These are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.
A parent function is the simplest form that a function can be. Its basic shape is not in any way altered. In mathematics, you see certain graphs over and over again. For that reason, these original, common functions are called parent graphs, and they include graphs of quadratic functions, square roots, absolute values, cubics, and cube roots.
For instance, when you see a u-shaped graph that is inverted and vertically stretched, you should still recognize that it is a parabola which has undergone different transformations.
We can take a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola.For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Now, there are 6 parent functions:
IdentityAbsolute ValueSquare RootQuadraticCubicReciprocalHence, these are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.
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A standard six-sided die is rolled, and P is the product of the five numbers that are visible. What is the largest number that is certain to divide P?
A. 6 B. 12 C. 24 D.14 E.720
The largest number which certain to divide P is 12. The correct option is B.
The product of all six numbers of the six-sided die is 6! = 720.
The products of numbers which can be visible are:
720 / 1, 720 / 2, …, 720 / 6.
In this case, the answer is the largest common divisor, that is:
720 / L
where L = the least common multiple of {1,2,3,4,5,6}.
So, it is clear that L = 60.
Thus, the answer is:
= 720 / L
= 720 / 6
= 12
Hence, the largest number which certain to divide P is 12, it is option B.
What is the largest number in the world?A Googolplex is studied to be the largest number in the world. It is stated as 10^googol. The number 10^googol can also be written in the exponential format which will equal 10^10^100. When writing the number googol in normal number writing format, the probability of losing count is very high. Thus, it is more convenient to write it in the form of exponent and powers.
The number googolplex is so extremely large which is unimaginable to be expressed in number writing format. Hence, the number remains a concept as it is of no use in mathematics for basic calculations.
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How do the angles and sides of the outline correspond to the angles and sides of the original triangle?
The Angles and sides of the outline correspond to the angles and sides of the original triangle is done as below.
What are corresponding sides and angles?Corresponding sides and angles are a pair of matching angles or sides that are in the same spot in two different shapes.
Given:
For Corresponding Angle
The same two angle pairs are touched by corresponding sides. When the sides are equivalent, you can multiply each side by the same value to move from one triangle to another. The corresponding sides of the triangles in the similar triangles diagram are the same colour.
Form Corresponding Side
If two triangles are similar and have sides A, B, C and a, b, c, respectively, then the pair of corresponding sides are proportional,
i.e., A : a = B : b = C : c.
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Liz is watching a film at the cinema. The film started at 14 30. The film is 105 minutes long. When the film ends, Liz takes 20 minutes to get to the bus stop. Does Liz get to the bus stop in time to get this bus? You must show all your working
The answer is yes, she does and she still has 10 minutes free.
What is time ?
Time can be defined as the sequence on which particular event exists and time can measured in minutes , seconds, and hours.
Given,
The film started at 14 30. The film is 105 minutes long.
When the film ends, Liz takes 20 minutes to get to the bus stop.
105min=1h 45min
14h 30min + 1h 45min= 16h 15min
16h 15min + 0h 20min=16h 35min
16h 45min - 16h 35min= 10min
Hence, the answer is yes, she does and she still has 10 minutes free.
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Using Euler's Method with a step size of h = 0. 2, estimate the value for y(1. 4) for the differential equation y plus 2 times dy dx equals the product of the natural logarithm of y and the sine of x, with y(1) = 2
during a lunch seminar chocolate caramel and strawberry toppings were available how many two-topping
There are 3 two topping sundaes possible.
How many two toppings are possible?It is not crucial to choose the toppings in any particular sequence. For instance, a caramel and strawberry topping is the same as a chocolate and caramel topping. To answer this question, we thus apply the combinations formula.
Mixtures Formula:
C,n,x is the amount of various ways there are to combine x items from a set of n components, as determined by the formula below.
Cn,x = n! / x!(n-x)!
sundaes with two toppings are possible
2 of a set of 3 toppings (chocolate, caramel and strawberry). So
C3,2 = 3! / 2! (3 - 2)! = 3.
Three two-topping sundae combinations are conceivable.
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-2y - 10 = x -10x
- y = −14
Answer:
Step-by-step explanation:
-2y-10=x-10x
-2(-14) - 10= x - 10x
28 - 10 = x - 10x
18= x-10x
18= -9x
/-9 /-9
-2=x
Each side when you plug in (-2) for x and (-14) for y you get 18.
If, when you plug in the number, you get different numbers for each side, then that means there's a mistake and the answer is wrong.
Hope this helps!
Tracy took a test and had 24 questions. She got 5/6 of the questions correct. How many questions did she answer correctly? Write an equation to model your work
Tracy got 20 questions correct in her test.
Tracy took a test in which there are 24 questions, out of which Tracy got 5/6 correct.
Hence he got 24 x 5/6 = 20 questions correct.
An equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign.
So ,an equation to model this would be:
x = 24 x 5/6
where x is the number of questions tracy answered correctly.
Hence Tracy answered 20 questions correctly.
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help help help help help help help
The required point-slope form of the equation of the line is y - 20= -5(x + 1).
Given that, To determine an equation in point-slope form for the line that passes through the point with the given slope. point: (-2,-20) and m=-5.
What is the slope of the line?The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.To learn more about point-slope refer to:
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Q14
How can I prove (a)
AE is congruent to CE.We can prove by assuming two triangle in the given diagram and by using SAS rule.
How do you find congruent triangles?If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.
What is an alternate angle in a triangle?Alternate angles are angles that occur on opposite sides of the transversal line. If two parallel lines are cut by a transversal then the alternate angles are equal.The pair of angles formed on the inner side of the parallel lines but on the opposite sides of the transversal are called alternate interior angles.
Now we have
Given a triangle ABC.Where E is the midpoint of AC. We have to prove that AE is congruent to CE.
In ΔAED and ΔCED
ED=ED (∵Common side are equal)
∠AED=∠CED (∵Alternate angles)
∠A=∠C (∵Alternate angles)
By ASA rule, ΔAED≅ΔCED
By Corresponding Parts of Congruent triangles
AE=EC
Hence, AE is conruent to CE.
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a salesman goes to Murano and buys three dozen vases paying €16.25 each. During transport if they break me 9. How much did each remaining vase sell for if he earned €360
The vase sells for € 34.41, and he made €360 during a break on the ninth transfer.
what is unitary method ?
The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)
given
A salesperson purchases three dozen vases (12 * 3 = 36),
at a cost of 36 * €16.25 (or $585),
with seventeen remaining.
The cost of selling each remaining vase is € 585 / 17
= € 34.41.
The vase sells for € 34.41, and he made €360 during a break on the ninth transfer.
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Is N2 equal to Avogadro's number?
Yes, N2 equal to Avogadro's number. The symbol for Avogadro's number is N₂
What is Avogadro's number?Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.
Yes, Avogadro's number is defined as the number of atoms, ions or molecules in one mole of substance, and is approximately 6.022 x 10^23. The symbol for Avogadro's number is N₂.
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What is the size of the augmented matrix for the linear system?
The augmented matrix, however, is a two-by-four matrix because it also contains the constants.
What do you meant by augmented matrix for the linear system?The augmented matrix will always include one additional column for every additional variable, and the same number of rows as there are equations. An easier technique to write a set of linear equations is to utilize enhanced matrices.
In an augmented matrix, two sides of the matrix are separated by a vertical line that serves as a representation of a succession of equal signs. The collection of linear equations, for instance, would be represented by the matrix. There is only ever one pivot in a column.
For (c): Three rows and four columns make up the augmented matrix of this system. As a result, it only has three pivot points at most. Thus, a pivot column cannot be represented by a single variable.
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Answer:
What is the size of the augmented matrix for the linear system?
B) 2x3
Identify the values for the elements in the augmented matrix:
a11 = 3
a12 = 7
a13 = 20
a21 = 1
a22 = -4
a23 = 9
Step-by-step explanation:
What baseball stat does Lawrence Hinman suggest is the most important stat for determining the best player in the game in a given year
A range of fundamental, unchanging values may exist in the world, according to ethical pluralism.
What is meant by Ethical Pluralism?According to ethical pluralism, the world may contain a variety of essential and unchangeable values. There may be more, but happiness and respect for people are two possible ones.
The notion of ethical plurality holds that there are various beliefs about what is "good" and "wrong" (moral norms), some of which may be incompatible and/or out of line with your own personal moral standards. Working in foreign societies, where you could encounter varying norms, is a component of international involvement.
The conviction that there are various viewpoints on a subject, each of which has some truth, but none of which contains the complete truth the conviction that while each moral theory somewhat captures the essence of what it means to live morally, none has the whole picture.
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Lawrence Hinman does not have a clear statement on the best baseball stat for determining the best player in a given year.
What do you mean by statistics?Statistics are a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In baseball, statistics are used to measure the performance of individual players, teams, and even entire leagues. Some common baseball statistics include batting average, home runs, runs batted in, earned run average, and wins. These statistics are used to evaluate the performance of players, compare them to other players, and even predict future performance.
What are some common baseball statistics?Baseball statistics are a set of metrics used to measure the performance of individual players and teams in baseball. Some common baseball statistics include:
Batting average (BA)Home runs (HR)Runs Batted In (RBI)Wins (W)It is likely that different analysts and experts would have different opinions on which stat is the most important for determining the best player in a given year. Some might argue that traditional stats like batting average, home runs, and RBIs are the most important, while others might argue that newer stats like on-base percentage, slugging percentage, and WAR are more informative.
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Explain the concept of extraneous solutions. Give examples with the different types of functions explored.
Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.
What is a function ?
Function can be defined as a relation , which relates an input to output is called as function.
In Mathematics, an extraneous solution (or spurious solution) is an solution, consisting of that to an equation, that emerges from the procedure of solving the hassle but isn't always a legitimate strategy to the problem.[1] A missing solution is an answer that is a valid strategy to the hassle,
however disappeared all through the process of solving the problem. each are frequently the consequence of acting operations that are not invertible for a few or all values of the variables, which prevents the chain of logical implications inside the proof from being bidirectional.
Hence , The Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.
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A watch increased in price by 4/5. After the increase it was priced at £126. What was the original price of the watch?
A watch increased in price by 4/5 is priced at £126, then the original price of the watch was £100.
We know that the price of the watch increased by 4/5. To find the original price of the watch, we can use the following formula:
original price = new price / (1 + increase percentage)
In this case, the new price of the watch is £126 and the increase rate is 4/5. So we have:
original price(1 + 4/5) = 126
original price = 126 / (1 + 4/5)
original price = 126 / (1+ 0.8)
original price = 126/1.8
original price = 70
So, the original price of the watch was £70.
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What would be the explicit equation for the sequence 3, 9, 27, 81 
Answer:
times it by
Step-by-step explanation:
3×3=9, 9×3=27, 27×3=81, 81×3=243
sorry if this isn't the answer your looking for.
help ! what's the value of x -
[tex] {x}^{4} + 4 = 100 \div 5[/tex]
Answer:
2
Step-by-step explanation:
100/5 = 20
x⁴ + 4 = 20
x⁴ = 20 - 4
x⁴ = 16
= 2 × 2 × 2 × 2
x⁴ = 2⁴
x = 2
Hence, the value of x is 2.
A rental car company charges $50 per day to rent a car and $0.15 for every mile driven. Mei Mei wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $130 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Mei Mei can afford to rent while staying within her budget.
Answer:
50x + 19.5 ≤ 130
Step-by-step explanation:
X is the number of days Mei Mei plans to rent the car
For driving 100 miles, Mei Mei will be charged $19.50. [130 times 0.15]
Mei Mei has a maximum budget of $130, so the inequality will have a less than or equal to sign
50x + 19.5 ≤ 130
Please help
VX is a midsegment of UWY
IF UY=13p-1 and VX=20p-95 what is UY
The length UY of the triangle is 90 units
How to determine the length UYFrom the question, we have the following parameters that can be used in our computation:
VX is a midsegment of triangle UWYUY = 13p - 1 and VX = 20p - 95This means that
UY = 2 * VX
Substitute the known values in the above equation, so, we have the following representation
13p - 1 = 2 * (20p - 95)
Evaluate the products
13p - 1 = 40p - 190
So, we have
40p - 13p = 190 - 1
So, we have
27p = 189
Divide by 27
p = 7
Substitute p = 7 in UY = 13p - 1
UY = 13 * 7 - 1
So, we have
UY = 90
Hence, the length is 90 units
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What is the value of v?
Answer: v = 100
Step-by-step explanation:
v+15 = v-37 + v-48
v + 15 = 2v - 85
85 + 15 = 2v - v
100 = v
please help me find the surface area of this triangular prism
The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.
How do you find the area of a prism?The surface area of a triangular prism is defined as the sum of the area of its five faces. To calculate the surface area, we need the values of the base, length, and height of the triangular prism. Its formula equals the sum of two times the base area and three times the product of the base and length of the prism.Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula A = 1 2 b h is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.To find the surface area of a prism, use the formula SA=2B+ph, where SA stands for surface area, B stands for area of the base of the prism, p stands for the perimeter of the base, and h stands for the height of the prism.Two triangles' area: 18×24÷6x3 = 432cm^2
The widest rectangle's area: 30×7 = 210cm^2
The rectangle facing the left's area: 18×7= 126cm^2
The rectangle facing the ground's area: 24×7= 168cm^2
Total Surface Area: 432+210+126+168 = 936cm^2
=936cm^2
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You have a pitcher that holds 35.2 oz. of iced tea. If each glass holds 8.8 ounces, how many glasses can you completely fill?
Answer: 4
Step-by-step explanation:
35.2/ 8.8= 4
4
The cost of a certain cell phone plan can be modeled by C(m) = 2m + 15, where C(m) is the total cost for m minutes of cell phone usage. State the meaning of the slope with respect to the cost associated with the cell phone plan.
The interpretation of the slope is that the cost per minute is $2
How to determine the interpretation of the slope?From the question, we have the following parameters that can be used in our computation:
C(m) = 2m + 15
Where
m = number of minutes
C(m) = cost function
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 2
This means that the slope is 2
And it means that the cost per minute is $2
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What should be taken away from 3x² 4y² 5xy 20 obtain X² y²+ 6xy 20?
4x2 - 3y2 - xy should be taken away from 3x² 4y² 5xy 20 obtain X² y²+ 6xy 20
A fraction is a percentage of a whole. This entire sentence could be referring to a single location or a collection of locations. The English word "fraction" originates from the Latin word "fraction," which means "to break." As the first society to comprehend fractions, the Egyptians used fractions to solve a number of mathematical problems, including the distribution of food and resources and the absence of a metal currency.
Assume X is the component that is absent.
As a result, the answer to the question is
(3x2 - 4y2 + 5xy + 20) - (X) = - x2 - y2 + 6xy + 20
To determine the value of X, let's change the words.
X is equal to (-x2 - y2 + 6xy + 20) = 3x2 - 4y2 + 5xy + 20.
X = 4x2 - 3y2 - xy X = 3x2 - 4y2 + 5xy + 20 + x2 + y2 - 6xy - 20
Thus, the expression that should be subtracted is 4x2 - 3y2 - xy.
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PLEASE PLEASE HELP!!
Need it by the end of the night!
4.
Kelly Waxman's annual salary is $30,000. She takes
a married exemption. Using the graduated income
tax rates in the figure on the right, find the annual
state tax withheld. (Section 2-3)
a. $1,877. 21
c. $1,877. 90
b. $2,159. 85
d. $1,662. 50
Personal Exemptions
Single
$1,500
Married
$3,000
Each Dependent
$ 750
State Tax
Annual Gross Pay Tax Rate
First $3,500
3%
Next $3,500
4. 5%
Over $7,000
7%
The annual state tax withheld for Kelly Waxman would be 1,662.50 dollars.
Therefore the answer is d) $1,662.50.
Here is the breakdown of the calculation:
Kelly's salary of $30,000 minus the married exemption of $3,000 = $27,000
The first $3,500 are taxed at 3%, which is
= 0.03×3500
= $105
The next $3,500 are taxed at 4.5%, which is
= 0.045×3500
= $157.50
The remaining $27,000 - $3,500 - $3,500 = $20,000 are taxed at 7%, which is
= 0.07×20000
= $1,400
Adding all three amounts together: $105 + $157.50 + $1,400 = $1,662.50. It is the annual state tax withheld.
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How to get the awnser
The slope and the y-intercept of the linear function in this problem are given as follows:
Slope: -2.y-intercept: 6.The equation of the linear function in this problem is given as follows:
y = -2x + 6.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing the rate of change of the linear function.b is the y-intercept, representing the value assumed by the linear function when x assumes a value of zero.From the table, we have that when x = 0, y = 6, hence the intercept b is given as follows:
b = 6.
When x increases by one, y decays by two, hence the slope m of the linear function is given as follows:
m = -2.
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Chapter 3 Lesson 4 Arithmetic Sequence
1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)
37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)
-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).
What is Arithmatic Sequence?The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence. As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulae for arithmetic sequences.
The equation to determine the nth term in an arithmetic series
The formula for calculating the sum of an arithmetic sequence's first n terms
There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."
Option 1, 4 and 6 are in Arithmatic Sequence as
In 1:
1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)
again in 4 :
37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)
and in 6
-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).
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a stationer sells 17 magazines for €2.70 each, 28 newspapers for €1.50 each and postcards for €0.30 each. If he collected €97.20 how many postcards did he sell?
It needs to be an expression
In order to calculate how many postcards he sold, multiply €0.30 by (45.9 + 42) to get €97.20.
what is expression ?Multiplication, division, addition, and subtraction are all possible in mathematics. Expression, number, and mathematical operator are the components of a mathematical expression (such as addition, subtraction, multiplication, or division, etc.). Expressions and phrases can be contrasted. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For instance, the phrase 4m + 5 consists of the terms 4m and 5, as well as the provided expression's variable m, all of which are separated by the arithmetic sign +.
given
A stationer sells 17 magazines for €2.70 each, for a total of €45.9; 28 newspapers cost €1.50 each,
for a total of €42; and
x postcards, for a total of €0.30x,
for a total of €97.20.
In order to calculate how many postcards he sold, multiply €0.30 by (45.9 + 42) to get €97.20.
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Please help I have a learning disablity and need help with this.
Use Distribute Property to rewrite the algebraic expression.
Please answer both parts
8(x + 7)
Answer here _____________
Use Distribute Property to rewrite the algebraic expression.
6(11 + x)
Answer here ____________
The value of 8(x + 7) is 8x + 56.
The value of 6(11 + x) is 66 + 6x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The distributive property of multiplication over addition states that,
a x (b + c) = a x b + a x c
Now,
8 x (x + 7)
= 8 x (x) + 8 x 7
= 8x + 56
6 (11 + x)
= 6 x 11 + 6 x (x)
= 66 + 6x
Thus,
The value is 8x + 56 and 66 + 6x.
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At an arts festival, Jamal, a camp counselor, bought food tickets for his hungry campers. The campers can use them to get hot dogs, which cost 4 tickets apiece, and burgers, which cost 5 tickets apiece. In total, the campers can use up to 21 tickets, which is how many Jamal bought. Write an Inequality that best describe this situation
Inequality in its most basic form explains this circumstance is 5x + 4y ≤ 21
What isan Inequality?Jamal, a camp counsellor, purchased meal tickets at an arts festival for his ravenous kids. The campers may use them to purchase burgers and hot dogs, both of which cost four tickets each.
A camp counsellor purchased meal tickets at an arts festival for her ravenous kids.
The campers may use them to purchase burgers and hot dogs, both of which cost four tickets each.
Let x be the number of hot dogs and y be the number of burgers. In all, campers are allowed to utilise up to 21 tickets.
Thus, inequality in its most basic form explains this circumstance.
= 5x + 4y ≤ 21
Inequality in its most basic form explains this circumstance is 5x + 4y ≤ 21
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