
Answer:
Step-by-step explanation:
uhh
Gabriel’s father has a garden in the back yard. The dimension of the garden are shown here 7 3/4 and 2 2/3
The area of Gabriel's father's garden is 62/3 square units, which is approximately 20.67 square units.
The question's purpose is obscure. But, based on its measurements of 7 3/4 by 2 2/3, I'm assuming you're interested in learning how to locate the location of Gabriel's father's garden.
We must multiply the length by the breadth in order to determine the garden's area. To make the calculation simpler, we can convert the mixed values to improper fractions as follows:
7 3/4 = (7 × 4 + 3)/4 = 31/4
2 2/3 = (2 × 3 + 2)/3 = 8/3
The garden is thus 8/3 in width and 31/4 in length. We multiply these values to determine the area:
Area is equal to 31/4 x (8/3), or 62/3 square units.
The size of Gabriel's father's garden is therefore 62/3 square units, or roughly 20.67 square units.
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IS MY ANSWER CORRECT ?? ASA IS THE WRONG ANSWER BTW
Answer:
yes
Step-by-step explanation:
How many different rays can be named?
Answer:
millions
Step-by-step explanation:
the possibilities are endless
Does anyone know answer please?
Answer:
Step-by-step explanation:
The complete question in the attached figure
we know that
When two lines are crossed by another line (transversal), a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal, are called Alternate Interior Angles.
When the two lines being crossed are Parallel Lines the Alternate Interior Angles are congruent
In this problem
---> by alternate interior angles
we have
therefore
The value of 0.01 gramis equivlent to
Answer:
10 milligrams
Step-by-step explanation:
Answer:
1 milligrams
milligrams
a) You have a piece of string that is 36m long. find the areas of all the shapes you can make which have a perimeter of 36m. b) A piece of land has an area of 100m². How many meters of wire fencing is needed to enclose it?
a. The areas of the square is 81m² and for rectangle is 72m²
b. The perimeter of the square is 40m
What are the areas of all the shapes you can make which have a perimeter of 36m?a. To determine the area of the shapes in which we have that have a perimeter of 36m, we can consider rectangle and square.
For a square;
Perimeter of square = 4L
36 = 4L
L = 9m
The area of the square will be L² = 9² = 81m²
For a rectangle;
The perimeter of rectangle is;
P = 2(L + W)
We can assume that two numbers which will represent the length and width are;
L = 12m, W = 6m or L = 6m, W = 12m
A = 12 * 6 = 72m²
b.
The area of the wire is 100m², the perimeter for this can be calculated when we consider square and rectangle;
Perimeter of square = 4L
Area of square = L² = 100m²
L = 10m
The perimeter of the wire is 4(10) = 40m
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Find the slope and y-intercept of the equation.
y=-07x-9
Answer:
Slope: -7
y-intercept: (0, -9)
Step-by-step explanation:
Calculate the circumference of a circle with a radius of 8 inches.
To calculate the circumference of a circle, you can use the formula:
\(\displaystyle C=2\pi r\)
Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.
Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:
\(\displaystyle C=2\pi (8)\)
Simplifying the expression:
\(\displaystyle C=16\pi \)
Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.
Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Fill in the missing statement and reason of the proof below.
Given:
A
E
‾
≅
E
B
‾
AE
≅
EB
and
∠
D
A
B
≅
∠
C
B
A
.
∠DAB≅∠CBA.
Prove:
△
A
D
E
≅
△
B
C
E
△ADE≅△BCE.
The included angle of one triangle are congruent to the corresponding parts of the other triangle. Since the sides AD and BE are congruent, as well as the included angle DAB and CBA, then △ADE≅△BCE.
By the Side-Angle-Side (SAS) congruence theorem, if two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, then the triangles are congruent. In this proof, the given statements provide that the sides AE and EB are congruent, as well as the angles DAB and CBA. This means that the two corresponding sides of the triangles △ADE and △BCE are congruent, and the included angles of the triangles are also congruent. Therefore, according to the SAS congruence theorem, the two triangles are congruent, and thus △ADE≅△BCE.
The SAS congruence theorem applies to any two triangles, regardless of the size or shape of the triangles. The congruence of the sides and angles is sufficient to prove that two triangles are congruent. This theorem can be used to prove other theorems, such as the Triangle Sum Theorem, which states that the sum of the angles in a triangle is equal to 180 degrees. To prove this theorem, one could use the SAS congruence theorem to show that two right triangles are congruent, and then use the congruent angles to prove that the sum of the angles in a triangle is 180 degrees.
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Suppose the derivative of a function is ′()=(−7)^7(−2)^2(+13)^10. Then the function is increasing on the interval _____.
4
(Graphing Proportional Relationships LC)
The table shows a proportional relationship.
x 12 8 24
y 3 26
Describe what the graph of the proportional relationship would look like.
O Aline passes through the point (0, 0) and continues through the point (3, 12).
O Aline passes through the point (0, 0) and continues through the point (2,8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
Question 2(Multiple Choice Worth 2 points)
(Graphing Proportional Relationships MG)
The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)
For the first question:
The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.
The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.
Now, let's analyze the answer options:
A. A line passes through the point (0, 0) and continues through the point (3, 12).
This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.
B. A line passes through the point (0, 0) and continues through the point (2, 8).
This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).
C. A line passes through the point (0, 0) and continues through the point (6, 24).
This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.
D. A line passes through the point (0, 0) and continues through the point (12, 3).
This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).
Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.
For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?
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A real estate agent works on 11% commission. What is her commission on house that she sold $346,000?
A real estate agent commission on the house that she sold $346,000 is $38,060.
Given that, a real estate agent works on 11% commission.
We need to find out what is her commission on the house that she sold $346,000.
What is the commission?The commission is a percentage of total sales as determined by the rate of commission. Commission=Rate of commission⋅Total sales. To find the commission on a sale, multiply the rate of commission by the total sales.
Now, the commission on the house=11% of 346,000
=11/100 × 346,000
=0.11 × 346,000
=$38,060
Therefore, a real estate agent commission on the house that she sold $346,000 is $38,060.
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Find the area of the rhombus.
Answer:
12 is the correct answer
Step-by-step explanation:
diameter is 12
Someone please help me fast! here is screenshot algebra. QUICK PLSSS
Answer:
\(\displaystyle{f(x)=3^x-5}\)
Step-by-step explanation:
Being translated up-down means that the value exists outside of x. Therefore, we can cancel B and C choice since those are horizontal (left-right) translation.
Our only choice is A and D. However, D is being translated up since it's +5. Thus, the only correct answer that a function is being translated down is:
\(\displaystyle{f(x)=3^x-5}\)
or A choice.
) 100 जना मानिसमा गरिएको सर्वेक्षणमा 65 जनाले दुध र 55 जनाले दही मन पराउँछन् । यदि 15 जनाले दुवै मन पराउँदैनन् भने भेनचित्र प्रयोग गरी दुध र दही दुवै मन पराउने मानिसको सङ्ख्या पत्ता लगाउनुहोस् । In a survey of 100 people, 65 like milk and 55 like curd. If 15 like none of these, by using Venn-diagram, find how many people like both milk and curd. 12- मूल्य अभिवृद्धि कर सहित बिक्री गरियो । यदि
Answer:
X=35
Step-by-step explanation:
if the translated part is the full question; the answer is attached ⬆️.
Hope it helps
2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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