The y-intercept of a graph y=-3.
Here, we have,
Given the graph of a function, the y-intercept is defined as the y-coordinate of the point(s) where the graph crosses the y-axis.
There might be more than one y-intercepts or even none.
The graph provided in the question is a line with a negative slope, i.e., a decreasing line.
Carefully looking it can be determined the graph touches the y-axis in the point (0,-3), thus the y-intercept of the graph is y=-3
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complete question:
The graph of the linear function is shown on the coordinate grid. * 910X -10 What is the y intercept of the graph of the linear function?
Write an equation of the form y = mx for the line shown below.
Answer:
y = (5/3)x + 2/3
Step-by-step explanation:
find slope
rise/run
(4--1)/(2--1)
(5)/(3)
M = 5/3
then plug in a point to get the y-intercept
4 = (5/3) * 2 + b
4 = 10/3 + b
subtract 10/3 on both sides
2/3 = b
in y =mx +b the equation is
y = (5/3)x + 2/3
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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A scientist discovered a rock formation that grows at a rate of 0.01 meters per year. To predict the height, h, of the rock formation after t years, she used the formula h(t)=1.3+0.01t.
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.
4) Jeanna sights the top of a building and the angle of elevation to be 35 degrees. She moves 100 feet closer and finds that the angle is now 40 degrees. What is the height of the building?
The vertical measurement of the structure corresponds to an estimated value of 119.53 feet.
How to Solve the Problem?The dimensions of the building can be represented by the variable h, whereas the proximity of Jeanna to the building in her initial stance can be identified as x. Utilizing the principles of trigonometry, it is feasible to express the following:
The trigonometric function involving the angle of 35 degrees and its corresponding acute triangle can be written as an equation in the form of tan(35) = h/x, which is denoted as equation 1.
Upon moving a distance of 100 feet from her initial position, Jeanna's distance from the building can be represented as x - 100. Additionally, the angle at which she must look up to view the top of the building is now 40 degrees. Through the application of comparable trigonometric reasoning, it is possible to articulate the following statement:
Equation 2 can be expressed as tan(40) = h/(x - 100), where h and x represent the height and horizontal distance, respectively.
Equation 1 can be manipulated in such a way as to express the variable x in terms of h. The value of x is obtained by dividing h by the tangent of 35 degrees.
The substitution of the given expression for variable x in equation 2 leads to the following result:
The equation tan(40) = h/(h/tan(35) - 100) is amenable for rephrasing in a more academic style of writing.
Upon performing reduction on this mathematical expression, it results in:
The given mathematical equation can be represented in an academic manner as follows: The equation tan(40) = tan(35)h/(h - 100tan(35)) holds true, where h denotes the height of an object located at an angle of 40 degrees to the horizontal plane. This equation specifies the relationship between the tangent values of two distinct angles, 40 degrees and 35 degrees, and the height of the object.
The present equation can be expressed in a more formal academic style as follows: "The function h is defined as the difference between the tangent of 40 degrees and the tangent of 35 degrees, i.e., h = tan(40) - tan(35). This formula can be simplified, resulting in h = -100tan(35)tan(40)."
By dividing each side of the equation by (tan(40) - tan(35)), we are able to obtain the following result:
The following expression denotes the value of h, computed using mathematical operations: h = -100tan(35)tan(40)/(tan(40) - tan(35)).
The value of h is approximately equal to 119.53 feet.
Hence, the vertical measurement of the structure corresponds to an estimated value of 119.53 feet.
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Un deportista se ejercita y recorre 350 metros, retrocede 125 metros avanza 80 metros. Si el punto de partida es su casa a que distancia de la misma se encuentra
The sportsman has a final distance with respect to his home equal to 305 meters.
How to determine the distance of a sportsman with respect to a home
In this problem we must the final distance of the sportsman with respect to his home. This can be determined by the following expression:
X = ∑ xₙ, for n = {1, 2, 3, ..., N}
Where the sportsman goes far away for his home for x > 0, in meters.
Now we proceed to determine the final distance:
X = + 350 m - 125 m + 80 m
X = + 305 m
The final distance of the sportsman with respect to his home is 305 meters.
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4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10??
When you multiply an inequality by a positive number, the direction of the inequality does not change. So if 4 < 7, then:
what is inequality?
Inequality is a mathematical statement that describes a relationship between two values or expressions that are not equal. In an inequality, we use the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to indicate the relationship between the values or expressions.
For example, "x < 5" is an inequality that means "x is less than 5", and "y ≥ 10" is an inequality that means "y is greater than or equal to 10". Inequalities are often used in algebra and other branches of mathematics to express relationships between variables or to solve problems.
Multiplying both sides by
7 gives: 28 < 49
Multiplying both sides by
6 gives: 24 < 42
Multiplying both sides by
3 gives: 12 < 21
Multiplying both sides by
10 gives: 40 < 70
All of these inequalities are still true, because we are multiplying both sides by a positive number.
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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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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
Dilate figure XYZ by a scale factor of 1/4 X(-2,4) Y(-4,-4) Z(4,2)
Therefore , the solution of the given problem of expressions comes out to be points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).
What is expression?Instead of using random estimates, shifting variable numbers should be employed instead, which can be growing, diminishing, or blocking. They could only help one another by transferring items like tools, knowledge, or solutions to issues. The explanations, components, or mathematical justifications for strategies like expanded argumentation, debunking, and blending may be included in the explanation of the reality equation.
Here,
Figure XYZ will be scaled down by 1/4, with the centres being X(-2,4), Y(-4,4), and Z(4,2)
=> Old_x - Center_x - Scale_factor * New_x + Center_x
=> Scale factor * (Old y - Centre y) + Centre y = New y
Regarding X:
=> New_x = 1/4 * (-2 - (-2)) + (-2) = -2
=> New_y = 1/4 * (4 - 4) + 4 = 4
Therefore, X'(-2,4) is the image of point X after dilation.
Regarding Y:
=> New_x = 1/4 * (-4 - (-2)) + (-2) = -3
=> New_y = 1/4 * (-4 - 4) + 4 = -1
Therefore, Y'(-3,-1) is the image of point Y following dilation.
Regarding Z:
=> New_x = 1/4 * (4 - (-2)) + (-2) = 0
=> New_y = 1/4 * (2 - 4) + 4 = 3
Therefore, Z'(0,3) is the image of point Z after dilation.
As a result, the image points for the dilated figure XYZ with the centre points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).
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2x-y=3 and 7x-y=13 solve the simultaneous equation
Answer:
x=4
y=5
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.
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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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
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.
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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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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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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i do not know the answer to this
Answer:
b
Step-by-step explanation:
b
Look at this expression.
Which of the following is the simplest form of the expression above?
A.
2a-2b-3
B.
2a-1b2
C.
2a-1/2b-3
D.
2a3b4
The simplest form of the expression "(14ab³)/(7a⁻²b⁻¹)" is represented by the expression (d) 2a³b⁴.
To simplify the expression (14ab³)/(7a⁻²b⁻¹), we first simplify the terms with the same base,
First, we simplify the coefficients "14" and "7" by dividing them to get:
⇒ (14ab³)/(7a⁻²b⁻¹) = 2ab³/a⁻²b⁻¹;
Next, we simplify the variables "a" and "b" by subtracting the exponents of "a" and "b" in the denominator respectively,
We get,
⇒ 2ab³/a⁻²b⁻¹ = 2a¹⁻⁽⁻²⁾b³⁻⁽⁻¹⁾ = 2a¹⁺²b³⁺¹ = 2a³b⁴,
Therefore, the simplest form of the expression (14ab³)/(7a⁻²b⁻¹) is 2a³b⁴, the correct option is (d).
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The given question is incomplete, the complete question is
Look at this expression. (14ab³)/(7a⁻²b⁻¹),
Which of the following is the simplest form of the expression above?
(a) 2a⁻²b⁻³
(b) 2a⁻¹b²
(c) 2[tex]a^{-\frac{1}{2} }[/tex]b⁻³
(d) 2a³b⁴.
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.
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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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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Connor has 3 3/4 feet of brown fabric and 3/4 yard of green to make a costume for the school play. How many more brown than green does Connor have?
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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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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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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Determine the rate of change of the function given by the table.
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Answer:
Step-by-step explanation:
1
Q6)Define the term 'Molar mass'. State its unit of measurement.
What is a ‘Mole’? Write the value for avogadro’s number
Answer:
The molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of said compound.
unit of measurement: g/mol.
A mole is the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon-12.
Avogadro's number= 6.02*10^23 particles.
what is the simplified answer to 49^{1/2}
Answer:
7
Step-by-step explanation: