Answer:
[tex]16x^2-24x+9[/tex]
Step-by-step explanation:
To find (c circle d)(x), we need to first find d(c(x)) and then simplify.
First, we need to find c(x) and substitute it into d(x), as follows:
d(c(x)) = d(4x - 2) = (4x - 2)^2 + 5(4x - 2)
Expanding the square and simplifying, we get:
d(c(x)) = 16x^2 - 24x + 9
Now, we have (c circle d)(x) = d(c(x)) = 16x^2 - 24x + 9.
Evaluate the expression. −8÷−4 CLEAR CHECK −2 −12 12 2
Evaluate the expression is -10.
How should examples of expressions be evaluated?You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. As 6 + 6 = 12, the variable x in the preceding example is equal to 6. We can replace our variables with their values if we know what they are, then evaluate the expression after doing so.
The division can be done as follows when assessing the phrase 8 4:
−8 ÷ −4 = 2
The expression is thus reduced to:
2 - 12
12 is subtracted from 2 to yield:
-10
Thus, -10 is the correct response.
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add
8/9 + 2/3 + 1/6
A 11/18
B 11/15
C 1 13/18
D 1 2/9
Answer:
Option C. 1 13/18
Step-by-step explanation:
8/9 + 2/3 + 1/6
Taking LCM as 18
8/9 × 2/2 + 2/3 × 6/6 + 1/6 × 3/3
16/18 + 12/18 + 3/18 = 31/18 = 1 13/18
Find an equation of the line that satisfies the given conditions.Through (−9, −11); perpendicular to the line passing through (−6, 1) and (−2, −1)
The equation of the line passing through (9,11) and perpendicular to the line passing through (6,1) and (2,1) is x = 6
Find the slope of the line passing through (6,1) and (2,1):
The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Substituting the given coordinates, we get:
slope = (1 - 1) / (2 - 6) = 0
Therefore, the slope of the line passing through (6,1) and (2,1) is 0.
Find the slope of the line perpendicular to the line passing through (6,1) and (2,1):
The slope of a line perpendicular to a line with slope m is given by:
perpendicular slope = -1/m
Substituting the slope of the line passing through (6,1) and (2,1), we get:
perpendicular slope = -1/0 (which is undefined)
This means that the line perpendicular to the line passing through (6,1) and (2,1) is a vertical line passing through the point (6,1) and (2,1).
Write the equation of the line passing through (9,11) and perpendicular to the line passing through (6,1) and (2,1):
Since the line passing through (6,1) and (2,1) is a horizontal line with equation y = 1, the line perpendicular to it is a vertical line passing through the point (6,1) and (2,1). The equation of a vertical line passing through a point (a,b) is given by:
x = a
Substituting the value of x = 6 (since the vertical line passes through (6,1) and (2,1)), we get:
x = 6
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what is the solution for the following system of equations? -y + 3x = 6 and y = -6x + 12
The answers to the equations y = -6x + 12 and y = -y + 3x = 6 are x = 2 and y = 0, respectively.
What does "system solution" mean?A location that satisfies every equation in a system of linear equations is the system's solution. You can graph a set of linear equations and find their points of intersection, or you can use algebra to figure out the variables.
Using substitution, we may solve by replacing y in the first equation with the second equation:
-(-6x + 12) + 3x = 6
Share the ominous symbol
6x - 12 + 3x = 6
combining similar terms
9x - 12 = 6
Separate the variable and add 12 to both sides to find the value of x:
9x = 18
x = 2
Substitute 2 with x in any equation to find the value of y:
-y + 3(2) = 6.
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density of air lb/ft3
The density of air in lb/ft³ based on the conversion using the formula is 0.08 lb/ft³.
We know that the density of air is 1.29 grams per litre. Now, to perform the conversion, we need to find the relation between grams and pounds and litre and feet.
So, we know that 1 gram is equal to 0.0022 pound and 1 litre is equal to 0.0353 cubic foot.
Therefore, keeping these values in the actual formula for conversion.
Density of air = 1.29 × 0.0022/0.0353
Performing division and multiplication on Right Hand Side of the equation
Density of air = 0.08 lb/ft³
Therefore, the density of air is 0.08 lb/ft³.
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1/4 + 3/8
???????????????????
Answer:
Step-by-step explanation:
5/8
Answer: it equal 5 /8
The price of petrol is increased from R 12.58 per litre to R 13.28per litre Determine the percentage increase in the price
The percentage increase in the price of petrol is approximately 5.56%.
What is percentage?Percentages are used to compare and express parts of a whole, and to express changes or differences in values. For instance, we can use percentages to express:
A discount or a markup in prices
The increase or decrease in a quantity or value
The proportion of a quantity compared to a whole
The probability of an event occurring.
In the given question,
To determine the percentage increase in the price of petrol, we need to calculate the difference between the old price and the new price, divide that by the old price, and then multiply by 100 to convert to a percentage.
The difference between the old price and the new price is:
R 13.28 - R 12.58 = R 0.70
Dividing the difference by the old price:
R 0.70 ÷ R 12.58 ≈ 0.0556
Multiplying by 100 to convert to a percentage:
0.0556 × 100 ≈ 5.56%
Therefore, the percentage increase in the price of petrol is approximately 5.56%.
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find three real-life examples of a continuous variable. which do you think may be normally distributed? why?
Of these three examples, height and weight are more likely to be normally distributed.
What is continuous variable ?
A continuous variable is a type of quantitative variable that can take on any value within a certain range. Continuous variables can be measured to any degree of precision, meaning they can be broken down into smaller and smaller increments.
Three real-life examples of a continuous variable are:
Height: Height is a continuous variable that can take any value within a certain range. It can be measured to any degree of precision, making it a continuous variable.
Time: Time is another continuous variable that can be measured to any degree of precision, from milliseconds to years.
Weight: Weight is also a continuous variable that can take any value within a certain range. It can be measured to any degree of precision, making it a continuous variable.
This is because these variables tend to follow a bell-shaped curve when plotted, with most values clustering around the mean and fewer values appearing further away from the mean. Time, on the other hand, may not be normally distributed because it can have different distributions depending on the situation, such as a bimodal distribution for the time of day people go to sleep or wake up. However, it's important to note that the normal distribution is just one of many possible distributions for continuous variables and may not always be the most appropriate or accurate for real-life situations.
Therefore, Of these three examples, height and weight are more likely to be normally distributed.
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A baker made 36 blueberry muffins on Monday. What percent of the total number of muffins were blueberry if the baker made 90 muffins?
The blueberry muffins made by baker on monday is 40% of the total muffins made by the baker .
What is Percentage ?A quantity or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. In order to determine the percentage of a number, divide it by its sum and then multiply the result by 100. The proportion thus refers to a component per 100. The word percent indicates a percentage of 100. The word "percent" denotes "per 100." The letter "%" stands for it.
Now in the given question,
Total number of muffins baker made = 90
Blueberry Muffins made by baker on monday = 36
Prcentage of blueberry muffins out of total muffins [tex]=\frac{36*100}{90} = 40 %[/tex]
So , the Blueberry Muffins were 40% of the total muffins baker made.
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we want to be rich refer to exercise 52. construct and interpret a 95% confidence interval for the true proportion p of all first-year students at the university who would identify being very well-off as an important personal goal. assume that the conditions for inference are met. explain why the interval in part (a) provides more information than the test in exercise 52.
The 95% confidence interval to estimate the population mean describes a range of values that a person can be 95% sure that it contains the population mean.
A 95% confidence interval for population mean () is an interval on which a person can be 95% confident that the true population mean lies in it.
i.e. The probability that it contains the true population mean is 95%.
i.e. P( Sample mean- margin of error < < Sample mean + margin of error) = 0.95.
Hence , The 95% confidence interval to estimate the population mean describes a range of values that a person can be 95% sure that it contains the population mean.
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50% of the machines at Bud's Suds are washing machines. If there are 10 washing machines, how many machines are at Bud's Suds in all?
If 50% of the machines at Bud's Suds are washing machines and there are 10 washing machines, then the total number of machines is:
10 / 0.5 = 20
So there are 20 machines in total at Bud's Suds.
Rosetta drives 85 kilometres in 1 hour 15 minutes. Work out her average speed in kilometres per hour.
Answer:
68 kilometers per hour
Step-by-step explanation:
Rosetta's average speed is 85 kilometers per hour. This can be determined by dividing the total distance traveled (85 kilometers) by the total time taken (1 hour and 15 minutes, or 1.25 hours). Therefore, 85 kilometers divided by 1.25 hours is equal to 68 kilometers per hour.
Answer: 68 kilometers per hour (look at the image for the explanation)
Step-by-step explanation:
Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.MarketWeekly Gross Revenue($100s)Television Advertising($100s)Newspaper Advertising($100s)Mobile101.351.5Shreveport51.933Jackson74.841.5Birmingham126.24.34.3Little Rock137.83.64Biloxi101.43.52.3New Orleans237.858.4Baton Rouge219.66.95.8(a)Use the data to develop an estimated regression with the amount of television advertising as the independent variable.Let x represent the amount of television advertising.If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)= + xTest for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship?The input in the box below will not be graded, but may be reviewed and considered by your instructor.(b)How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain?If required, round your answer to two decimal places.%(c)Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables.Let x1 represent the amount of television advertising.Let x2 represent the amount of newspaper advertising.If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)= + x1 + x2Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters β0, β1, and β2 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?The input in the box below will not be graded, but may be reviewed and considered by your instructor.(d)How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain?If required, round your answer to two decimal places.%(e)Given the results in part (a) and part (c), what should your next step be? Explain.The input in the box below will not be graded, but may be reviewed and considered by your instructor.(f)What are the managerial implications of these results?The input in the box below will not be graded, but may be reviewed and considered by your instructor.
The results of the regression analysis indicate that television and newspaper advertising are both important in driving weekly gross revenue. This means that the owners of Dixie Showtime can use the results of the regression analysis to make informed decisions about their advertising budgets in order to maximize their weekly gross revenue.
The results of part (a) and part (c) indicate that advertising plays a significant role in the weekly gross revenue of Dixie Showtime Movie Theaters, Inc. The results of the regression analysis indicate that television and newspaper advertising are both important in driving weekly gross revenue. This means that the owners of Dixie Showtime can use the results of the regression analysis to make informed decisions about their advertising budgets in order to maximize their weekly gross revenue. They can allocate their advertising budget based on the amount of impact each form of advertising has on their weekly gross revenue. Additionally, the owners can use the results of the regression analysis to determine the amount of weekly gross revenue they will generate based on their chosen advertising budget.
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it is assumed that approximately 15% of adults in the u.s. are left-handed. consider the probability that among 100 adults selected in the u.s., there are at least 30 who are left-handed. given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? why or why not?
Option C. No, because the 100 adults were selected without replacement, the selections are dependent.
The binomial probability formula assumes that the trials are independent, meaning that the probability of success or failure for each trial remains the same regardless of the outcomes of previous trials. However, in this case, the 100 adults were selected without replacement, so the probability of being left-handed for each selection depends on the outcomes of previous selections. Therefore, the binomial probability formula cannot be used to find the probability in this situation. Instead, the hypergeometric distribution can be used to account for the dependence between selections.
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Complete question:
It is assumed that approximately 15% of adults in the U.S. are left-handed. Consider the probability that among 100 adults selected in the U.S., there are at least 30 who are left-handed. Given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? Why or why not?
A. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.
B. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent.
C. No, because the 100 adults were selected without replacement, the selections are dependent.
D. No, because the probability of being right-handed is greater, x must count the number of right-handed adults.
one face of a cubed-shapped package has an area of 7(5)/(8) square inches.what is the lateral surface area of the package
Therefore, the lateral surface area of the cube is 35/2 square inches.
What is area?In mathematics, area is the measure of the size of a two-dimensional region or surface. It is usually measured in square units, such as square meters, square feet, or square centimeters. The area of a shape or surface is determined by the amount of space it covers in a plane or on a flat surface. Areas are commonly used to describe the size of objects or spaces in a variety of contexts, including geometry, architecture, engineering, and physics. They are also used in everyday life, such as calculating the amount of carpet needed to cover a floor or the amount of paint needed to cover a wall.
Here,
Since the package is a cube, all of its faces are identical squares. Therefore, the area of one face is equal to the length of one side squared.
Let x be the length of one side of the cube. Then we have:
x² = 7(5)/8
Solving for x, we get:
x = √(7(5)/8) = sqrt(35/8)
The lateral surface area of the cube is the sum of the areas of the four non-base faces. Since the cube has six faces in total, the lateral surface area is:
Lateral surface area = 4 * (side length)²
Lateral surface area = 4 * x²
Lateral surface area = 4 * (√(35/8))²
Lateral surface area = 4 * 35/8
Lateral surface area = 35/2
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y=100(0.5)^x growth or decay
Answer: Decay
Step-by-step explanation:
Working out is required please. 25 points!
Answer:
46.8 cm²
Step-by-step explanation:
3.9 x 6 = 23.4 (We are multiplying by 6 because there are 6 tiles)
23.4 x 2 = 46.8 (We are multiplying by 2 because when Suki is adding more tiles, she makes a hexagon double the side lengths.)
Help! 50 points, Sorry not the best picture…
The completed table in the question used to prove the proportional BD/AB = BC/(AB + AC), when AD is an angle bisector can be presented as follows;
Statement [tex]{}[/tex] Reason
1. EB ║ AD, AD bisects ∠ABC [tex]{}[/tex] 1. Given
2. ∠BEC = ∠DAC [tex]{}[/tex] 2. Corresponding angles theorem
3. ∠C = ∠C [tex]{}[/tex] 3. Reflexive property of congruence
4. ΔBEC = ΔDAC [tex]{}[/tex] 4. AAA similarity postulate
5. DC/AC = BC/EC [tex]{}[/tex] 5. Similar triangles have equivalent ratios
6. EC = EA + AC [tex]{}[/tex] 6. Segment addition postulate
7. DC/AC = BC/(EA + AC)[tex]{}[/tex] [tex]{}[/tex] 7. Similar triangles have equivalent ratios
8. AD/AB = DC/AC [tex]{}[/tex] 8. Triangle angle bisector theorem
9. BD/AB = DC/AC [tex]{}[/tex] 9. Substitution property
10. ∠EBA = ∠DAB [tex]{}[/tex] 10. Alt int. angles theorem
11. ∠DAB = ∠DAC [tex]{}[/tex] 11. Definition of a bisector
12. ∠EBA = ∠BEC [tex]{}[/tex] 12. Alt int. angles theorem
13. ΔEBA is isosceles [tex]{}[/tex] 13. Definition of isosceles triangles
14. CA = AB [tex]{}[/tex] 14. Side length of isosceles
15. BD/AB = BC/EC [tex]{}[/tex] 15. Similar triangles have equal ratios
16. BD/AB = BC/(EA + AC) [tex]{}[/tex] 16. Substitution property
17. EA = AB [tex]{}[/tex] 17. Definition of isosceles triangle ΔEBA
18. BD/AB = BC/(AB + AC) [tex]{}[/tex] 18. Substitution property
What is an angle bisector?An angle bisector is an line that divides an angle into two angles of the same measure.
The details of the some of the reasons useds to prove the specified proportion are presented as follows;
Corresponding angles theorem
The corresponding angles theorem states that the corresponding angles formed between parallel lines and a transversal are congruent
Reflexive property of congruence
The reflexive property of congruence states that a geometric figure, such as an angle is congruent to itself
AA similarity postulate
The AA similarity postulate states that triangles are similar two angles in one triangle are congruent to two angles in the other triangles.
Similar triangles have equivalent ratios
Segment addition postulate
The segment addition postulate states that the point B is located between the points A and C on a segment, only if AC = AB + BC.
Ratios of corresponding sides ar
Triangle angle bisector theorem
The triangle angle bisector theorem states that an angle bisector of a triangle divides the side facing the bisected angle in the ratio of the lengths of the other two sides.
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Can someone solve 8 and 9??? (Will give brainliest!!!)
The amount of curry that would be needed is 1/2
Margerite would need 3 * 4 / 5 to make the batches of cookies
How to solve the fractions8. If Harry is doubling the recipe and the recipe is originally said to be 2/8 of curry we would have
2 * 2/8
= 4/8
= 1/2
9. If one batch of chocolate chips is made with 4/5 cups of chips
In order to make 3 batches, Margerite would have to use 3 * 4 / 5
= 12 / 5
Option C is correct
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Jesse is a full-time college student and is 20 years old. Can he be claimed as a dependent? Txplain.
Answer:
Step-by-step explanation:
yes
NEED HELP SUR TOMORROW!!!!!!!
The image below shows a circle with radius and central angle measurements Find the area of the shaded sector, and the length of the arc defined by the sector.
Answer:
Below
Step-by-step explanation:
The shaded fraction is 160 / 360 ths of the entire area
160/360 * pi (5)^2 = shaded area =~ 35 in^2
Similarly , the arc is 160/360 ths of the entire circumference
160/360 * pi ( 2 * 5) = 13.96 = ~ 14 inches
how to convert mm to nm
The conversion method from milimeter to nanometer is Quantity in nanometer = quantity in milimeter × 10⁶.
In the question, the two short forms mm and nm are representative of milimeter and nanometer. As per the known information, the milimeter represents 1/10³ meters and nanometer represents 1/10⁹ meters. So, we see that the difference between the exponents of 10 is 6 (as 9 - 3 = 6).
Therefore, the conversion of milimeter to nanometer will be through the mentioned formula -
Quantity in nanometer = quantity in milimeter × 10⁶
For instance, the quantity 3 mili meters in nanometer will be calculated as follows.
Quantity in nanometer = 3 × 10⁶ nanometer
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£1=1. 62 usd
How much is £650 in $
How much is £450 in $
if £1=1. 62USD then, £650 is equivalent to $1053 in US dollars and £450 is equivalent to $729 in US dollars.
To convert British pounds to US dollars, we can multiply the pound amount by the exchange rate of pounds to dollars.
£650 in USD:
£1 = $1.62, so we can write:
650 x 1.62/1 = 1053
Therefore, £650 is equivalent to $1053 in US dollars.
£450 in USD:
Using the same method, we can calculate the value of £450 in US dollars as follows:
450 x 1.62/1 = $729
Therefore, £450 is equivalent to $729 in US dollars.
The conversion of British pounds to US dollars is a common currency exchange process, as both currencies are widely used in international trade and finance. The exchange rate between the two currencies represents the value of one currency in terms of the other. In this case, the exchange rate of £1 to $1.62 means that one British pound is worth 1.62 US dollars. To convert a certain amount of British pounds to US dollars, we simply multiply the pound amount by the exchange rate. The resulting dollar amount reflects the value of the pounds in the equivalent US dollars. Exchange rates can fluctuate frequently due to various economic and political factors, affecting the value of currencies and international transactions.
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Properties of Operations
Use your knowledge of properties of operations to fill in the blanks.
HELP PLEASE
Using distributive property, the expression 55x+5 can be written as 5(11x+1).
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Expression Property Equivalent expression
3(2+x) Distributive 6+3x
2+(3+4) Associative (2+3)+4
24x+18y Distributive 8(3x+y)
4x+5x Commutative 5x+4x
5+2+3 Commutative 3+2+5
(5x.3y).2 Associative 5x.(3y.2)
12-3x Distributive 3(4-x)
6+3 Commutative 3+6
(2x.3y).5z Associative 2x(3y.5z)
4(5-2y) Distributive 20-8y
y+0 Identity y
a.b Commutative b.a
3x.1 Identity 3x
(a+b)+c Associative a+(b+c)
55x+5 Distributive 5(11x+1)
8(y-2) Distributive 8y-16
2x+5y Commutative 5y+2x
Therefore, using distributive property, the expression 55x+5 can be written as 5(11x+1).
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Given f(x)= x^2+9 and g(x)=-x-7,find(f-g)(x)
Answer:The Algebra of Functions
Like terms, functions may be combined by addition, subtraction, multiplication or division.
Example 1. Given f ( x ) = 2x + 1 and g ( x ) = x2
+ 2x – 1 find ( f + g ) ( x ) and
( f + g ) ( 2 )
Solution
Step 1. Find ( f + g ) ( x )
Since ( f + g ) ( x ) = f ( x ) + g ( x ) then;
( f + g ) ( x ) = ( 2x + 1 ) + (x2
+ 2x – 1 )
= 2x + 1 + x2
+ 2x – 1
= x
2
+ 4x
Step 2. Find ( f + g ) ( 2 )
To find the solution for ( f + g ) ( 2 ), evaluate the solution above for 2.
Since ( f + g ) ( x ) = x2
+ 4x then;
( f + g ) ( 2 ) = 22
+ 4(2)
= 4 + 8
= 12
Example 2. Given f ( x ) = 2x – 5 and g ( x ) = 1 – x find ( f – g ) ( x ) and ( f – g ) ( 2 ).
Solution
Step 1. Find ( f – g ) ( x ).
( f – g ) ( x ) = f ( x ) – g ( x )
= ( 2x – 5 ) – ( 1 – x )
= 2x – 5 – 1 + x
= 3x – 6
Step 2. Find ( f – g ) ( 2 ).
( f – g ) ( x ) = 3x – 6
( f – g ) ( 2 ) = 3 (2) – 6
= 6 – 6
= 0
Step-by-step explanation:
algebra 1 i need help 100 points
An equation for each situation in terms of x include the following:
A = 3x + 65
B = 2x + 100
The number of miles driven that would make the cost of each company the same is $35.
How to write a system of equation to model this situation?Based on the information provided above, Company A charges an initial fee of $65 for the rental plus $3 per mile driven. Therefore, the total cost, A, can be represented by this equation:
A = 3x + 65
Since Company B charges an initial fee of $100 for the rental plus $2 per mile driven. Therefore, the total cost, A, can be represented by this equation:
B = 2x + 100
For the cost of each company to be the same, we have the following:
3x + 65 = 2x + 100
3x - 2x = 100 - 65
x = $35.
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Sydney read
50
50 pages in
40
40 minutes. She reads at a constant rate.
How many pages can Sydney read per minute?
when you shining a flashlight on the book that is 12 cm tall and 8 cm wide . it makes a shadow on the wall that is 18 cm tall and 12 CM wide . then what is the scale factor of The book to it's Shadow?
Answer:
The scale factor of the book to its shadow is 2/3 or 66.67%
Step-by-step explanation:
Shadow (cm): 18 x 12
Book (cm) : 12 x 8
We want the scale factor of the book (12x8) to the shadow (18x12).
We can write each dimension ratio (book/shadow) as:
12/18 and 8/12
2/3 and 2/3
The scale factor is 2/3 or 66.67%
PLEASE HELPPPPPPP!!!!!!!!!
Answer:
This pair of equations is solvable by substitution, as I can easily substitute for y because it is already isolated in both equations. After substituting for y, I will solve the equations to get the value of x and then substitute that x-value into the simpler of the two equations, y = x - 1. Once I have both the x-value and y-value, they will be put into a point (x,y).
y = 3x + 3
y = x - 1
x - 1 = 3x + 3
x = 3x + 4
-2x = 4
x = -2
y = x - 1
y = ( -2 ) - 1
y = -3
The final answer to the pair of inequalities is ( -2,-3 )
Step-by-step explanation:
y = 3x + 3
y = x - 1
"substitution" means we are defining one variable by an expression of the other variable and use this identity in one of the original equations.
in our case here the main work was already done (even twice) : y is defined as expressions in x.
we even have the luxury to pick which one and then to use it in the other.
it does not matter which one you pick, it will lead to the same result.
so, let's use the identity of equation 1 in equation 2 : we replace every occurrence of y by the defined identity
y = x - 1
turns into
3x + 3 = x - 1
now we subtract x from both sides
3x + 3 - x = x - 1 - x
2x + 3 = -1
now we subtract 3 from both sides
2x + 3 - 3 = -1 - 3
2x = -4
and finally we divide both sides by 2
2x/2 = -4/2
x = -2
this result we use now in one of the original equations to get y :
e.g.
y = x - 1
y = -2 - 1 = -3
so, the solution is (-2, -3)
Your parents opened a college investment account for you when you were in the first grade. They made an initial deposit of $5000 with an annual interest rate of 5% compounded quarterly.
a. Write a function A, that represent the balance (in dollars) of the investment after t years.
b. What is the current balance of the account (presuming they only made the one deposit)?
c. Will this cover your first year of school? If it does do you have any money left over? If not, how much more money do you need?
Answer:
La fórmula para calcular el balance (en dólares) de una inversión con una
A = P(1 + r/n)^(nt)
Donde:
A es el balance total después de t años
P es el depósito inicial
r es la tasa de interés anual expresada como decimal (5% = 0.05)
n es la frecuencia de capitalización por año (en este caso, 4 para compuestos trimestrales)
t es el tiempo en años
Sustituyendo los valores dados, la función que representa el balance después de t años es:
A(t) = 5000(1 + 0,05/4
b. Para encontrar el balance actual, podemos simplemente evaluar la función A en t = 0, lo que nos da:
A(0) = 5000(1 + 0,05/4
Por lo tanto, el balance actual de la cuenta es de $5000.
c. Supongamos que el costo de la matrícula y los gastos de su primer año en la universidad suman $20,000. Para determinar si la inversión cubrirá el costo, podemos evaluar la función A en t = 12 (es decir, después de 12 años desde el depósito inicial) y compararla con el costo de la matrícula y los gastos.
A(12) = 5000(1 + 0.05/4)^(4(12)) = $10,768.49
Como el balance de la cuenta después de 12 años es menor que el costo de la matrícula y los gastos, se necesitará más dinero para cubrir el costo del primer año de universidad. La cantidad adicional requerida será:
$20,000 - $10,768.49 = $9,231.51
Por lo tanto, se necesitarán $9,231.51 adicionales para cubrir el costo del primer año de universidad.
Step-by-step explanation:
tal vez te sirve esto
