To consider two nonnegative numbers x and y where x y=11, the minimum value of 7x² + 13y is 146.
To find the minimum value of 7x² + 13y, we need to use the given constraint that xy = 11. We can solve for one variable in terms of the other by rearranging the equation to y = 11/x. Substituting this into the expression, we get:
7x² + 13(11/x)
Simplifying this expression, we can combine the terms by finding a common denominator:
(7x³ + 143)/x
Now, we can take the derivative of this expression with respect to x and set it equal to 0 to find the critical points:
21x² - 143 = 0
Solving for x, we get x = √(143/21). Plugging this back into the expression, we get:
Minimum value = 7(√(143/21))² + 13(11/(√(143/21))) = 146
Therefore, the minimum value of 7x² + 13y is 146.
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What is the difference between expression and polynomial class 8?
Expression and polynomial are both mathematical terms that are used to represent mathematical equations.
An expression is any combination of symbols, numbers, and operations that represent a value or a quantity. Expressions can be represented as algebraic equations, numerical equations, or verbal phrases. A polynomial is a specific type of expression that is composed of one or more terms with each term containing a power of a single variable. A polynomial can be represented with a single variable or multiple variables.
A formula is an expression or equation that represents an idea or a relationship between two or more variables. A calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.
In summary, an expression is any combination of symbols, numbers, and operations that represent a value or quantity, while a polynomial is a specific type of expression composed of one or more terms with each term containing a power of a single variable. A formula is an expression or equation that represents an idea or relationship between two or more variables, while a calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.
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Is it possible to have a triangle with the following sides 6cm 7cm 2cm?
We can form a triangle with sides 6cm, 7cm, and 2cm.
Now, According to the question:
We know that:
What is triangle inequality rule?
The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the third side. The Triangle is a polygon with three line segments as its boundaries.
Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.
We have the sides:
6cm, 7cm, 2cm
Here,
6 + 7 > 2
Hence, we can form a triangle with sides 6cm, 7cm, and 2cm.
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40 points Is this correct please help
35 POINTS TO WHOEVER CAN ANSWER THIS!!!!!
Answer:
y = (-5/2)x + 8
slope = -2.5
b = 8
x-intercept = 3.2
y-intercept = 8
Step-by-step explanation:
What are the 3 types of triangles according to sides describe each?
Three types of triangles according to scalene, isosceles and equilateral triangle.
What is meant by scalene?
Every triangle side in a scalene triangle has a different length.Two triangle sides that are of the same length are called isosceles triangles.All of the sides of a triangle are the same length in an equilateral triangle.An equilateral triangle naturally has three equal internal angles and three equal length sides because, as the triangles above demonstrate, the length and internal angles of a triangle are closely connected.A scalene triangle is a triangle whose three sides are all of various lengths and whose three angles are all of different sizes. Scalene triangle angles always add up to 180 degrees and adhere to the angle sum property.To learn more about scalene refer to
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Find the value of the remainder. Enter the value of the remainder (only the number, you do not need to place it over the divisor)
It is simple to locate the rest. Simply divide the number by another number with its multiples to obtain the remaining.
What is a remainder?Always less than the divisor is the remainder. It indicates that the division is not complete if the remainder exceeds the divisor. It might either be higher or lower than the quotient. For instance, the remaining is six when the number seven is divided by 41, leaving five as the quotient.
It's simple to locate the rest of them. To obtain the remainder, we simply divide the number by a different integer that is one of its multiples.
the surplus after division (happens when the first number does not divide exactly by the other). Example: Dividing 19 exactly by 5 is not possible. The closest you can go to 19 without going over is 3 x 5, which is 15 and 4 less. 4 remains as a result.
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Why is it called substitution method?
It is called the substitution method because we substitute the value of one variable with another one and solve the equation.
By changing the value of another variable in an equation, the variable can be eliminated using this method. Thus, the elimination by substitution method is the name given to this technique.
As we are aware, the substitution approach entails solving the equation to determine the value of the variable, which is then substituted in the other equation. The elimination approach, in contrast, involves removing variables from the equation such that the equation's system can be reduced to being the function of a single variable.
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The measures of the interior angles of a convex octagon are 45x,40x, 155, 120, 155, 38x, 158x, and 41x. What is the measure of the smallest interior angle
Select the correct answer.
Which graphs represent functions?
-4
14
●
4-
24
+2
4
Graph A
y
4
-2
4
2
2
2
4
X
-2
F
4
2
2
>4
Graph B
4
•
2
2 4
x
►x
Answer:
Graph B
Step-by-step explanation: No point has the same x-axis
How would the equation f (x) = log (x - 2) + 8 be shifted with respect to the parent function
Answer:
right 2 up 8 units
Step-by-step explanation:
the (x-2) is basically the opposite of what u think so it goes right
and +8 is normal so its up 8
How many images are formed If two plane mirror are position at an angle of 450?
There are seven images are formed If two plane mirrors are positioned at an angle of 45°.
The formula for the number of images formed by two plane mirrors placed at a certain angle is
⇒360/n
where n=angle between the mirrors
The most important thing to remember is that every time the number of images formed is only ODD numbers, if the result is even then you need to subtract 1 from that.
if it is odd u need not subtract, since the number of images ever formed is only odd.
so for an angle, of 45° the number of images formed are:
⇒360/45=8
in this case, since the images formed are even u need to subtract 1 from it i.e
8–1=7
So, the number of images formed is 7.
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the rate of change of a linear function is 4 what could be the two points on the line of this function
For the rate of change of 4 the two points will be A(2,8) and B(4,16).
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the rate of change of the linear function is 4. The coordinates of the two points will be calculated as,
Rate of change = ( y₂ - y₁ ) / ( x₂ - x₁ )
Rate of change = ( 16 - 8 ) / ( 4 - 2 ) = 8 / 2 = 4
Compare the coordinates,
( x₁, y₁ ) = ( 2, 8 )
( x₂, y₂ ) = ( 4, 16 )
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Simplify the expression (StartFraction 1 Over 4 a b EndFraction) Superscript negative 2. Assume a not-equals 0, b not-equals 0.
Negative StartFraction 1 Over 16 a squared b squared EndFraction
StartFraction a squared b squared Over 4 EndFraction
Negative 16 a squared b squared
16 a squared b squared
The simplified form of the (StartFraction 1 Over 4 a b EndFraction) Superscript negative 2 expression is Negative StartFraction 1 Over 16 a squared b squared EndFraction. Option A
What are index forms?Index forms of a number can simply described as can be defined as that number written as an exponential expression.
They are also referred to standard form and scientific notation.
These index forms could also be written as single numbers raised to an exponent.
From the information given, we have that;
1//4 ab superscript negative 2
This is represented as;
(1/4 ab)⁻²
Now, expand the bracket, we have;
(16 a⁻²b⁻²)
This is further simplified to
1/16 a²b²
Hence, the expression is 1/16 a²b²
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Find the perimeter of the polygon if
5cm, 4cm, and 3cm
P=
The perimeter of the polygon is found as the 42 cm.
Define the term perimeter of the polygon?The perimeter of an enclosed plane figure is referred to in geometry. The perimeter of an enclosed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides. All sides add up to the perimeter.For the shown polygon:
Points A, B, C and D are tangents on the circle.
Thus, these tangent will subtend equal length from the points.
So,
AB = 3 + 4 = 7 cm
BC = 4 + 5 = 9 cm
As, ∠B ≅ ∠D, sides must also be equal.
CD = 5 + 4 = 9 cm
DA = 4 + 3 = 7 cm
Perimeter = AB + BC + BC + BC
= 7 + 9 + 9 + 7
Perimeter = 42 cm
Thus, the perimeter of the polygon is found as the 42 cm.
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pls helppppppp dont worry abt the one i have marked
What is equality in Class 8?
In Class 8, equality is likely to be defined as a state of being where all individuals are treated fairly and have the same rights, opportunities, and access to resources, regardless of factors such as race, gender, socioeconomic status, and other characteristics. Equality is often contrasted with inequality, which is a state of being where individuals or groups have unequal access to resources and opportunities.
In class 8, students may learn about different types of equality, such as:
Political equality: This refers to the idea that all individuals have an equal say in the political process and equal representation in government.
Social equality: This refers to the idea that all individuals have the same rights and opportunities, and are treated with the same respect and dignity, regardless of their background or characteristics.
Economic equality: This refers to the idea that all individuals have access to the same economic opportunities and resources, regardless of their background or characteristics.
Educational equality: This refers to the idea that all individuals have access to quality education, regardless of their background or characteristics.
Equality of opportunity: This refers to the idea that all individuals have an equal chance to succeed and reach their full potential, regardless of their background or characteristics.
In class 8, students may also learn about the importance of equality and the ways in which inequality can negatively impact individuals and society. They may also learn about different strategies for promoting equality and reducing inequality in society.
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Given f(x) = x^2 - 6x + 1, what is the domain of f(x)?
A,B,C or D?
Any values of x will result in a real value of the quadratic equation f(x), which is written as f(x). Your minimum score is therefore (3,1).
what is domain ?A function's acceptable range of values is referred to as its domain. These numbers serve as representations of the x-values of a function like f. (x). The set of potential values that a function can be applied to is known as its domain. When the x value is inserted, the method returns the value that is contained in this set. A function's definition is Y = f, where x is the independent variable and y is the dependent variable (x). If it is possible to successfully use a value of x to generate a single value of y using the value of x, that value of x .
given
Let y = f(x) be a function where x and y are the independent and dependent variables.
then that selected x-value is said to belong to the domain of f.
Any values of x will result in a real value of the quadratic equation f(x), which is written as f(x). Your minimum score is therefore (3,1).
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is 3(5a + 9) + 5a and 4(5a+6) equivalent
Answer:
no although they were close
Step-by-step explanation:
What is a domain of the functions Mcq?
A function's range is the collection of all possible values that it can accept, and its domain is the set of all values for which the function is defined.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x. The following requirements are frequently verified when a function's output y-value is required to be a real number:
1. The numerator cannot be zero.
2. Even roots (square roots, etc.) radicands (expressions denoted by a radical symbol) cannot have a negative value.
3. Only positive values can be used in logarithms.
4. Physical or other real-world constraints may be placed on word problems, such as the fact that time is not negative or that the number of items is an integer.
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Find the area. Simplify your answer.
x+8
x+5
Answer:
9x+5
Step-by-step explanation:
Add x and 8x
solve this for me. and get a brainlist.
Answer:
below
Step-by-step explanation:
Isosceles triangle have TWO equal legs....so
Leg + leg + base = perimeter
(4x-4) + ( 4x-4) + x = 37
9x -8 = 37
9x = 45
x = 5
Select the correct answer from each drop-down menu.
As x approaches positive infinity, m(x) approaches positive infinity.
As x approaches negative infinity, m(x) approaches negative infinity.
What is meant by function?An expression, rule, or law in mathematics that establishes a connection between one variable (the independent variable) and another variable (the dependent variable).
A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.
If a function produces the same outcome regardless of how the input is represented without changing its value, it is said to be well defined.
A function is a rule that is applied to a number, known as an input, in order to produce a result, known as an output.
when [tex]$x^n$[/tex] ( n is odd number and n > 0), a > 0 and c is any constant,
[tex]$$x \rightarrow \infty, a x^n+c \rightarrow+\infty[/tex]
[tex]$x \rightarrow-\infty, a x^n+c \rightarrow-\infty$[/tex]
The complete question is;
The function f(x) = x^3 has been transformed, resulting in function m.
m(x) = 1\3x^3 + 6
As x approaches positive infinity, m(x) approaches___
As x approaches negative infinity, m(x) approaches___
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How do you solve a 3d triangle?
If the base of the prism has dimensions x and y, and the diagonal along the base is represented by c, then x² + y² = c². The longest diagonal in the solid, s, is the hypotenuse of the triangle formed by the sides c and the height of the solid, z. So we know that, c² + z² = s².
What is a triangle in 3D called?
Triangular Prism (3D shape with identical triangle bases) Cone (3D triangle with a circular base)
In the case of a cylinder, one or several of the following data must be provided: the total area/lateral area and the circumference/area of the base or the area of the base and the volume. Ex: provided the circumference of the base = 10π inches, and the lateral area = 50π inches², the equation can be written as 50π ÷ 10π = 5 inches.
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To get snacks for a class trip, Clare went to the “bulk” section of the grocery store, where she could buy any quantity of a product and the prices are usually good.
Clare purchased some salted almonds at $6 a pound and some dried figs at $9 per pound.
She spent $75 before tax.
If she bought 1 pounds of figs, how many pounds of almond did she buy?
Find the vale of :
sin 1230°
Answer:
1/2
Step-by-step explanation:
I think it is 1/2 Sorry If i am Wrong
A alone can do piece of work in 6 day and B alone in 8 day. A and B undertook to do it for $3200. With the help of C, they completed the work in 3 day. How much i to be paid to C?
If A alone can do a piece of work in 6 days and B alone in 8 days, then A and B undertook to do it for $3200 and complete the work in 3 days with the help of C, then C would be paid 400 dollars.
Therefore the answer is $400.
This is a work and time problem that can be solved using the concept of rate of work. Let's call the amount to be paid to C as "x".
A can do 1 piece of work in 6 days. Therefore, his rate of work is 1/6.
B can do 1 piece of work in 8 days. Therefore, his rate of work is 1/8.
Amount of work A and B can do in 3 days is
= 3×(1/6) + 3×(1/8)
= 3×(1/6)×(4/4) + 3×(1/8)×(3/3)
= 12/24 + 9/24
= 21/24
= 7/8
So amount of work C doing is
= 1 - 7/8
= 1/8
As C do 1/8 amount of work, the amount C would receive is
= 3200 × (1/8)
= 400
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What are the 6 basic graphs?
The six different types of graphs are frequency distribution graphs, exponential graphs, logarithmic graphs, trigonometric graphs, and statistical graphs (such as bar, pie, and line graphs).
A vertical and horizontal line connect at the origin to form a simple two-dimensional graph. The x axis is horizontal, whereas the y axis is vertical. The x and y axes in basic line graphs are each subdivided into uniformly spaced subdivisions and given integer values.
There are eight primary types of graphs: linear, power, quadratic, polynomial, and they all aid in organising the presentation of data or information.
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you are standing 10 feet from the base of a tree. the angle of elevation to the top of the tree is 70 degrees. what is the height of the tree
The height of the tree is 17.32 feet.
What is height?Height is the measurement of a person's or object's vertical distance from the ground. It is usually expressed in units of meters or feet. Height is an important factor in determining physical characteristics, such as BMI, or Body Mass Index. Height can also be used to estimate the age of a person, and to measure the effects of a growth-promoting treatment. Height is also used in many sports, as it is often an advantage for athletes.
Using the tangent formula, the height of the tree is approximately 17.32 feet. To calculate this, take the tangent of 70 degrees (which is 1.19175) and multiply it by the 10 feet of distance.
The result is 11.9175 feet, which when rounded to the nearest hundredth is 17.32 feet.
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How do you dilate by a scale factor of 3 4?
16 is a scale factor of 3 4
What is scale factor ?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.Scale factor is a number that is used to draw the enlarged or reduced shape of any given figure. It is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It helps in changing the size of the figure but not its shape.To learn more about scale factor refers to:
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Taylor writes an expression with 5 terms. All 5 terms are like terms. How many terms are in the equivalent expression with the least number of terms
Answer:
An equivalent expression with the least number of terms will have 1 term if all 5 original terms are like terms. This is because like terms can be combined using the distributive property and addition, resulting in a single term with a combined coefficient.
Step-by-step explanation: