In her work, Maya misidentified the associative property as the identity property in step 2 and the commutative property in step 4.
Explanation:The question pertains to the simplification of the given expression: (5.2 − 4.5) − 5.5 + 4.8. The error lies in Maya's interpretation of the mathematical properties used in the simplification process. In Step 2, she has referred to the rearrangement of minus signs as the result of the 'identity property'. However, this should be the 'associative property' which allows the grouping of numbers to be changed. In Step 4, she refers to her re-ordering of the addition and subtraction as the 'commutative property'. However, it should be 'associative property' as it allows changing of grouping but the order within groups must be maintained.
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zachary purchased a computer for 1800 on a payment plan. three months after he purchased the computer, his balance was 1350. five months after he purchased the computer, his balance was 1050. what is an equation that models the balance b after m months
The equation that models the balance b after m months is b = 1800 - 150m
Initial cost = 1800
Difference in balance = 1350 - 1050 = 300
Number of months used = 5 months - 3 months = 2 months
Therefore, the equation that models the balance b after m months will be:
b = 1800 - (300/2)m
b = 1800 - 150m
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a mathematical term that does not include an equal or inequality sign is called an
Can someone please help me with this? I will appreciate it
Claudia is reading a book that has 360 pages. she read some book last week. She plans to read 46 pages today when she does she will be 4/5 of the qay through the book. How many pages did she read last week?
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x/3 >-1 graph and check solutions
[tex]\dfrac{x}{3} > -1\ \ \ \ |\cdot3\\\\x > -3\to x\in(-3;\ \infty)[/tex]
Jeff left 13% tip at a restaurant where the bill was $29.62. How much did Jeff leave as a tip?
Final answer:
To calculate Jeff's tip, multiply 13% as a decimal (0.13) by the bill amount of $29.62, which equals a tip of $3.85.
Explanation:
To calculate how much Jeff left as a tip at the restaurant, we need to find 13% of his bill total, which was $29.62. To do this, convert the percentage to a decimal by dividing by 100 (which makes 13% become 0.13) and multiply that by the bill amount.
So, the calculation will be:
0.13 * $29.62
When you perform this calculation:
$3.85 (rounded to the nearest cent)
Jeff left a $3.85 tip at the restaurant.
4y−2(3/2y−5) simplify
A water desalination plant can produce 2*10^6 gallons of water in one day. How many gallons can it produce in 79 days?
Write your answer in scientific notation.
The water desalination plant can produce 1.58 x 10^8 gallons of water in 79 days, expressed in scientific notation.
To calculate how many gallons of water a desalination plant can produce in 79 days, we will multiply the daily production capacity by the number of days. The plant's daily production capacity is given as 2 x 106 gallons. So, for 79 days, the calculation would be:
(2 x 106 gallons/day) x 79 days = 1.58 x 108 gallons
Expressed in scientific notation, the plant can produce 1.58 x 108 gallons of water in 79 days.
65 in. =__ft.
A. 6 5/12 ft.
B. 12 ft.
C. 5 5/12 ft.
D. 780 ft
Danielle works as a cashier in a bookstore she works 35 hours a week and earns $11 an hour each week Daniella spends $300 answer saves the rest . Danielle estimates that she earns about $20000 per year is this estimate accurate? explain
Danielle's estimate of earning about $20,000 per year is accurate, as the calculation based on her hourly wage and weekly hours worked gives an actual annual income of $20,020.
Danielle's estimate of earning about $20,000 per year is accurate based on her hourly wage and weekly hours worked. To assess the accuracy of her estimate, we need to calculate her actual annual income.
Danielle earns $11 per hour and works 35 hours a week. Therefore, her weekly earnings are:
35 hours/week × $11/hour = $385/week.
As there are typically 52 weeks in a year, her estimated annual income would be:
52 weeks/year × $385/week = $20,020/year.
This calculation shows that Danielle's estimate of making about $20,000 per year is indeed accurate.
what does a negative y-intercept mean for real world application?
Final answer:
A negative y-intercept in a real-world context indicates that the system or condition being measured starts below the baseline or has a deficit to begin with. It can represent an initial loss in economics, such as starting with debt or needing initial investment. The slope of the line is critical to understanding how changes in one variable affect another.
Explanation:
A negative y-intercept in a real-world application can have various implications depending on the context. In many scientific experiments, the y-intercept represents the baseline level of the system without any experimental conditions applied. If the y-intercept is negative, this might indicate that in the absence of a certain factor (represented by the x-variable), the system has a deficit or a reduction in the measured quantity. For instance, if we are plotting a graph of growth over time, a negative y-intercept could imply that there was an initial debt or loss before measurements began.
When it comes to economics and data models, a negative y-intercept on a graph could represent a starting deficit. For example, a company might have initial losses (negative y-intercept) that it seeks to overcome as production (x-variable) increases. Supply and demand models, cost projections, and similar economic graphs can also have negative y-intercepts indicating starting positions below zero on the graph—such as starting with a debt or having to invest before seeing any return.
The y-intercept and the slope (m-term) together specify a particular line on a graph that can offer a reasonable approximation of real-world data. Economists find the slope particularly useful as it shows the relationship between two variables, like how a change in price affects the quantity supplied.
what is the range of 34, 56, 13, 98, 75
Answer:
Range = 85
Step-by-step explanation:
The formula for range of a data set is
Range = Maximum value - Minimum value
The given data set is
34, 56, 13, 98, 75
In this data set we have,
Maximum value = 98
Minimum value = 13
The range of given data set is
Range = 98 - 13
Range = 85
Therefore, the range of the data is 85.
Classify -2x4 - x3 + 8x2= 12 by degree.
Question 12 options:
cubic
quadratic
quartic
quintic
The solution is Option C.
The equation A = -2x⁴ - x³ + 8x² = 12 is a quartic equation as the degree of the equation is 4
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
-2x⁴ - x³ + 8x² = 12 be equation (1)
On simplifying the equation , we get
Adding 2x⁴ + x³ on both sides of the equation , we get
2x⁴ + x³ + 12 = 8x²
Subtracting 8x² on both sides of the equation , we get
2x⁴ + x³ - 8x² + 12 = 0 be equation (2)
Now , the highest degree of the variable x in the equation is x⁴ which is 4
Therefore , the equation is quartic
Hence , the equation is 2x⁴ + x³ - 8x² + 12 = 0
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in triangle abc,angle a=3x+1,angle b=4x-17,and angle c=5x-20.what type of triangle is angle abc
The sum of the three internal angles in a triangle is equal to 180 degrees.
a = 55°
b = 55°
c = 70°
The triangle abc is an acute isosceles triangle.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three internal angles is equal to 180 degrees.
We have,
Three angles of the triangle:
a = 3x + 1
b = 4x - 17
c = 5x - 20
The sum of the three angles of a triangle is 180 degrees.
a + b + c = 180
3x + 1 + 4x - 17 + 5x - 20 = 180
12x - -36 = 180
12x = 180 + 36
12x = 216
x = 216/12
x = 18
Now,
The angles are :
a = 3 x 18 + 1 = 54 + 1 = 55
b = 4 x 18 - 17 = 72 - 17 = 55
c = 5 x 18 - 20 = 90 - 20 = 70
We see that all their internal angles are acute angles.
This is an acute isosceles triangle.
Thus,
The triangle abc is an acute isosceles triangle.
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Please help asap! Number 2 , picture is included! (10 points)
Explain whether or not you think the relationship is linear or not.
The pond in Tom’s backyard holds 50 gallons of water and recedes at a rate of 5 gallons per day.
the soccer field at Mario's school has an area of 6,000 square meters. how can mario show the area as a whole number multiplied by a power of 10?
Answer: [tex]6\times10^3[/tex] square meters.
Step-by-step explanation:
Given : The soccer field at Mario's school has an area of 6,000 square meters.
Here, 6,000 can be written as [tex]6\times1,000[/tex]
And [tex]1000=10\times10\times10=10^3[/tex] [using exponents]
Then, 6,000 can be written in the form of a whole number multiplied by a power of 10 as [tex]6,000=6\times10^3[/tex]
Hence, Maria can show the area as [tex]6\times10^3[/tex] square meters. .
Convert: 2°C to °F (to the nearest tenth).
A used electronics store pays $30 for each cell phone, spends $20 refurbishing the phone, and sells the refurbished phone to a customer for $115.
a. Write an expression in simplest form that represents the company's earnings (in dollars) from buying, processing, and selling cell phones. Use x to represent the number of cell phones they sell.
An expression is ([answer]) dollars.
Which of the following is an equivalent statement?
CD overbar is similar to XY overbar
CD overbar is congruent to XY overbar
CD overbar equals XY overbar
CD overbar is an element of XY overbar
Answer:
3
Step-by-step explanation:
Which is bigger? 0.5 or 0.2
A cube has a volume of 216 cubic centimeters. What can be concluded about this cube?
volume = 216
side = cubic root(216)
the length of a side = 6 centimeters
Jason works at least 5 hours but not more than 10. He earns $15.30 per hour. The function f (t) = 15.3t represents the money he earns for working t hours. What is the practical range? Show all your work.
1. Correctly determine the minimum and maximum money earned.
2. Correctly identify the practical range as inclusive or exclusive.
3. Correctly state the practical range.
1. The minimum number of hours is 5 hours, so the minimum money earned is:
minimum money = 15.30 * 5 = $76.50
The maximum number of hours is 10 hours, so the maximum money earned is:
maximum money = 15.30 * 10 = $153
2. Since the words “at least” and “not more than” are used, hence this is inclusive.
3. The practical range is:
$76.50 ≤ f(t) ≤ $153
Answer:
$76.50 ≤ f(t) ≤ $153
Step-by-step explanation:
List factor pairs of 56
The coordinates of the vertices of ΔXYZ are (4, –1), (2, –4),
and (7, –4).
The coordinates of image ΔXʹYʹZʹ are (−4, −1), (−2, −4), and (−7, −4).
This transformation can be expressed as (x, y) ⟶ (−x, y).
Is the orientation of ΔXYZ the same as the orientation of ΔXʹYʹZʹ?
Why or why not?
Please help I dont know what to do!!!
#1 x÷4=3.5÷28
#2 3/5 + 4/5x +7/10x + 1 1/2 = 5 3/5
Thank you so much guys!!!!!!!!
can a quadrilateral have 4 obtuse angles
A quadrilateral cannot have 4 obtuse angles
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
A quadrilateral
By definition, the sum of angles in a quadrilateral is 360
And an obtuse angle is greater than 90
So, we have
Sum = 4 * greater than 90
Evaluate
Sum = greater than 360
This means that a quadrilateral cannot have 4 obtuse angles
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What is −412√+75√ in simplest radical form?
Step-by-step explanation: Given radical expression 4√12 + √75.
Let us simplify each of the radical separately first.
√12 = √(2×2×3) = 2√3
Therefore, 4√12 = 4 × 2√3 = 8√3.
√75 = √(3×5×5) = 5√3
Therefore 4√12 + √75 => 8√3 + 5√3.
Adding like radicals, we get
8√3 + 5√3 = 13√3.
Therefore, 4√12 + √75 = 13√3.