The sum of three consecutive integers is −261−261. Find the three integers.
You and a friend of getting ready to study for an assessment on expressions and
equations. Knowing that your friend is still getting expressions and equations mixed
up and doesn’t always know how to tell if two expressions or two equations are
equivalent, your job is to create a set of problems (and solutions) to help your friend
study. Create a minimum of six problems that will address your friend’s misconcep-
tions and include the solutions for her/him to study. Make sure your reasoning is
clearly articulated in the solutions.
Here are six problems and their solutions to help you study expressions and equations.
Explanation:Here are six problems to help you study expressions and equations:
Simplify the expression (3x - 4) + (2x + 5).Solution: Combine like terms: 3x + 2x - 4 + 5 = 5x + 1.Solve the equation 2x + 3 = 9.Solution: Subtract 3 from both sides: 2x = 6. Divide both sides by 2: x = 3.Determine if the expressions 2x + 5 and 5 + 2x are equivalent.Solution: Since addition is commutative, the expressions are equivalent.Determine if the equations 2x + 3 = 9 and 2x + 6 = 12 are equivalent.Solution: Subtracting 3 from both sides of the first equation gives 2x = 6, which is equivalent to the second equation.Simplify the expression 2(3x + 4) - (5x - 2).Solution: Distribute the 2: 6x + 8 - (5x - 2). Use the distributive property: 6x + 8 - 5x + 2. Combine like terms: x + 10.Solve the equation 3(x - 2) = 9.Solution: Distribute the 3: 3x - 6 = 9. Add 6 to both sides: 3x = 15. Divide both sides by 3: x = 5.Learn more about Expressions and Equations here:https://brainly.com/question/11537309
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The length of a rectangle is 18 cm less than five times it's width. It's area is 35 cm². Find the dimensions of the rectangle.
1 penny has a mass of 4 grams and is 1.55 millimeters thick. How much mass will a stack of 20 pennies tall have?
To find the mass of a stack of 20 pennies, multiply the mass of a single penny by 20.
Mass of a single penny: A single penny weighs around 3 grams on average.
Calculate the total mass: Multiply the mass of a single penny by the number of pennies in the stack (4 grams/penny * 20 pennies).Answer: A stack of 20 pennies will have a mass of 80 grams.Andrew is planning a tailgate party before the big football game. He has budgeted a maximum of $60 for hamburgers and hot dogs. Hamburgers cost $3 per pound, and hot dogs cost $2 per pound. Write an inequality to describe the possible number of pounds of hamburgers and of hot dogs he can purchase.
The inequality that describes the the possible number of pounds of hamburgers and of hot dogs he can purchase is 3x + 2y ≤ 60.
We have,
Let x be the number of pounds of hamburgers that Andrew purchases, and let y be the number of pounds of hot dogs that he purchases.
The cost of x pounds of hamburgers is 3x dollars, and the cost of y pounds of hot dogs is 2y dollars.
According to the problem, Andrew has budgeted a maximum of $60 for hamburgers and hot dogs.
Therefore, we can write the following inequality:
3x + 2y ≤ 60
This inequality describes the possible combinations of x and y that Andrew can purchase, such that the total cost of hamburgers and hot dogs does not exceed his budget of $60.
Thus,
The inequality that describes the the possible number of pounds of hamburgers and of hot dogs he can purchase is 3x + 2y ≤ 60.
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897100 rounded to the nearest ten thousand/5756492/ec680fa8?utm_source=registration
what is length of DE
i need help to evaluate this p + (-q) - 2 where p = -3 and q =5
What number is 2 hundred 15 tens and 6 one
URGENT
The depth of water in the port at hinchinbrook is given by: d(t)= 2.6 sin (Pi over 6 t) + 13.1, where d is in meters and t is the number of hours since high tide.
Use the model to determine how many hours are there between high tides.
If high tide was at midnight, draw a graph to determine during which hours should it be safe for the boats to be in the port and between which hours they would have to stay away from the port. Justify answers mathematically
evaluate the expression 4(2x + 3) + 2(x + 1)-7
Juan's baseball card collection was worth 800$. Over the last 5 years,thw collection decreased $300 in value. What integer representa the average decrease in value each year.
Final answer:
The average yearly decrease in the value of Juan's baseball card collection, which decreased by $300 over 5 years, is $60. This integer represents the yearly reduction in value.
Explanation:
Juan's baseball card collection was worth $800. Over the last 5 years, the collection decreased by $300 in value. To find the average decrease in value each year, we can use the formula: Average decrease per year = Total decrease / Number of years.
Given that the total decrease is $300 and the time period is 5 years, the calculation would be:
Average decrease per year = $300 / 5 = $60.
Therefore, the integer that represents the average decrease in value each year for Juan's baseball card collection is $60.
A piece of land is to be fenced and subdivided as shown to that each rectangle has the same dimensions. Express the total amount of fencing needed as an algebraic expression in x. Find the total amount of fencing.
A sample of n = 8 scores has ss = 50. if these same scores were a population, then the ss value for the population would be ____.
Answer:
5.69999
Step-by-step explanation:
What is a number greater than 1,000 whose prime factorization contains 1 prime number that does not repeat, 1 prime number that repeats three times, and 1 prime number that repeats twice
What is the range of f(x) = 4x?
Answer:
D. All positive real numbers
Step-by-step explanation:
The range of a function f(x) are all the possibles values that f(x) can take. So in the function of the question it doesn't matter what value takes x, f(x) is always going to be a positive number. For example:
f(0)=[tex]4^{0}[/tex]=1
f(-1)=[tex]4^{-1}[/tex]=1/4
f(2)=[tex]4^{2}[/tex]=16
Then, the range of f(x) is all positive real numbers.
Find the domain of each function. (enter your answers using interval notation.) (a) f(x) = 2 4 + ex
The sum of three numbers is 105 . The third number is 3 times the first. The second number is 5 more than the first. What are the numbers?
how can you use absolute value to represent a negative number in a real world situation
Solve your formula from problem 12 for m. Then find the taxi driver’s hourly rate of his pickup rate is $2 and he charges $19.50 for a 7 - mile trip
Answer: Cost per mile m = $4.78.
Step-by-step explanation:
Since we have given that
Pick up rate = $2
Charges for a 7 mile trip = $19.50
Charges for a mile trip would be
[tex]\dfrac{19.50}{7}\\\\=2.78[/tex]
So, amount of taxi's drivers is given by
[tex]\$2.78+\$2\\\\=\$4.78[/tex]
Hence, cost per mile m = $4.78.
What is the expression for the calculation double 5 and then multiply by 3?
Write forty and eight tenths as a decimal
Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice altogether
What is the retail price of a couch at a furniture store that has a wholesale price of $115 and is marked up by 75 percent? $86.25 $190.00 $201.25 $316.25
A percentage is a way to describe a part of a whole. The retail price of a couch at a furniture store that has a wholesale price of $115 and is marked up by 75% is $201.25.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that the wholesale price of the couch at a furniture store is $115. Now, as the retail price is marked up by 75%, therefore, the new price of the couch can be written as,
The new price of the couch = 175% of the wholesale price
= 1.75 × $115
= $201.25
Hence, the retail price of a couch at a furniture store that has a wholesale price of $115 and is marked up by 75% is $201.25.
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What is the fourth term in the arithmetic sequence 13,10,7
The fourth term in the arithmetic sequence 13, 10, 7 is 4.
Explanation:The arithmetic sequence 13, 10, 7 has a common difference of -3. To find the fourth term, we can start with the first term and keep subtracting the common difference. So, 13 - 3 = 10, 10 - 3 = 7, and 7 - 3 = 4. Therefore, the fourth term in the arithmetic sequence 13, 10, 7 is 4.
subtracting 3 from the product of 6 and a number results in the number added to 52. how would i write this out
Maria wrote the equation of a line that has a slope of 4/3and passes through point (3, 5). Which statement is true?
Answer:
B
Step-by-step explanation:
The slope intercept equation is [tex]y=\frac{4}{3}x+1[/tex] is true statement. Option C is correct.
From the given information the slope of the line is 4/3 and it is passing through point (3, 5).
Now, determine the equation of line in slope intercept form.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
To find the equation, first find the y intercept by considering the point values (3, 5).
[tex]5 = \frac{4}{3}+b[/tex]
[tex]5=4+b[/tex]
[tex]b=1[/tex]
Now plug in the values of slope and y intercept in slope intercept form:
[tex]y=\frac{4}{3}x+1[/tex]
Hence, Option C is correct, he equation of the line is [tex]y=\frac{4}{3}x+1.[/tex]
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The complete question is given in the attachment.
In the parabola y = (x + 1)2 + 2, what is the vertex?
The vertex form of a quadratic equation is expressed as y = a(x - h)^2 + k. The vertex of the parabola is (-1, 2)
Vertex form of an equationThe vertex form of a quadratic equation is expressed as:
y = a(x - h)^2 + k
where (h, k) is the vertex of the equation
Given the equation of the parabola as y = (x - 1)^2 + 2, On comparing;
h = -1
k =2
Hence the vertex of the parabola is (-1, 2)
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If y = 8 when x = 3, determine y when x = 45 (write an equation)
Which of the various ways of orienting the definitional triangle must be used to resolve n⃗ into components in the tilted coordinate system shown? (in the figures, the hypotenuse is blue (long dashes), the side adjacent to θ is red (short dashes), and the side opposite is yellow (solid).)?