A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.
To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.
For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:
y = mx + b
3 = m*2 + b
7 = m*5 + b
Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.
A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.
For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:
y = ax^2 + bx + c
6 = a*1^2 + b*1 + c
13 = a*2^2 + b*2 + c
24 = a*3^2 + b*3 + c
Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.
An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.
For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:
y = a*b^x
16 = a*b^2
24 = a*b^3
Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.
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Julian went shopping for a new pair of sneakers. Sales tax where he lives is 5.75%. If the price of the pair of sneakers is pp dollars and cents, which expression represents the total price plus tax?
The expression that represents the total price plus tax that Julian paid during shopping is 1.0575pp
How to write the expression of the total price Julian paid
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
5.75%
= 5.75 percent
= 5.75 / 100
= 0.0575
The factor 0.0575 of the price (pp dollars and cents) gives the total price paid
when the price paid is pp dollars and cents
= 0.0575 * pp + pp
= 1.0575pp
The total price paid is 1.0575pp
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( r - 8 ) - ( r + 15 )
Find the Sum or Difference! :)
Answer:
-23
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
Answer:-23 ITS SUPER EASY:0
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
23x² + 6x + 7 please help
Answer:
the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
Step-by-step explanation:
The expression 23x² + 6x + 7 is in the form of a quadratic equation. A quadratic equation is an equation in the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the coefficients of the x², x, and the constant term are a = 23, b = 6, c = 7.
One way to factor a quadratic equation is by using the factoring by grouping method, where we group the terms in pairs and factor out the greatest common factor (GCF) from each group.
Here is one way to factor this equation:
23x² + 6x + 7 = (23x² + 6x) + 7
= (23x² + 6x) + 7
= (23x² + 6x + 6x) + 7
= (23x² + 12x) + 7
= (23x(x) + 3x(4)) + 7
= (23x(x+4) + 7)
= (x+4)(23x + 7)
So the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
It's important to note that the above expression factors into a product of two binomials and not two factors of 23x² + 6x + 7
You can also use Quadratic formula to solve the above expression if this method seems confusing.
Dylan opened a credit card account with $575.00 of available credit. Now that he has made some purchases, Dylan's account only has $465.75 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?
Answer:
19%
Step-by-step explanation:
First, we have to find how much did he spend by taking
$575.00 - $465.75 = $109.25
Then we find the percentage decrease by taking
109.25 divided by 575, then times 100% = 19%
So, the percentage decrease of the amount of available credit in Dylan's account is 19%
A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events. The probabilities assigned were , , and a. If an individual recalls seeing the advertisement, what is the probability that the individual purchased the product (to 1 decimals)
0.30 is the probability that the individual purchased the product
What is probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.
Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.
Let, B = individual purchased the product
S = individuals recalls seeing the advertisement.
Here, P(B) = 0.20
P(S) = 0.40
P(B ∩ S) = 0.12
Thus, P(B | S) = P(B ∩ S) / P(S)
= 0.12/0.40
= 0.30
P(B) = 0.20 < P(B | S) =0.30
Yes, thus the probability that an individual will purchase the product will increase if the individual sees the advertisement first.
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The complete question is as follows:
How do you solve equivalent questions?
One of the way by which we can solve equivalent questions is by multiplying both the numerator and the denominator by a same number .
The number chosen for the purpose should be same and should be a non zero number. Example, if we want to find the equivalent of 2/8 then we can simply multiply 2 and 8 which are the numerator and the denominator by a same number say 3 .
Then we will get the result as 2 x 3 /8 x 3 = 6 / 24 .
The result will be a number equivalent to the given fraction. This can be checked by reducing the result to its lowest terms.
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a club treasurer is solving a problem using the expression shown. -23.50 + 5 which problem is the treasurer MOST LIKELY solving? A. There is a club member who pays 23.50$ in dues each month for 5 months. What is the total amount, in dollars, that the member pays in dues? B. There are 5 club memebers who each owe the club 23.50$ in dues. What is the total balance, in dollars, of the members accounts? C. a total of 23.50$ in dues is owed to the club. There are 5 club memebrs who each owe the same account in dues. What is the amount, in dollars, that each member owes in dues? D. A total of 23.50$ in dues is owed to the club. There are 5 club members who each owe the same amount in dues. What is the balance,in dollars, of each members account?
When the treasurer is solving a problem using the expression shown. -23.50 ÷ 5, the problem that the treasurer is lost likely solving is D. A total of -$23.50 in dues is owed to the club. There are 5 club members who each owe the same amount in dues. What is the balance,in dollars, of each members account?
How to illustrate the expression?From the information, the club treasurer is solving a problem using the expression shown. -23.50 ÷ 5. An expression show the relationship between the variables.
In this case, a total of $23.50 in dues is owed to the club. There are 5 club members who each owe the same amount in dues.
The correct option is D.
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3x + 2y = 5
x = 2y + 7
Answer:
I hope this helps you...
please mark me as brainliest..
150 people went to see "Ode to Algebra" performed in the school auditorium. If the number of children that attended the performance was c, how many adults attended?
Answer:
150-c
Step-by-step explanation:
150= total
c= children
adults=x
x=150-c
Refer to the equation a-6 equals b if a equals 45 what is the value of b?
Answer:
Step-by-step explanation: a=4, b=2.
Answer:
b = 39
Step-by-step explanation:
[tex]a-6=b[/tex]
if a = 45:
[tex]45-6=b\\39=b[/tex]
Hope this helps
How do you write 10000000 in words?
Write an equation of the line that passes through the given point and is perpendicular to the given line.
(2, 5); x = -6
well, since the given line is a horizontal line, a perpendicular line to that will just be, yeap, you guessed it, a vertical line, Check the picture below.
Graph the line with slope of 3/4 passing through the point (-1, 2)
Answer:
Step-by-step explanation:
The probability that a student studied is 0.85. The probability that a student will not pass, given that the student studied is 0.10.
a) Find the probability that a student will study and will pass.
b) Suppose that the probability that a student will either study or pass is 0.8. Find the probability that a student will pass.
a) The probability that a student will study and will pass is 0.765.
b) The probability that a student will pass is 0.715.
What is probability?
Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.
Define some events -
A: A student studies.
B: A student will pass.
Given that P(A)=0.85 and
P(B|A)=1-P([tex]\bar{B}[/tex]|A)
=1-0.10
=0.90
a) P(a student will study and will Pass)= P(A∩B)
= P(A)·P(B|A)
= 0.85×0.90
= 0.765
b) Given that P( student will either study or pass), the probability is -
=P(A∪B)= 0.8 then P(a student will pass)
=P(B)
It is known that P(A∪B)= P(A)+P(B)-P(A∩B)
Then P(B)=P(A∪B) -P(A) +P(A∩B)
=0.8-0.85 + 0.765
=0.715
Therefore, the probabilities are 0.765 and 0.715.
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Pretend you are constructing a histogram for describing the distribution of salaries for individuals who are 40 years or older, but are not yet retired.
Salary age
$57,000. 00 27
$40,200. 00 21
$21,450. 00 44
$21,900. 00 27
$45,000. 00 40
Required:
a. What is on the Y-axis? Explain.
b. What is on the X-axis? Explain.
c. What would be the probable shape of the salary distribution? Explain why?
a) The data on the y-axis: the numbers of people in each salary category.
b) The data on the x-axis: salaries
c) The distribution of salaries is skewed to the right.
We know that a histogram is a graph in which the x-axis is a quantitative variable split into bins, and the y-axis is the frequency.
For given distribution of salaries for individuals, the Y-axis would have the frequency i.e., the numbers of people in each salary category.
And x-axis would have income, because this is out quantitative variable of interest.
consider the following histogram.
We can observe that the graph of distribution of salaries is skewed to the right, because most income data are positively skewed. There would be a substantial number of individuals at or near the lowest salary level, but some people make a tremendously high salary.
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Whats 3x+1? for in high school its really hard to solve none of my friend cant do it
As per the zeros of the function, the value of the function 3x + 1 is x = -1/3.
Zeros of the function in math is defined as the values of the variable of the function such that the function equals 0.
Here we have given the function 3x + 1.
Now, we have to equate the function with zero, in order to solve it, then we get,
=> 3x + 1 = 0
Now, we have to subtract 1 on both sider to individualize the x value then we get the rewritten expression as,
=> 3x = -1
Now, we have to divide each side by 3, then we get the value of x as,
=> x = -1/3
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A rectangle measures 1 3/4
inches by 3 3/4
inches. What is its area?
please help!
Answer:
6 and 9/16
Step-by-step explanation:
The area of a rectangle can be calculated by multiplying the width and length. So 1 3/4*3 3/4=7/4*15/4=105/16 or 6 and 9/16
A convenience store sell pre-paid mobile phones. It purchases them for $12 each and uses a mark up rate of 250%.
a. The markup rate is the constant of proportionality in the equation y= kx. Write an equation that can be used to find the amount of markup on the cost x of a phone
b. Use the equation to calculate the markup amount. What is the retail price of a phone?
c. Next week the store is going to reduce the price to $31. 50. Calculate what percent the sale price is of the retail price.
d. Based on your answer to part C, what is an equation in the form y = kx that relates the sale price to the retail price x?
Answer:
a. y = 2.5x
b. markup: $30; retail price: $42
c. 75%
d. y = 0.75x
Step-by-step explanation:
You want equations relating markup, retail price, and sale price on a phone that costs $12, is marked up 250%, then put on sale for $31.50.
a. Markup equationThe problem statement tells you the markup is 250% of the cost. You could write the equation as ...
y = (250%)x
Or you can simplify it to a decimal number:
y = 2.5x
b. Markup amountThe markup amount is ...
y = 2.5(12) = 30
The markup amount is $30.
That is added to the cost to get the retail price:
retail = $12 +30 = $42
The retail price of the phone is $42.
c. Sale priceThe sale price as a percent of the retail price is ...
percent = (sale price)/(retail price) × 100%
percent = 31.50/42 × 100% = 75%
The sale price is 75% of the retail price.
d. Sale price equationAs in part (a), we could write this as ...
y = (75%)x
or, in decimal, as ...
y = 0.75x
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A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters. Find the area of the parking lot. *
The area of the parking lot is 2,025 .81 meter2.
How do you calculate a triangle's area?In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.
A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters.
Triangle Height Determination Using Area
Now that you are aware of the triangle's area, you may use the triangle formula A=1/2bh to get the triangle's height.
s = a + b+ c /2
90 + 54 + 128 / 2 = 136
A = [tex]\sqrt{s (s-a) (s-b) (s-c)}[/tex]
A = [tex]\sqrt{136(136-90)(136-54)(136-128}[/tex])
A = 2,025 .81
The area of the parking lot is 2,025 .81 meter2.
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Is math in Grade 6 hard?
Sixth grade math class can be difficult, even for students who have done well in math previously. In sixth grade you begin to learn more advanced topics such as ratios and rates.
You also work more with fractions. Sixth grade is also when you begin building the foundations of algebra, geometry, and statistics.
example
given problem in maths
- x + 8 > 6 ( isolate the term in x by subtracting 8 from both sides )
- x > - 2 ( multiply both sides by - 1 )
Remembering to reverse the inequality symbol when multiplying/dividing by a negative quantity
x < 2 ← reverse symbol
From the given list the only value less than 2 is 1, hence
x = 1 ← is the only possible solution
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Standardized tests for certain subjects, given to high
Which of the following is the correct interpretation of P(X
school students, are scored on a scale of 1 to 5. Let X
> 4)?
represent the score on a randomly selected exam. The
distribution of scores for one subject's standardized test
• The probability of a of a randomly selected test having
is given in the table.
score of at most 4 is 0.36.
• The probability of a randomly selected test having a
Score
score of at least 4 is 0.36.
Probability
0.18
0.20
0.26
0.21
0.15
• The probability of a randomly selected test having &
score lower than 4 is 0.85.
• The probability of a randomly selected test having a
score higher than 4 is 0.15.
Answer: • The probability of a randomly selected test having a score higher than 4 is 0.15.
This is the correct interpretation of P(X > 4). P(X > 4) represents the probability of a randomly selected test having a score that is greater than 4. This is calculated by summing up the probability of all the scores that are greater than 4 in the distribution table.
Step-by-step explanation:
The model below represents 2 x + 1 = negative x + 4. 2 green long tiles and 1 green square tile = 1 long red tile and 4 square green tiles What is the value of x when solving the equation 2 x + 1 = negative x + 4 using the algebra tiles? x = negative 3 x = negative 1 x = 1 x = 3
Answer:
The model you described is a mathematical representation using algebra tiles, and it represents the equation 2x + 1 = -x + 4.
Step-by-step explanation:
To solve this equation for x, we need to isolate x on one side of the equation by using the operations of algebra (such as addition, subtraction, multiplication, and division).
In this case, we can start by adding x to both sides:
2x + 1 + x = -x + 4 + x
This gives us:
3x + 1 = 4
The next step would be to subtract 1 from both sides:
3x = 3
then we divide both sides by 3
x = 1
So x=1 is the solution.
The algebra tiles help to visualize the manipulation of equations, but the actual solving process is algebraic manipulation of the equation.
Baldwin took a total of 35 quizzes over the course of 7 weeks. After attending 9 weeks of school this quarter how many quizzes will Baldwin have taken in total
The total number of quizzes in 9 weeks will be 45.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Baldwin took a total of 35 quizzes over the course of 7 weeks. After attending 9 weeks of school this quarter.
The number of quizzes in 9 weeks will be,
7 weeks = 35 quizz
1 week = 35 / 9 quizz
9 week = ( 35 x 7 ) / 9
9 weeks = 45 quizzes.
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A manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Round your answer to the nearest hundredth.
Probability that computer chosen at random has defect is 0.0075.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.
What is probability?It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12.
Total number of computers=1200
Total number of damage computers=9
Probability that question chosen at random has defect = 9/1200=0.0075
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Are 3 4 5 triangles always right?
No, three 4 5 triangles are not always right triangles.
A right triangle is a triangle in which one of the angles is a right angle (90°). Therefore, in order to be a right triangle, the following criteria must be met: a^2 + b^2 = c^2, where c is the longest side and a, b are the other two sides. In a 3 4 5 triangle, the longest side is 5, so a^2 + b^2 = c^2 becomes 3^2 + 4^2 = 5^2. Using simple algebra, this equation becomes 9 + 16 = 25, which is true. Therefore, a 3 4 5 triangle is a right triangle. However, if one of the sides is different, for example a 3 4 6 triangle, the equation becomes 9 + 16 = 36, which is not true. Therefore, a 3 4 6 triangle is not a right triangle. To summarize,3 4 5 triangles are right triangles, but three 4 6 triangles are not.
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is the relationship between the variables in the table an inverse variation or a direct variation? write an equation to model it.
x= 2 6 7 14
y= 21 7 6 3
The relationship between the variables in the table is an inverse variation The equation to model is y = 42/x.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 8 is an equation.
We have,
x: 2 6 7 14
y: 21 7 6 3
Now,
When x = 2, y = 21
This can be written as,
y = kx
21 = 2k
k = 21/2
The equation is y = (21/2)x _____(1)
or
y = k/x
21 = k/2
k = 42
The equation is y = 42/x _____(2)
Now,
We will check which equation fits the table.
From (1)
y = (21/2)x
When x = 6,
y = (21/2) x 6 = 21 x 3 = 63
From (2),
When x = 6,
y = 42/6 = 7
When x = 7,
y = 42/7 = 6
When x = 14,
y = 42/14 = 3
This equation satisfies the table.
Thus,
The relationship is an inverse variation.
The equation is y = 42/x.
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Is 6 A positive number?
Yes, 6 is an positive number.
Now, According to the question:
What Is A Positive Number?
A positive number is any number that represents more than zero of anything. If you are talking about dollars in your bank account, a positive number will definitely make you feel positive too.
1, 2, 3, 4, 5, 6, 7, ........ are positive integers and -1, -2, -3, -4, -5, -6, -7, ........ are negative integers. 0 is an integer which is neither positive nor negative. On an integer number line, all numbers to the right of 0 are positive integers and all numbers to the left of 0 are negative integers.
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What is the answer of 7 to the power of 2?
The answer to 7 to the power of 2 is 49.
This is because when a number is raised to a power, it means that it is multiplied by itself that number of times. 7 to the power of 2 is 7 multiplied by itself 2 times, which is 7 x 7, which equals 49.
An expression known as "power" denotes the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.
As an illustration, the power 63 demonstrates how three times the number 6 is multiplied.
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3. Mr. Langley is painting the exterior of his house. He uses 7 1/2 gallons of paint for the surface
and 2/3 of a gallon of paint for the trim. He had estimated that he would use 11 gallons of paint. How
many gallons of paint was he away from his estimation?
The amount he estimated (11 gallons). 11 - 8.16 = 0.21 gallons.
What is estimation?Estimation is the process of making an educated guess about the value of something, such as a quantity, cost, or other measurement, based on the available information. It's used in many fields, including mathematics, engineering, economics, business, and project management. Estimation is an important skill which can help people make decisions and solve problems quickly.
Mr. Langley was away from his estimation by 0.21 gallons of paint. This is calculated by subtracting the total amount of paint he actually used (7.5 + 0.66 = 8.16 gallons) from the amount he estimated (11 gallons). 11 - 8.16 = 0.21 gallons.
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What are the 7 different triangles?
The seven different types of triangles are Equiangular Triangle , Acute Angled Triangle , Right Angled Triangle , Obtuse Angled Triangle , Equilateral Triangle , Isosceles Triangle and Scalene Triangle .
The Triangle is defined as a polygon with three sides having three vertices .
The Seven different types of Triangles are :
(i) Equiangular Triangle :
It is a type of triangle in which the measure of all the three sides of triangle are equal .
(ii) Acute Angled Triangle :
It is a type of triangle in which all the angles of triangle are acute , that means angle is less than 90 degree .
(iii) Right Angled Triangle :
It is the type of triangle in which the measure of one angle is 90 degree .
(iv) Obtuse Angled Triangle :
It is defined as a triangle in which one angle of the triangle is obtuse , that means the angle is greater than 90 and less than 180 degree .
(v) Equilateral Triangle :
It is a triangle in which the measure of all the sides of the triangle are equal .
(vi) Isosceles Triangle :
It is a type of triangle in which the measure of the two sides of the triangle are equal .
(vii) Scalene Triangle :
It is defined as a triangle in which the measure of all the sides of triangle are different ,
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