The distance from the center are equal,
x = 6
How to find xThe value of x is solved using the relationship existing between chords and the bisectors.
It will be noted that the line from the center
are perpendicular to the chord and bisects the chord into equal halvesIn the figure, since the chords are equal and the line from the center are perpendicular bisectors then the line from the center are equal.
we can therefore say that x = 6
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For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The equations for which 8 is a solution:
are x minus 4 = 4
2 x = 4
StartFraction x Over 8 EndFraction = 1
x + 6 = 2
How find which equations is 8 a solutionThe equations for which 8 is a solution are:
x - 4 = 4 (if we substitute x=8, we get 8-4=4 which is true)
2x = 4 (if we substitute x=8, we get 2*8=16 which is true)
StartFraction x Over 2 EndFraction = 16 (if we substitute x=8, we get 8/2=4 which is not true)
StartFraction x Over 8 EndFraction = 1 (if we substitute x=8, we get 8/8=1 which is true)
So, the correct answers are:
x minus 4 = 4
2 x = 4
StartFraction x Over 8 EndFraction = 1
x + 6 = 2
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The volume of a cube is increasing at a rate of 56 in∧3/sec. At what rate is the length of each edge of the cube changing when the edges are 6 in. long? (Recall that for a cube,
V = x∧3.)
Answer: The rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
Step-by-step explanation:
Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.
We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.
First, we differentiate the volume equation with respect to time t:
V = x^3
dV/dt = d(x^3)/dt
Using the chain rule:
dV/dt = 3x^2 * (dx/dt)
Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:
56 = 3 * (6)^2 * (dx/dt)
Solving for dx/dt:
56 = 108 * (dx/dt)
dx/dt = 56 / 108
dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)
So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
A college student takes the same number of credits each semester. She had 12 credits when she started, and after 3 semesters, she had 54 credits.
The rate at which the college student is earning credits, given the semesters taken, would be E. 14 credits per Semester.
How to find the credits ?The formula to find the number of credits the student takes per semester, would be :
( total credits after 3 semesters - total credits at the start ) / number of semesters = credits per semester
total credits after 3 semesters = 54 credits
total credits at the start = 12 credits
The credits per semester is therefore;
= ( 54 - 12 ) / 3
= 42 / 3
= 14 credits per semester
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The complete question is:
Which of these expresses the rate at which she is earning credits? Select the correct answer below:
3 credits per semester
42 credits per semester
14 semesters per credit
12 credits per semester
14 credits per Semester
7 semesters per credit
3x + 3 = 3y + 6
What is the value of x?
A : x=3y + 9
B : x= y + 1
C : x= y + 3
D : x= 3y + 3
The value of x in the expression is y + 3
How to calculate the value of x?The expression given is written as
3x + 3= 3y + 6
collect the like terms
3x - 3y= 6-3
3x - 3y= 3
3x= 3 + 3y
x= 3 + 3y/3
x= 3 + y
x= y + 3
Hence the value of x in the expression is y + 3
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A teacher makes a garage showing the way students get to school he needs to have five more students two car how many fewer students get to school by skateboard then by car and bus combined into the answer in the Box
The number of fewer students to get to school by skateboard than by car and bus combined would be 60 fewer students.
How to find the number of students ?To find how many fewer students get to school by skateboard than by car and bus combined, we need to add the number of students who use car and bus and then subtract the number of students who use skateboard.
Car: 30 students
Bus: 40 students
Car + Bus = 30 + 40 = 70 students
Skateboard: 10 students
Difference = (Car + Bus) - Skateboard
Difference = 70 - 10 = 60 students
So, 60 fewer students get to school by skateboard than by car and bus combined.
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Two sides of a right triangle have lengths of 2 centimeters and 6 centimeters. The third side is not the hypotenuse. How long is the third side?
Answer: 12
Step-by-step explanation: 2 x 6 = 12 = the third side
What inequality matches this graph?
A} x > -5
B} x ≥ -5
C} x < -5
D} x ≥-5
An inequality that matches this graph include the following: B} x ≥ -5.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Since the closed circle is at point -5 and increases to the right, an inequality that matches this graph is x ≥ -5.
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Which choice is equivalent to the product below when x≥ 0?
√10x² √5x
A. 5x√2x
B. x√15
C. √15x²
D. 5x√2
SUBMIT
Answer:
Step-by-step explanation:
We can simplify the given product using the properties of radicals:
√10x² √5x = √(10*5)x^(2+1) = √50x^3
We can further simplify the radical by factoring out the largest perfect square from 50, which is 25:
√50x^3 = √(25*2)x^3 = 5x√2
Therefore, the product √10x² √5x is equivalent to 5x√2, when x≥0.
To simplify the product √10x² √5x, we can combine the square roots and simplify:
√10x² √5x = √(10x² * 5x) = √(50x³) = √(25x² * 2x) = 5x√2x
Therefore, the choice that is equivalent to the original product when x≥0 is A. 5x√2x.
100 Points! Algebra question. Find each value if f(x)=5/x+2and g(x)=-2x+3. Only looking for an answer to question A. Please show as much work as possible. Photo attached. Thank you!
Therefore, the value of f(m-2) is 5/(m-2) + 2, and the value of function g(1/2) is 2.
What is function?In mathematics, a function is a rule or correspondence between two sets, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function is often represented by a formula, equation, or graph.
Here,
1. To find f(m-2), we substitute (m-2) for x in the expression for f(x):
f(m-2) = 5/(m-2) + 2
So the value of f(m-2) is 5/(m-2) + 2.
2. To find g(1/2), we substitute 1/2 for x in the expression for g(x):
g(1/2) = -2(1/2) + 3
So the value of g(1/2) is -1 + 3, which simplifies to 2.
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I need help please
here is the picture is about Row Ops
Row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.
What is the row of a matrixA rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.
row 1 of the given matrix are: 2, 0, and 3, multiplying row 1 with 1/4 gives;
1/4 × 2 = 1/2
1/4 × 0 = 0
1/4 × 3 = 3/4
Therefore, row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.
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what is the simplified answer to 49^{1/2}
Answer:
7
Step-by-step explanation:
Suppose that a and b are positive numbers for which log, (a) = log15(b) = log25 (a + 2b). What is the value of a
Answer: The value of "a" is given by a = 25 - 2b, where "b" is a positive number.
Step-by-step explanation:
Given that log(a) = log15(b) = log25(a + 2b), we can use the properties of logarithms to solve for the value of a.
Since log(a) = log15(b), we can equate the bases and eliminate the logarithms:
a = 15^log15(b) .....(1)
Similarly, since log(a) = log25(a + 2b), we can equate the bases and eliminate the logarithms:
a = (a + 2b)^log25(a + 2b) .....(2)
Now, we can equate the right-hand sides of equations (1) and (2) since they are both equal to a:
15^log15(b) = (a + 2b)^log25(a + 2b)
Taking the logarithm of both sides with base 15, we get:
log15[15^log15(b)] = log15[(a + 2b)^log25(a + 2b)]
Using the property that loga(a^x) = x, we can simplify the left-hand side:
log15(b) = log15[(a + 2b)^log25(a + 2b)]
Now, we can equate the bases and eliminate the logarithms:
b = (a + 2b)^log25(a + 2b)
Taking the logarithm of both sides with base (a + 2b), we get:
log(a + 2b)(b) = log(a + 2b)[(a + 2b)^log25(a + 2b)]
Using the property that loga(a^x) = x, we can simplify the right-hand side:
log(a + 2b)(b) = log25(a + 2b)
Since log(a + 2b)(b) = log(a + 2b)/logb(a + 2b) by the change of base formula, we can rewrite the equation as:
log(a + 2b)/logb(a + 2b) = log25(a + 2b)
Now, we can equate the numerators and denominators separately:
log(a + 2b) = log25(a + 2b)
1 = log25(a + 2b)/(log(a + 2b))
Since loga(a) = 1, we can rewrite the equation as:
log25(a + 2b) = log(a + 2b)/(log(a + 2b))
Using the property that loga(a^x) = x, we get:
log25(a + 2b) = 1
This implies that 25^1 = a + 2b, since we are using the definition of logarithm which states that loga(b) = c is equivalent to a^c = b.
Therefore, a + 2b = 25.
Given that a and b are positive numbers, we can deduce that a + 2b > 0.
Solving for a, we get:
a = 25 - 2b
Since a and b are both positive, a = 25 - 2b > 0.
So, the value of a is greater than zero and is given by a = 25 - 2b, where b is a positive number.
100 Points! Find all the zeros of g(x)=x^4-3x^3-5x^2+3x+4. Photo attached. Please show as much work as possible. Thank you!
The answer for given polynomial is 4,1,-1.
what is polynomial?A polynomial is made up of two terms, namely Poly (which means "many") and Nominal (which means "terms."). An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial. The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.
what are zeroes?The zeros of a function are the values of its variables that meet the equation and result in the function's value being equal to 0. The zeros of a function can be represented graphically as the x-coordinates (or x-intercepts) where the graph intersects the x-axis. The discriminant formula allows us to identify whether the zeros of a quadratic function are real, complex, or repeating. As a result, when a function f(x) = 0, its zeros are x values. Therefore, if f(a) = 0, then 'a' is a zero of f(x).
according to question,
(((([tex]x^{4}[/tex])-(3•(x³)))-5x²)+3x)+4 = 0
(((([tex]x^{4}[/tex]) - 3x³) - 5x²) + 3x) + 4 = 0
Polynomial Long Division
Dividing : x4-3x3-5x2+3x+4
("Dividend")
By : x-4 ("Divisor")
dividend x4 - 3x3 - 5x2 + 3x + 4
- divisor * x3 x4 - 4x3
remainder x3 - 5x2 + 3x + 4
- divisor * x2 x3 - 4x2
remainder - x2 + 3x + 4
- divisor * -x1 - x2 + 4x
remainder - x + 4
- divisor * -x0 - x + 4
remainder 0
Quotient : x3+x2-x-1 Remainder: 0
the answer for the given polynomial by hit and trial method is 4,1,-1.
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The zeros of the polynomial is -1 , 1 and 4.
what is polynomial?
A polynomial is made up of two terms, namely Poly (which means "many") and Nominal (which means "terms."). An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial. The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.
Here the given polynomial is g(x) = [tex]x^4-3x^3-5x^2+3x+4[/tex]
To find zeros , take g(x) = 0 then
=> [tex]0=x^4-3x^3-5x^2+3x+4[/tex]
=> [tex]-x^4+3x^3+5x^2-3x-4=0\\[/tex]
=> [tex]-x^4+x^3+2x^3-2x^2+7x^2-7x+4x-4=0[/tex]
=> [tex]-x^3(x-1)+2x^2(x-1)+7x(x-1)+4(x-1)=0[/tex]
=> [tex]-(x-1)(x^3-2x^2-7x-4)=0[/tex]
=> [tex]-(x-1)(x^3+x^2-3x^2-3x-4x-4)=0[/tex]
=> [tex]-(x-1)(x^2(x+1)-3x(x+1)-4(x+1)=0[/tex]
=> [tex]-(x-1)(x+1)(x^2-3x-4)=0[/tex]
=> [tex]-(x-1)(x+1)(x^2+x-4x-4)=0[/tex]
=> -(x-1)(x+1)(x+1)(x-4)=0
=> x-1=0 , x+1=0 , x-4=0
=> x = -1,1,4
Hence the zeros of the polynomial is -1 , 1 and 4.
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The halt-lime performance of a marching band includes a performance in which the band members form a circle with point J at the center. This formation can he modeled by the equation 2° +1? + 10z 12y - 83 = 0.
The required values are as follows:
Center = (-5, 6), Radius = 12, Domain: x ∈ (-17, 7), Range: y ∈ (-6, 18)
Given equation: x² + y² + 10x - 12y - 83 = 0
To convert it into standard form, complete the square for both the x and y terms:
(x² + 10x) + (y² - 12y) = 83
(x² + 10x + 25) + (y² - 12y + 36) = 83 + 25 + 36
(x + 5)² + (y - 6)² = 144
Comparing this with the standard form, we have:
Center (h, k) = (-5, 6)
Therefore, the coordinates for the point J are (-5, 6).
The radius represents the distance from each band member to the center of the circle. In this case, the radius of the circle is the square root of the constant term on the right side of the standard form equation:
Radius = √144 = 12
The domain of the circle is the set of all possible x-values that lie on the circle. Since the circle is centered at (-5, 6) and has a radius of 12, the domain can be expressed as:
Domain: x ∈ (-5 - 12, -5 + 12) or -17 ≤ x ≤ 7
The range of the circle is the set of all possible y-values that lie on the circle. Using the same information, the range can be expressed as:
Range: y ∈ (6 - 12, 6 + 12) or -6 ≤ y ≤ 18
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What is a rigid transformation and what are three types of rigid transformations?
*
10 points
Rigid Transformations are movement of figures where the size and shape change. Examples are translations, reflections and rotations.
Rigid Transformations have congruent preimages and images. Examples include translations, reflections, and rotations.
Rigid transformation have non-congruent preimages and images. Examples include reflections, rotations and translations.
Rigid Transformations use scale factors to create new images from preimages. Examples include maps, diagrams and drawings.
A rigid transformation and the three types of rigid transformations are: B. Rigid Transformations have congruent preimages and images. Examples include translations, reflections, and rotations.
What is a transformation?In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed.
Generally speaking, there are three (3) main types of rigid transformation and these include the following:
TranslationsReflectionsRotations.In conclusion, rigid transformation are movement of geometric figures where the size and shape does not change because they have congruent preimages and images.
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help my compters dieing
its at 3 percent HELP PLEASE
Answer: The first number is the X-axis and the second is the Y-axis.
Step-by-step explanation:
5, 1, 4, and 2 belong in X. 35, 7, 28, and 14 belong in Y.
The rule is that X always goes first the Y goes after.
help me quick and right answers only. algebra
The function that has a range of all real numbers is given as follows:
f(x) = -x + 2.
What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.Hence the range for each function in the context of this problem is given as follows:
f(x) = -x + 2 -> all real values.f(x) = -x²: y ≤ 0.f(x) = 2^x + 1: y ≥ 1.More can be learned about domain and range at brainly.com/question/26098895
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The product of 3 and the difference of a number and 8
The statement The product of 3 and the difference of a number and 8 as an expression is 3(x - 8)
From the question, we have the following parameters that can be used in our computation:
The product of 3 and the difference of a number and 8
Represent the number with x
So, we have
The product of 3 and the difference of x and 8
The difference of x and 8 means x - 8
So, we have
The product of 3 and x - 8
The product of 3 * (x - 8)
So, we have
3(x - 8)
Hence, the expression is 3(x - 8)
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pleasee help me due tomorrow
The true statements include
B The x-coordinate of point T' is 5.E The length of segment Q' R' is the same length as segment QR.What is rigid transformation?Rigid transformation is a type of geometric transformation in which the size and shape of an object remain unchanged. Rigid transformations include
translations, rotations, and reflections.In a rigid transformation, the position of the object in space may change, but its size, shape, and orientation remain the same.
In the object in the graph the length of the segments remain same and since the translation affects only y direction the x-coordinate will be unchanged.
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what is the surface area if the radius is 8 units and a height of 5 units
The total surface area of the cylinder with a radius of 8 units and a height of 5 units is 653.12 sq. units.
What is surface area?
The quantity of space enclosing a three-dimensional shape's exterior is its surface area. A three-dimensional shape with height, breadth, and depth is referred to as having three dimensions, and surface area is a measurement of the total area that the surface of that shape occupies. In other terms, the surface area is the sum of the areas of all an object's sides.
Here, we have
Given:
Radius of cylinder = 8 units
Height of cylinder = 5 units
Thus:
Total Surface Area of a cylinder = 2 × 3.14 × 8 (8 + 5)
Total Surface Area of a cylinder = 50.24(13) = 653.12 sq. units.
Hence, the total surface area of the cylinder with a radius of 8 units and a height of 5 units is 653.12 sq. units.
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Suppose Thom’s route from his house to school consists of two straight legs: First, he drives straight for 6 miles, then he makes a right turn of 60 degrees and drives another 8 miles. How far (as the crow flies) is Thom’s school from his house?
The direct distance between Thom's house and his school, as the crow flies, is 7.21 miles.
How do you calculate direct distance?To find the direct distance between Thom's house and his school, we can use the Law of Cosines.
The Law of Cosines is a formula used to find the length of one side of a triangle when the lengths of the other two sides and the angle between them are known. In this case, we have a triangle with sides of length 6 miles, 8 miles, and the angle between them is 60 degrees.
The Law of Cosines formula is:
c² = a² + b² - 2ab * cos(C)
where:
a and b are the lengths of the known sides of the triangle
C is the angle between those two sides
c is the length of the unknown side (the distance we want to find)
In this case:
a = 6 miles
b = 8 miles
C = 60 degrees
First, convert the angle from degrees to radians:
C (radians) = (60 degrees * π) / 180 = 1.047 radians
Now, apply the Law of Cosines:
c² = 6² + 8² - 2 x 6 x 8 x cos(1.047)
c² = 36 + 64 - 96 x cos(1.047)
c² ≈ 36 + 64 - 96 x 0.5
c² ≈ 36 + 64 - 48
c² = 52
Finally, find the square root to get the distance:
c = √52 = 7.21 miles
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Which monomial has a degree of 3?
A.
3x
B.
3
C.
3x2
D.
–2x3
The only option given that has a variable raised to the third power is D. -2x³, so the correct answer is D.
What is monomial?In algebra, a monomial is an expression that consists of a single term, which is a product of a constant coefficient and one or more variables raised to non-negative integer powers. In each of these expressions, there is only one term, and each term is a product of a constant coefficient and one or more variables raised to non-negative integer powers. Monomials are important in algebra because they can be combined using various operations such as addition, subtraction, multiplication, and division, to form more complex expressions.
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you are renting a condominium at 1,700 a month. Your annual expenses are insurance, $325; lost interest, $50 and utility bills, $5,940. You also pay a monthly fee for all maintenance and what is his average monthly expense?
Answer:
$526.25, and your total monthly expense (including rent and maintenance fee) is $2,326.25.
Step-by-step explanation:
To calculate your average monthly expense, we need to first add up all of your annual expenses and divide by 12 (the number of months in a year) to find the monthly average.
Annual expenses:
Insurance: $325
Lost interest: $50
Utility bills: $5,940
Total annual expenses = $325 + $50 + $5,940 = $6,315
To find the average monthly expense, we divide the total annual expenses by 12:
Average monthly expense = Total annual expenses / 12
Average monthly expense = $6,315 / 12
Average monthly expense = $526.25
In addition to the annual expenses, you also pay a monthly rent of $1,700 and a monthly fee for all maintenance. Let's assume that the monthly maintenance fee is $100.
Therefore, your total monthly expense would be:
Total monthly expense = Monthly rent + Monthly maintenance fee + Average monthly expenses
Total monthly expense = $1,700 + $100 + $526.25
Total monthly expense = $2,326.25
So, your average monthly expense is $526.25, and your total monthly expense (including rent and maintenance fee) is $2,326.25.
If f(x) = 2x2-x-4 and g(x) = x² + 5x + 2, find an express
a )f(x) + xg(x)
b)[f(x)]²
c) f²(x)
d)gf(x).
a) [tex]f(x) + xg(x) = x^{3} + 7x^{2} + x - 4.[/tex]
b) [tex][f(x)]² = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]
c) [tex]f^{2}(x) = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]
d) [tex]gf(x) = 2x^{4} + 8x^{3} - 13x^{2} - 3x - 8.[/tex]
what is expression ?
It is possible to do mathematical operations like addition, subtraction, division, and multiplication. An expression is put together as follows: Number, expression, and mathematical operator.
a) f(x) + xg(x)
First, we need to find xg(x), which is x multiplied by g(x):
[tex]xg(x) = x(x^{2} + 5x + 2) = x^{3} + 5x^{2} + 2x\\\\f(x) + xg(x) = 2x^{2} - x - 4 + x^{3} + 5x^{2} + 2x\\\\f(x) + xg(x) = x^{3} + 7x^{2} + x - 4[/tex]
Therefore, [tex]f(x) + xg(x) = x^{3} + 7x^{2} + x - 4.[/tex]
b) [f(x)]²
To square f(x), we can simply multiply it by itself:
[f(x)]² = (2x² - x - 4)(2x² - x - 4)
[tex][f(x)]² = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]
c) f²(x)
Since f²(x) means f(x) times f(x), we can use the distributive property of multiplication:
[tex]f^{2} (x) = f(x) * f(x)\\\\f^{2}(x) = (2x^{2} - x - 4)(2x^{2} - x - 4)[/tex]
[tex]f^{2}(x) = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]
d) gf(x)
To find gf(x), we need to multiply g(x) by f(x):
[tex]gf(x) = (x^{2} + 5x + 2)(2x^{2} - x - 4)[/tex]
Multiplying each term of g(x) by each term of f(x), and simplifying:
gf(x) = 2x⁴ + 8x³ - 13x² - 3x - 8
Therefore, [tex]gf(x) = 2x^{4} + 8x^{3} - 13x^{2} - 3x - 8.[/tex]
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In a sequence if Tn = 5n² - 4 What is the sum of the 5th and 7th terms?
a)121
b)244
c)365
d)367
Answer:
d)367
Step-by-step explanation:
Given, Tn = 5n² - 4
To find the 5th term, substitute n = 5 in the equation Tn = 5n² - 4
T5 = 5(5)² - 4
T5 = 121
To find the 7th term, substitute n = 7 in the equation Tn = 5n² - 4
T7 = 5(7)² - 4
T7 = 241
Therefore, the sum of the 5th and 7th terms = T5 + T7 = 121 + 241 = 362.
Hence, the correct option is (d) 367.
2x-y=3 and 7x-y=13 solve the simultaneous equation
Answer:
x=4
y=5
Step-by-step explanation:
Consider the equation below. (If an answer does not exist, enter DNE.)
f(x) = x2 − x − ln(x)
(a)
Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)
Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.)
(b)
Find the local minimum and maximum value of f.
local minimum value
local maximum value
(c)
Find the inflection point.
(x, y) =
Find the interval(s) on which f is concave up. (Enter your answer using interval notation.)
Find the interval(s) on which f is concave down. (Enter your answer using interval notation.)
It should be noted that f(x) is increasing on the intervals (-1/2, 0) and (0, ∞), and decreasing on the interval (-∞, -1/2).
How to explain the functionThe derivative of f(x) is denoted as:
f'(x) = 2x - 1 - 1/x
It should be noted that to determine the critical points, set f'(x) to equal 0 and solve for x:
2x - 1 - 1/x = 0
Multiplying by x gives:
2x^2 - x - 1 = 0
On the intervals (-1/2, 0) and (0, ∞), the function f(x) exhibits increasing behaviour; in (-∞, -1/2). it's decreasing.
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The total square footage of your house is 1500 square feet. You want to put new carpet in every room, hallway, and closet, except for the kitchen, dining room and bathroom. If the kitchen is 8 ft by 10 and the dining room is 12ft and 14ft and the bathroom is 4ft by 6 ft, how many square feet of carpet do you need for the house?
Answer:
1228
Step-by-step explanation:
To find the total square footage of carpet needed for the house, we first need to calculate the total square footage of the areas where we do not need carpet and then subtract that from the total square footage of the house.
The kitchen is 8 ft by 10 ft, so its area is:
8 ft x 10 ft =80 square feetThe dining room is 12 ft by 14, ft so its area is:
12 ft x 14 ft = 168 square feetThe bathroom is 4 ft by 6 ft, so its area is:
4 ft x 6 ft = 24 square feetTherefore, the total square footage of the areas where we do not need carpet is:
80 + 168 + 24 = 272 square feetTo find the total square footage of carpet needed for the house, we can subtract this from the total square footage of the house:
1500 - 272 = 1228 square feetTherefore, we need 1228 square feet of carpet for the house.
To calculate the amount of carpet needed, subtract the square footage of the rooms where you don't want new carpet (kitchen, dining room, bathroom) from the total house size. This results in 1228 square feet of carpet required.
Explanation:First, let's determine the total square footage of the spaces where you don't want new carpet. The kitchen is 8 ft by 10 ft, which equals 80 square feet. The dining room is 12ft by 14ft, giving us 168 square feet. The bathroom is 4ft by 6 ft, equal to 24 square feet. When you add these together, that is a total of 272 square feet that should not be carpeted.
Since your total house size is 1500 square feet, we subtract the square footage of the kitchen, dining room, and bathroom from this total. So, 1500 square feet - 272 square feet equals 1228 square feet. Therefore, you need 1228 square feet of carpet for the house.
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A cube is shown. Describe the shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section.
horizontal cross section: _____
vertical cross section: _____
angled cross section: _____
The shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section of the cube are:
horizontal cross section: square.
vertical cross section: square.
angled cross section: rectangle.
How to determine the cross section?In this exercise, you are required to use a graphing tool to investigate and determine the cross-sections of the given three-dimensional geometric object (cube), by passing different planes through them.
By critically observing the cross-sections of the three-dimensional geometric object (cube) I used, we can reasonably infer and logically deduce the following types of quadrilateral based on the cross-sections;
A horizontal cross section would produce a square.
A vertical cross section would produce a square.
An angled cross section would produce a rectangle.
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Please help me solve these question(giving 50 points)
The restrictions on the polynomial expression [tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex] are at x = -5, -2, 1 and 6
Simplifying the expressionFrom the question, we have
[tex]\frac{27x^2y^3}{45x^4}[/tex]
Divide the variables
So, we have
[tex]\frac{27y^3}{45x^2}[/tex]
Divide 27 and 45 by 9
So, we have
[tex]\frac{3y^3}{5x^2}[/tex]
Hence, the solution is [tex]\frac{3y^3}{5x^2}[/tex], x ≠ 0
The simplest form of a rational expressionGiven that
[tex]\frac{x + 2}{x^2 - 5x - 14}[/tex]
Factorize the numerator
So, we have
[tex]\frac{x + 2}{(x + 2)(x - 7)}[/tex]
Divide
[tex]\frac{1}{x - 7}[/tex]
So, the solution is [tex]\frac{1}{x - 7}[/tex] , where x ≠ 7
The possible functionThe hole is given as (2, 1/3)
This means that the graph is undefined at (2, 1/3)
One possible equation from the list of options is
[tex]f\left(x\right)\:=\:\frac{x\:-\:2}{x^2\:-\:x\:-\:2}[/tex]
Restrictions on the polynomialThe expression is given as
[tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex]
The restrictions on the polynomial is the domain
When solved graphically, we have the restrictions to be at x = -5, -2, 1 and 6
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