The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
What is composite function?Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.
Given:
u(x) = x^2 + 3
w(x) = √x+2
We have to find (w о u)(2) and (u о w)(2).
First to find (w о u)(x)
(w о u) = w(u(x))
= w(x^2 + 3)
(w о u) = √(x^2 + 3) + 2
(w о u)(2) = √(2^2 + 3) + 2
(w о u)(2) = √7 + 2
Now to find (u о w).
(u о w)(x) = u(w(x))
= u(√x+2)
= (√x+2)^2 + 3
= x + 4√x + 4 + 3
(u о w)(x) = x + 4√x + 7
(u о w)(2) = 2 + 4√2 + 7
(u о w)(2) = 9 + 4√2
Hence,
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
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Which is the equation of the axis of symmetry of the graph of y = –3(x – 6)2 + 5?
x = –6
x = –5
x = 5
x = 6
The equation that represents the axis of symmetry of the graph of the quadratic function is the line; x = 6
What is a quadratic function?A quadratic function is a function that has 2 as the highest exponent. The shape of the graph of a quadratic function is a parabola, which is U shaped.
The equation of the axis of symmetry of the graph of y = -3·(x - 6)² + 5 is obtained as follows.
The specified equation is in the vertex form of a quadratic function, which is; f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinate of the vertex
The equation of the axis of symmetry is x = h
Comparison of the equation, y = -3·(x - 6)² + 5 and the vertex form of a quadratic equation, we get.
The vertex, (h, k) = (6, 5)
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How many square inches of cloth are cut from the square (n = 3.14) if it’s 38inches
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The radius is given as,
r = 36 / 2
r = 18 inches
The area of the circle is given as,
A = π x (18)²
A = 3.14 x 324
A = 1,017.36 square inches
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
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The complete question is given below.
A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth is cut from the square?
(π = 3.14)
1,017.36 in2
1,489.24 in2
1,182.96 in2
1,276.00 in2
arthur benjamin says that the current top of the pyramid of mathematics curriculum is
railroad crew can lay 5 miles of track each day. They need to lay 140 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function.
Answer:
L = 140 - 5d
Step-by-step explanation:
To get the length left to lay you're going to have to multiply 5 and the number of days and further subtract it from 140
What is the sum of the 2 solutions of the equation x^2-4x-45=0???
PLEASE HELP!!
Answer:
The first x is 9
The second x is -5
Step-by-step explanation:
if (-1)^n+(-1)^4n =0 then n is?
a) any positive number b) any negative number c)any odd number d)any even number
The correct statement regarding the value of n is given as follows:
c) any odd number.
How to obtain the value of n?The expression for this problem is given as follows:
(-1)^n+(-1)^4n.
The numeric value for the expression is given as follows:
0.
The n powers of -1 are given as follows:
Negative 1 if n is odd.Positive 1 if n is even.(-1)^4n will always be an even power due to the multiplication by the even number 4, hence it is positive.
As (-1)^4n is always positive and the numeric value of the expression is of zero, we have that (-1)^n is always negative one, meaning that the value of n is an odd number.
This means that option c is correct.
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Solve for m.D:
D (9x-44)
X =
(6x+7)
Answer:
m∠D = 109
Step-by-step explanation:
This is a parallelogram.
In parallelograms, the opposite interior angles are congruent, so we can write the following equation to find, first value x the measure of m∠D:
9x - 44 = 6x + 7
Transfer like terms to the same side of the equation.9x - 6x = 7 + 44
Add/subtract.3x = 51
Divide both sides by 3x = 17
Now we can calculate measure of m∠D:
m∠D = 9x - 44
Rewrite equation using the value we found for x.9×17 + 44 = 109
Write a quadratic equation in x such that the sum of its roots is 9 and the product of its roots is −19.
x² - 9x-19=0 is a quadratic equation in x such that the sum of its roots is 9 and the product of its roots is −19.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
If the Sum of zeroes and Product of the zeroes of a quadratic equation is given then the quadratic equation is
x² - sum of the zeroes x + Product of the zeros =0
In the given question sum of its roots is 9 and the product of its roots is −19.
So the equation will be x² - 9x-19=0
Hence, x² - 9x-19=0 is a quadratic equation in x such that the sum of its roots is 9 and the product of its roots is −19.
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Question
Name the included angle between JK¯¯¯¯¯¯¯¯
and KL¯¯¯¯¯¯¯¯
.
Answer:
K is the angle between JK and KL. It is called the included angle of sides JK and KL.
A pizza delivery man makes $50.00 a shift. If he makes $3.00 on each shift he makes, how much money will he make if he makes 22 deliveries in one shift?
The total money to make 22 deliveries in one shift is, $116.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
A pizza delivery man makes $50.00 a shift.
And, He makes $3.00 on each shift.
Now, For the total money to make 22 deliveries in one shift is,
⇒ $50 + $3 × 22
⇒ $50 + $66
⇒ $116
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2.Find the GCF(224,264) using Euclid division algorithm.
Answer:
GCF = 8.
Step-by-step explanation:
First, we divide 264 by 224 and we get the identity:
264 = 1*224 + 40 ( That is 264 divided by 224 goes once and the remainder is 40)
Now we divide 224 by 40 to get:
224 = 5*40 + 24
Repeating this process, we get:
40 = 1*24 + 16
24 = 1*16 + 8
16 = 2*8 + 0 <------ we stop because the remainder is 0.
So, The GCF is 8.
How many types of polynomials are there in class 9?.
There are three types of polynomials in class 9 there are linear, quadratic, and cubic polynomials.
The words Nominal, which means "terms," and Poly, which means "many," are combined to make the word polynomial.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Linear polynomials are straightforward and simple to solve. Isolate the variable term first, then set the equation's solution equal to zero.
First, rewrite the expression using a quadratic polynomial in the order of decreasing degree. To find the equation's solution, equate the equation and use polynomial factorization.
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The perimeter of a rectangular garden is 4.8 meters. Its length is twice its width. How wide is the garden? (Full Answer)
Answer:
0.8 meters is the width.
Step-by-step explanation:
Answer: 0.8
Step-by-step explanation: All you have to do is set the equation up so you're looking at the length being twice the width (which in equation form would be l=2w) then you say there is two lengths, so you have 4w. Then you add the original width to the lengths (2w) so you have 6w= 0.8
B is the midpoint of AC. AB - 6x + 1 and BC - 2x + 9. Find the length of AC
The length of AC in the line segment is 26 units.
How to find the length of a line segment?B is the midpoint of AC.
AB = 6x + 1
BC = 2x + 9
A midpoint is a point lying between two points and is in the middle of the line joining the two points.
Hence,
AB = BC
6x + 1 = 2x + 9
6x - 2x = 9 - 1
4x = 8
divide both sides by 4
x = 8 / 4
x = 2
Therefore,
AC = 2AB
AC = 2(6x + 1)
AC = 2(6(2) + 1)
AC = 2(12 + 1)
AC = 26 units
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Why do parallel lines require the undefined terms of line and plane?.
Parallel lines require the terms line and plane because line and plane that are parallel cannot cross each other. Thus, they will never create a point of intersection. The characteristics of that parallel lines consist of lines and planes.
The characteristics of parallel lines are;
The shortest distance between parallel lines is the same at all points along the lines.
The lines are on the same plane.
As the plane is prolonged indefinitely, the lines do not intersect.
The characteristic of these geometric figures that create the different requirements would be how these undefined terms are situated. In the case of parallel lines, these are lines that would not intersect no matter how long the line is extended or whether it goes infinitely; thus, the lines lie on the same plane.
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The lengths of the sides of a triangle are x, x + 11, and 2x + 5. a. Write a formula for the perimeter, simplifying your answer. b. If the perimeter is 72 cm, find the value of x.
What is the ratio of a 30 60 90 triangle?.
The angles of a 30-60-90 triangle are in the ratio 1: 2 : 3.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Circle X has a diameter of 5 inches. Circle Y has a diameter of 3 inches. Which measurement is the closest to the difference between the circumference of circle X and the circumference of Circle Y
The difference between the circumference of circle X and the circumference of Circle Y will be 6.28 inches.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference. Let d be the diameter of the circle.
The circumference of the circle will be
C = πd units
Circle X has a diameter of 5 inches. Then the circumference is given as,
⇒ π x 5
⇒ 3.14 x 5
⇒ 15.7 inches
Circle Y has a diameter of 3 inches. Then the circumference is given as,
⇒ π x 3
⇒ 3.14 x 3
⇒ 9.42 inches
The difference is calculated as,
⇒ 15.70 - 9.42 inches
⇒ 6.28 inches
The difference between the circumference of circle X and the circumference of Circle Y will be 6.28 inches.
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How to solve triangles?.
There are several methods to solve a triangle such as SSS, SAS, ASA, and HL, using the Pythagorean theorem, the Law of Sines, and the Law of Cosines.
SSS (Side-Side-Side) Congruence: If the lengths of all three sides of one triangle are equal to the lengths of all three sides of another triangle, the two triangles are congruent.SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the two triangles are congruent.ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the two triangles are congruent.HL (Hypotenuse-Leg) Congruence: If the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the two triangles are congruent.Using the Pythagorean theorem: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.Law of Sines: states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.Law of Cosines: states that the square of the length of the hypotenuse of a triangle is equal to the sum of the squares of the lengths of the legs, minus twice the product of the lengths of the legs and the cosine of the angle between them.To learn more about the triangle, visit:
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halp i need this asap
Answer: 126 mm^2 - C
Step-by-step explanation: Hello! The formula for area of a triangle is 1/2(b)(h). b = base and h = height. You would multiply the base and height by 1/2 because a triangle is 1/2 the size of a square. The formula for the area of a square is (b)(h), and you would have to multiply (b)(h) to find the area of a triangle with the same base and height. The base of this triangle is 28 mm, and the height of this triangle is 9 mm. Substitute 28 mm in for the base, and 9 mm in for the height. (28)x(9) = 252. Now you have to multiply 252 x 1/2. 252 x 1/2 = 126. The answer is C, 126.
What are characteristics of perpendicular lines?.
The characteristics of perpendicular lines:
1) Perpendicular lines are intersecting lines.
2) The perpendicular lines are coplanar.
3) The perpendicular intersect at a 90° angle.
4) The product of slopes of perpendicular lines is -1.
We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90°
Since these lines are inclined at 90° to each other, hence they create right angles.
Perpendicular lines are intersecting lines.
Also, the perpendicular lines are coplanar.
Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.
If two lines l₁ and l₂ are perpendicular to each other then they are represented as l₁ ⊥ l₂.
The product of slopes of perpendicular lines is always -1.
Let m₁ be the slope of line l₁ and m₂ be the slope of line l₂.
If line l₁ and l₂ are perpendicular to each other then m₁ × m2₂ = -1
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How do you find the mean median and mode in class 9?.
To find the mean, median and mode add up the values and divide, the value of set in middle of the list and identify the most number of times a number is repeated.
The sum of all observations divided by the total number of observations yields the arithmetic mean of a set of data. For illustration, a cricketer's five ODI scores are as follows: 12, 34, 45, 50, 24. We compute the arithmetic mean of the data using the mean formula in order to get his typical score in a game:
Mean = Sum of all observations/Number of observations
Mean = (12 + 34 + 45 + 50 + 24)/5
Mean = 165/5 = 33
The median of the data is the value of the middle observation after the data have been arranged in either ascending or descending order.
Take these numbers as an example: 4, 4, 6, 3, 2. Let's organize these numbers ascending: 2, 3, 4, 4, 6.
Median = (n + 1)/2th observation
A data mode is the value that appears the most frequently in the provided data, or the observation with the highest frequency.
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Reason What can you conclude about the domain and the range of a relation if a vertical line at =x equals 5 passes through 2 points? 1 point? No points? Explain.
The required domain of the vertical line is {5} and the range is all real numbers.
Given that,
Domain and range of the vertical line x = 5 is to be determined.
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
Here,
We can infer that the domain of this relation can only be constrained if a vertical line at x = 5 passes through 0 locations. This function's range can only be a collection of real numbers or a constraint.
Thus, the required domain of the vertical line is {5} and the range is all real numbers.
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Use the graph to write a linear function that relates y to x
The linear function of the graph is written as: y = 4/3x + 2.
How to Write a Linear Function that Relates y to x of a Graph?The most common form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept.
To write a linear function in this form, you will need to find the slope and y-intercept of the line.
The slope is the ratio of the change in y to the change in x, and the y-intercept is the point at which the line crosses the y-axis. Once you have these two values, you can substitute them into the equation and write the linear function.
Using the given graph:
Slope (m) = rise/run = 8/6
Slope (m) = 4/3
The y-intercept (b) = 2.
To write the linear function, substitute m = 4/3 and b = 2 into y = mx + b:
y = 4/3x + 2
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What are the 7 properties of equality?.
The 7 properties of equality are the following,
Reflexive SymmetricTransitiveSubstitutionAdditionDivisionMultiplicationThe properties of equality is used to represent the relation between the two sides of an equation and state that the two sides remain equal even after applying the same arithmetic operation on each side.
1) The Reflexive equality property : As per reflexive property, x = x ; x R
2) The Symmetric equality p : If x = y, then y = x .
3) The Transitive equality property : If x = y and y = z, then x = z.
4) The Addition equality Property :
If x = y, then x+z = y+p.
5) Subtraction equality property :
If x = y, and z = p, then x - z = y- p.
5) The Multiplication equialty Properties :
If x = y, then xc = ycIf x = y, and z = d, then xz = yd.6) The Division equaility properties : If x = y, and c≠ 0, then x/c = y/c. If x = y, and c = d ≠0, then x/c = y/d.
Consider the example : Assume the expression is 10 + x = 4(x - 2).
Solution: Solution of this using above properties, 10 + x = 4(x - 2)
=> 10 + x = 4x - 8
=> 10 = 3x - 8
=> 18= 3x
=> 6 = x
=> x = 6
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Please help this question is on my test and if u help me and it’s right I will memorize the answer u gave me. Btw 20 points
Answer: a. w=3x+8 in b. P=24+6x in, c. P=27 in
Look at the Image Below for work.
Step-by-step explanation:
At the beginning of the year, Gabriel had $25 in savings and saved an additional $14
each week thereafter. Adrian started the year with $80 and saved $9 every week. Let
G represent the amount of money Gabriel has saved t weeks after the beginning of
the year and let A represent the amount of money Adrian has saved t weeks after the
beginning of the year. Write an equation for each situation, in terms of t, and
determine the number of weeks after the beginning of the year until Gabriel and
Adrian have the same amount of money saved.
Answer: 11 weeks
Step-by-step explanation:
G(t) = 25 + 14t
A(t) = 80 + 9t
set G equal to A and find t
25 + 14t = 80 + 9t
5t = 55
t = 11
Which type of isometry is the equivalent of two reflections across parallel lines?
glide reflection
rotation
reflection
translation
The equivalent of two reflections across parallel lines is a glide reflection. Therefore, choice A is the best one.
What is isometry in a nutshell?d(f(x,y))=d(x,y) is a bijective map between two metric spaces that maintains distances, where f is the map and d(a,b) is the distance function. Congruence transformations are another name for isometries. Congruent refers to two figures that an isometry can change into one another (Coxeter and Greitzer 1967, p. 80). A linear transformation with length preservation is called an isometry of the plane. Rotation, translation, reflection, gliding, and the identity map are all examples of isometries. Geometrically congruent refers to two geometric figures that are connected by an isometry (Coxeter and Greitzer 1967, p. 80).
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The equivalent of two reflections across parallel lines is a glide reflection. Therefore, choice A is the best one.
What is isometry in a nutshell?A mapping of a metric space such that any two points' distances in the original space are equal to the distances between their images in the second space. d(f(x,y))=d(x,y) is a bijective map between two metric spaces that maintain distances, where f is the map and d(a,b) is the distance function. Congruence transformations are another name for isometries. Congruent refers to two figures that an isometry can change into one another. A linear transformation with length preservation is called an isometry of the plane. Rotation, translation, reflection, gliding, and the identity map are all examples of isometries.
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please help me !!! i need answers asap and i’ll give brainlist
You would need to know the values of each letter in the alphabet to prove AMNO~ATUV.
What other piece of information would you need to prove MNO~TUV?In order to prove that MNO~TUV, we would need to know the values of M,N,T,U,V,O. We would need to know the relationship between these variables in order to determine if MNO~TUV is true. For example, if MNO is equal to TUV, then MNO~TUV would be true.We would also need to know the type of relationship between the variables. For example, if the variables are related by addition, then if M + N = T + U, then MNO~TUV would be true.Additionally, we would need to know the context of the equation. For example, if the equation is related to a geometric problem, then we would need to know the type of shape and the number of sides in order to prove if MNO~TUV is true.Finally, we would need to know any other constraints or conditions that would be affecting the equation. For example, if there is a time limit, then the equation would need to be solved within that time limit in order to prove if MNO~TUV is true.To learn more about to prove MNO~TUV refer to:
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Please view the image and answer the questions.
On solving the provided question, we can say that the equation [tex]8x^3 - 1[/tex][tex]= (2x- I) (4x^2 + 2x + I)[/tex] so, a = 2 and b = 1
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
here the equation is
[tex]8x^3 - 1[/tex]
[tex]= (2x- I) (4x^2 + 2x + I)[/tex]
so, a = 2 and b = 1
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