Answer:
Proving that the limit of the equation 10 - 2x as x approaches -3 is 16 involves using the definition of a limit.
Here's how you would approach it:
Let epsilon be a small positive number. We want to find a value of delta such that if x is within a distance of delta from -3, then 10 - 2x is within a distance of epsilon from 16.
So, we start with:
|10 - 2x - 16| < epsilon
Simplifying,
|-2x - 6| < epsilon
And using the reverse triangle inequality,
|2x + 6| > ||2x| - |6||
Now, we can choose a value for delta such that if x is within delta of -3, then |2x + 6| is within delta + 6 of |-6| = 6.
So,
||2x| - |6|| < epsilon
and therefore:
|2x - 6| < epsilon
Choosing delta = epsilon/2, we can prove that:
0 < |x + 3| < delta -> |2x - 6| < epsilon
Therefore, we have proved that the limit of 10 - 2x as x approaches -3 is 16 using the definition of a limit.
Step-by-step explanation:
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Which is the best deal over 5 years? Investing at 7.87% compounded semi annually, 7.8% compounded quarterly, or 7.72% compounded every minute?
The best deal over 5 years would be investing at 7.8% compounded quarterly.
Although the interest rates of 7.87% compounded semi-annually and 7.72% compounded every minute may appear slightly higher, the frequency of compounding plays a significant role in determining the overall return.
Compounding more frequently leads to a higher effective annual rate. In this case, compounding quarterly provides a greater compounding frequency than semi-annual or minute-by-minute compounding, resulting in higher returns over time.
When interest is compounded quarterly, the compounding occurs four times a year, whereas semi-annual compounding only occurs twice a year. Compounding every minute may seem more frequent, but the actual effect on the return is minimal since there are a large number of minutes in a year.
Therefore, the 7.8% compounded quarterly is the best deal over 5 years as it offers a higher effective annual rate compared to the other options.
In summary, investing at 7.8% compounded quarterly is the most advantageous choice over a 5-year period. The frequency of compounding plays a crucial role in determining the overall return, and compounding quarterly provides a greater compounding frequency compared to semi-annual or minute-by-minute compounding.
It is essential to consider both the interest rate and the compounding frequency when evaluating investment options to make an informed decision.
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When five times a number is decreased by 8, the result is 37. What is the number?
Answer:
5n - 8 = 37
5n = 45
n = 9
The number is 9.
TIME REMAINING
01:48:30
On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2).
Which statement best explains the relationship between lines FG and HJ?
They are perpendicular because their slopes are equal.
They are perpendicular because their slopes are negative reciprocals.
They are not perpendicular because their slopes are equal.
They are not perpendicular because their slopes are not negative reciprocals.
Answer:
Its b i bealive
Step-by-step explanation:
If the expenditure of a person is 75% of his income and his income tax which is 13% of his income is $585. What is his expenditure?
The person's expenditure is $1,755. (30 words)
To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.
Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)
In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.
Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.
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taber invested money in an account where interest is compounded every year. he made no withdrawals or deposits. the function A(t) = 525(1+0.05) represents the amount of money in the account after t years. how much money did taber originally invest?
Geometric mean and Harmonic mean for the values 3, -11, 0, 63, -14, 100 are
Select one:
a. 0 and 0
b. 3 and -3
c. 3 and 0
d. Impossible
e. 0 and 3
Note: Answer C is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
The correct answer is an option (d): Impossible.
Both the geometric mean and harmonic mean require positive values. However, in the given set of values, we have negative values (-11 and -14), which makes it impossible to calculate the geometric mean and harmonic mean. Therefore, the correct answer is that it is impossible to calculate the geometric mean and harmonic mean for the given values.
Determine the equation of the circle graphed below 100pts
Answer:
[tex](x +5)^2+(y-1)^2=25[/tex]
Step-by-step explanation:
To determine the equation of the graphed circle, we need to find the coordinates of its center and the length of its radius.
The center of the circle is a single point that lies at an equal distance from all points on the circumference of the circle.
From inspection of the graphed circle, we can see that its domain is [-10, 0] and its range is [-4, 6]. The x-coordinate of the center is the midpoint of the domain, and the y-coordinate of the center is the midpoint of the range.
[tex]x_{\sf center}=\dfrac{-10+0}{2}=-5[/tex]
[tex]y_{\sf center}=\dfrac{-4+6}{2}=1[/tex]
Therefore, the center of the circle is (-5, 1).
The radius of the circle is the distance from the center to all points on the circumference of the circle. Therefore, to calculate the length of the radius, find the distance between x-coordinate of the center and one of the endpoints of the domain.
[tex]r=0-(-5)=5[/tex]
Therefore, the radius of the circle is r = 5.
To determine the equation of the circle, substitute the center and radius into the standard formula.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
As h = -5, k = 1 and r = 5, then:
[tex](x - (-5)^2+(y-1)^2=5^2[/tex]
[tex](x +5)^2+(y-1)^2=25[/tex]
Therefore, the equation of the graphed circle is:
[tex]\boxed{(x +5)^2+(y-1)^2=25}[/tex]
7. What is the slope of a line that is perpendicular to the line represented by the equation y=-2/5x+4/5
5
5/4
2/5
5/2
Answer: the correct answer is 5/2
Step-by-step explanation:
To find the slope of a line perpendicular to a given line, we can use the property that the product of the slopes of two perpendicular lines is equal to -1.
The given line has an equation of y = -2/5x + 4/5.
The slope of this line can be determined by comparing it to the slope-intercept form (y = mx + b), where "m" represents the slope. In this case, the slope of the given line is -2/5.
To find the slope of the line perpendicular to this line, we take the negative reciprocal of the given slope. The negative reciprocal of -2/5 is 5/2.
Write the numeral in base ten. 7,001eight
The numeral 7,001 eight is equal to 3585 in base ten.
To convert the numeral 7,001 in base eight to base ten, we need to multiply each digit by the corresponding power of eight and sum them up.
Starting from the rightmost digit, we have:
[tex]1 * 8^0 = 1\\0 * 8^1 = 0\\0 * 8^2 = 0\\7 * 8^3 = 3584[/tex]
Adding these values together, we get:
1 + 0 + 0 + 3584 = 3585
Therefore, the numeral 7,001eight is equal to 3585 in base ten.
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Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
Answer:
0
Step-by-step explanation:
Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
The equation y-20000(0.95)* represents the purchasing power of $20,000, with an inflation rate of five percent. X represents the
number of years
Use the equation to predict the purchasing power in five years.
Round to the nearest dollar.
$15,476
$17,652
$18,523
$19,500
The purchasing power in five years will be $15,476.
To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.
Plugging in X = 5, we have:
[tex]y = 20000(0.95)^5[/tex]
Calculating the expression, we find:
[tex]y ≈ 20000(0.774)[/tex]
Simplifying further, we get:
[tex]y ≈ 15480[/tex]
Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.
Therefore, the closest option to the predicted purchasing power in five years is $15,476.
So the correct answer is:
$15,476.
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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.
To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.
The equation provided is: y = 20000(0.95)^x
Substituting x = 5 into the equation, we have:
y = 20000(0.95)⁵
Now, let's calculate the result:
y ≈ 20000(0.95)⁵
≈ 20000(0.774)
y ≈ 20000(0.774)
≈ 15,480
This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.
By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.
The example equation is: y = 20000(0.95)^x
When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵
Let's now compute the outcome:
y ≈ 20000(0.95)⁵ ≈ 20000(0.774)
y ≈ 20000(0.774) ≈ 15,480
This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.
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NO LINKS!! URGENT HELP PLEASE!!
Please help with 21
Answer:
34.45%
Step-by-step explanation:
A tree diagram shows all possible outcomes of two or more events.
Each branch is a possible outcome and is labelled with the probability of that outcome.
Draw lines (branches) to represent the first event (main meal). Write the outcomes on the ends of the branches: "sandwich" and "slice of pizza". Write the given probabilities on the branches.
Draw the next set of branches to represent the second event (side). Write the outcomes on the ends of the branches: "chips" and "veggies with hummus". Write the given probabilities on the branches.
We assume that the events in this scenario are independent, so the probability of the first event happening has no impact on the probability of the second event or the third event happening. Therefore, to find the probability of each combination of events, multiply along the branches.
Sandwich and chips = 35% × 47% = 16.45%
Sandwich and veggies with hummus = 35% × 53% = 18.55%
Slice of pizza and chips = 65% × 47% = 30.55%
Slice of pizza and veggies with hummus = 65% × 53% = 34.45%
Therefore, the probability that Sophie selects a slice of pizza and veggies is 34.45%.
The probability that Sophie selects a slice of pizza and veggies is 34.45%.
Calculating the probability of pizza and veggiesFrom the question, we have the following parameters that can be used in our computation:
Sandwich = 35%Chips = 47%Veggies with hummus = 53%Pizza = 65%The probability of pizza and veggies is calculated as
P = Pizza * Veggies
Substitute the known values in the above equation, so, we have the following representation
P = 65% * 53%
Evaluate
P = 34.45%
Hence, the probability that Sophie selects a slice of pizza and veggies is 34.45%.
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The graph below shows the solution to which system of inequalities?
O A. x< 1 and yz x
OB. ys 1 and y> x
O C. x≤ 1 and y> x
OD. y< 1 and yz x
6
The system of inequalities shown in this problem is defined as follows:
d) y < 1 and y ≥ x.
How to obtain the system of inequalities?The line in the image has an intercept of zero and slope of 1, hence it is given as follows:
y = x.
Points above the solid line are plotted, hence the first condition is:
y ≥ x.
The upper bound, represented by the dashed horizontal line, is y = 1, hence the second condition is:
y < 1.
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A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.
What is the probability that all four cards are clubs?
13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026
13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023
1/4 because 1/4 of the cards are clubs
The probability that all four cards are clubs is approximately 0.0026. Option A.
To understand why, let's break down the calculation. In a well-shuffled deck, there are 13 clubs out of 52 cards.
When dealing the first card, there are 13 clubs out of the total 52 cards, so the probability of getting a club on the first draw is 13/52.
For the second card, after the first club has been removed from the deck, there are now 12 clubs left out of the remaining 51 cards. Therefore, the probability of getting a club on the second draw is 12/51.
Similarly, for the third card, after two clubs have been removed, there are 11 clubs left out of the remaining 50 cards. The probability of drawing a club on the third draw is 11/50.
Finally, for the fourth card, after three clubs have been removed, there are 10 clubs left out of the remaining 49 cards. The probability of drawing a club on the fourth draw is 10/49.
To find the probability of all four cards being clubs, we multiply the probabilities of each individual draw:
(13/52) * (12/51) * (11/50) * (10/49) ≈ 0.0026.
This calculation takes into account the fact that the deck is being dealt without replacement, meaning that the number of available clubs decreases with each draw.
The third option, 1/4, is incorrect because it assumes that each card dealt is independent and has an equal probability of being a club. However, as cards are drawn without replacement, the probability changes with each draw. So Option A is correct.
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Note the complete question is
A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.
What is the probability that all four cards are clubs?
A.) 13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026
B.) 13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023
C.) 1/4 because 1/4 of the cards are clubs
The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X - N b. What is the median giraffe height? ft. c. What is the Z-score for a giraffe that is 22 foot tall?
d. What is the probability that a randomly selected giraffe will be shorter than 18.9 feet tal?
e. What is the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall?
f. The 80th percentile for the height of giraffes is ft.
a. The distribution of X is a normal distribution.
b. The median giraffe height is also 19 feet.
c. The Z-score for a giraffe that is 22 foot tall is 3.
d. The probability that a randomly selected giraffe will be shorter than 18.9 feet tall is less than -0.1.
f. The 80th percentile represents the value below which 80% of the data falls.
a. The distribution of X is a normal distribution (or Gaussian distribution) with a mean of 19 feet and a standard deviation of 1 foot. This can be denoted as X ~ N(19, 1).
b. The median of a normal distribution is equal to its mean.
c. To find the Z-score for a giraffe that is 22 feet tall, we can use the formula: Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (22 - 19) / 1 = 3.
d. To find the probability that a randomly selected giraffe will be shorter than 18.9 feet tall, we need to calculate the area under the normal curve to the left of 18.9. This can be done using the Z-score and a standard normal distribution table or a calculator.
Alternatively, we can use the Z-score formula from the previous question. The Z-score for 18.9 feet can be calculated as Z = (18.9 - 19) / 1 = -0.1. We can then look up the corresponding probability in the standard normal distribution table or use a calculator to find the probability that Z is less than -0.1.
e. To find the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall, we need to calculate the area under the normal curve between these two values.
Again, we can use the Z-score formula to standardize the values and then find the corresponding probabilities using a standard normal distribution table or a calculator.
f. To find the height at the 80th percentile, we can use the standard normal distribution table or a calculator to find the Z-score that corresponds to the 80th percentile.
Once we have the Z-score, we can use the formula Z = (X - μ) / σ to solve for X. Rearranging the formula, we have X = Z * σ + μ. Plugging in the values for Z (obtained from the percentile) and μ (mean) and σ (standard deviation), we can calculate the height at the 80th percentile.
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NO LINKS!! URGENT HELP PLEASE!!
Find the value of x
Answer:
x = 4
Step-by-step explanation:
You want the value of x in the figure of a circle with intersecting secants.
Secant relationThe product of lengths from the near and far circle intercepts to the point where the secants intersect is the same for both secants:
6(6+10) = 8(8+x)
6·16 = 8·(8+x)
12 = 8 +x . . . . . . . divide by 8
4 = x . . . . . . . . . . subtract 8
The length x is 4 units.
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which f(x) function is this?
Answer:
[tex]f(x) = - 3 {x}^{2} - 6x - 1[/tex]
Reynold’s company has a product with fixed costs of $334,000, a unit selling price of $22, and unit variable costs of $19. The break-even sales (units) if the variable costs are decreased by $4 is
The break-even sales (units) when the variable costs are decreased by $4 is approximately 47,714 units.
To find the break-even sales (units) when the variable costs are decreased by $4, we need to calculate the new unit variable costs and then use the break-even formula.
Fixed costs (F) = $334,000
Unit selling price (P) = $22
Unit variable costs (V) = $19
Change in unit variable costs = $4
New unit variable costs (V') = V - Change in unit variable costs
= $19 - $4
= $15
Now, let's calculate the break-even sales (units) using the formula:
Break-even sales (units) = Fixed costs / (Unit selling price - Unit variable costs)
Break-even sales (units) = $334,000 / ($22 - $15)
= $334,000 / $7
= 47,714.29
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15) Find one positive and one negative coterminal angle to 87°
There are 40 black marbles, 20 blue marbles, and 4 red marbles in a jar.
а. What is the probability of selecting one red marble?
b. What is the probability of selecting one black marble?
c. What is the probability of selecting one blue marble?
d. Which has the highest probability of being selected?
e. Which has the lowest probability of being selected?
Step-by-step explanation:
a. 4/64= 1/16 for red marble
b. 40/64= 5/8 black marbles
c. 20/64= 5/16 blue marble
d. highest: black marble
e. lowest: red marble
Solve b + 6 < 14.
Write your answer in set builder notation
Two mechanics worked on a car. The first mechanic charged $75
per hour, and the second mechanic charged $95
per hour. The mechanics worked for a combined total of 20
hours, and together they charged a total of $1800
. How long did each mechanic work?
The first mechanic worked for 12 hours, and the second mechanic worked for 8 hours.
Let's assume the first mechanic worked for x hours. Since the first mechanic charged $75 per hour, their earnings can be represented as 75x dollars.
Similarly, the second mechanic worked for (20 - x) hours, and at a rate of $95 per hour, their earnings can be represented as 95(20 - x) dollars.
According to the problem, the combined earnings of both mechanics are $1800. Therefore, we can write the equation:
75x + 95(20 - x) = 1800
Simplifying this equation, we get:
75x + 1900 - 95x = 1800
-20x = -100
x = 5
Substituting x back into the equation, we find that the first mechanic worked for 5 hours, and the second mechanic worked for (20 - 5) = 15 hours.
Therefore, the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours.
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The linear inequality represented by the graph is y < 3x + 2. Option A.
To determine the linear inequality represented by the graph, let's analyze the given information and the slope-intercept form of a linear equation (y = mx + b), where m represents the slope and b represents the y-intercept.
We are given two points on the line: (-3, -7) and (0, 2). Using these points, we can calculate the slope (m) as follows:
m = (y2 - y1) / (x2 - x1)
= (2 - (-7)) / (0 - (-3))
= 9 / 3
= 3
Therefore, the slope of the line is 3.
Next, we can substitute the slope and one of the given points into the slope-intercept form to find the y-intercept (b). Let's use the point (0, 2):
y = mx + b
2 = 3(0) + b
2 = b
So, the y-intercept (b) is 2.
Now we have the equation of the line: y = 3x + 2.
The shaded region is to the left of the line. To express this region as an inequality, we need to find the inequality symbol. Since everything to the left of the line is shaded, we need the inequality to represent values less than the line.
Therefore, the correct inequality is y < 3x + 2.
Hence, the linear inequality represented by the graph is y < 3x + 2. So Option A is correct.
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Note the complete question is
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
A.) y < 3x + 2
B.) y > 3x + 2
C.) y < 1/3x + 2
D.) y > 1/3x + 2
A requested task is subject to be reported when:
Answer:
A requested task is subject to be reported when it has been completed according to the instructions provided.
To demonstrate this with chain of thought reasoning:
1. The task requested will have details outlining what needs to be done.
2. To fulfill the request of the task, the instructions outlined must be followed.
3. Once all instructions are met, the task is complete.
4. Completion of the task means it is subject to be reported.
Step-by-step explanation:
Please solve these:
[tex] \frac{7}{2} - (5x + 4) + 2[/tex]
[tex] - 2 = - \frac{1}{4} (x - 3)[/tex]
[tex] \frac{1}{2} (x - 3) + 6[/tex]
Step-by-step explanation:
1. Answer is 2
2. Answer is -3
3. Answer is 4
Answer:
i) -5x + 3/2
ii) x = 11
iii) x + 9/2
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what is the number of births in year 5?
Answer:
Step-by-step explanation:
the image is the question
a) c = 22 feet
b) c = 23
c) c = 24
d) c = 30
The length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."
The Pythagorean theorem, which asserts that given a right triangle, the sum of the squares of the two shorter sides (a and b), is equal to the square of the hypotenuse (c), can be used to determine the length of the triangle's hypotenuse (c).
a = 10 feet
b = 20 feet
Using the Pythagorean theorem, we can calculate c as follows:
c^2 = a^2 + b^2
c^2 = 10^2 + 20^2
c^2 = 100 + 400
c^2 = 500
To find c, we take the square root of both sides:
c = √500
c ≈ 22.36
Rounding the answer to the nearest whole number, we get c ≈ 22.
Therefore, the length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."
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Find the surface area of the regular pyramid shown to the nearest whole number.
to scale.
13 m
6.5-√3 m
9m
For which values is this expression undefined?
Answer:
x=3
Step-by-step explanation:
You can get the answer by substituting the value of x in the equations, your aim is to find a number that will make both equations equal zero.
Select the correct text.
Regina’s teacher recently gave her a homework assignment on solving equations. Since she has been thinking about saving for a new cell phone, she decided to use the assignment as an opportunity to model a savings plan.
She created this equation to model the situation. In it, y represents the total amount saved for the new cell phone, 74 is the amount of money she has now, 40 is the amount of money she saves each month for the phone, and x represents the number of months since she started saving a regular amount:
74 + 40x = y.
She then solved the equation to determine how many months she’d need to save to have enough to purchase the new cell phone. Review her work, and select the error.
Justification
1: given
2: subtraction property of equality
3: simplification
4: multiplication property of equality
5: simplification
6: substitution, y = 834
7: simplification
Step 1: 74 + 40x = y
Step 2: 74 + 40x − 74 = y − 74
Step 3: 40x = y − 74
Step 4:
=
Step 5: x =
Step 6: x =
Step 7: x = 19