The expression
28 (78-14)9-13(78-49)9
can be
rewritten as
(X-y)" (262 + y? + gxy). Whatis the value of p?
Answers
Answer:
p =1 0
Step-by-step explanation:
x³(x - y)⁹ - y³(x - y)⁹ = (x - y)⁹[x³ - y³]
= (x - y)⁹(x - y)(x² + y² + xy)
= (x - y)¹⁰(x² + y² + xy)
where p = 10 and q = 1
Answer:
p = 10
Step-by-step explanation:
Given expression:
[tex]x^3(x-y)^9 - y^3(x-y)^9[/tex]
Factor out the common term (x - y)⁹:
[tex](x-y)^9(x^3- y^3)[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of two cubes}\\\\$x^3-y^3=(x-y)(x^2+y^2+xy)$\\\end{minipage}}[/tex]
Rewrite the second parentheses as the difference of two cubes.
[tex](x-y)^9(x-y)(x^2+y^2+xy)[/tex]
[tex]\textsf{Apply\:the\:exponent\:rule:} \quad a^b\cdot \:a^c=a^{b+c}[/tex]
[tex](x-y)^{9+1}(x^2+y^2+xy)[/tex]
[tex](x-y)^{10}(x^2+y^2+xy)[/tex]
Comparing the rewritten original expression with the given expression:
[tex](x-y)^{10}(x^2+y^2+xy)=(x-y)^p(x^2+y^2+qxy)[/tex]
We can see that [tex](x-y)^p[/tex] corresponds to [tex](x-y)^{10}[/tex] in the given expression.
Therefore, we can conclude that p = 10.
Related Questions
Which of the following is equal to the fraction below? (7/4)11
Answers
Answer:
It's A
Step-by-step explanation:
Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
Use the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set model
For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Sally purchased 7 shares in the software company and 87 shares in the biotech firm, which cost a total of $8,315. At the same time, Katle invested a total of $7,338 in 84 shares in the software company and 50 shares in the biotech firm. How much did each share cost?
Answers
The cost of one share in the software company (x) is $32, and the cost of one share in the biotech company (y) is approximately $93.
Let's denote the cost of one share in the software company as 'x' dollars and the cost of one share in the biotech company as 'y' dollars.
According to the given information, Sally purchased 7 shares in the software company and 87 shares in the biotech company, which cost a total of $8,315. We can express this as the following equation:
7x + 87y = 8315 ----(Equation 1)
Similarly, Katle invested a total of $7,338 in 84 shares in the software company and 50 shares in the biotech company. This can be represented as the following equation:
84x + 50y = 7338 ----(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.
Multiply Equation 1 by 50 and Equation 2 by 87 to eliminate the 'y' terms:
350x + 4350y = 415750 ----(Equation 3)
7308x + 4350y = 638526 ----(Equation 4)
Now, subtract Equation 3 from Equation 4:
(7308x + 4350y) - (350x + 4350y) = 638526 - 415750
Simplifying the equation:
7308x - 350x = 222776
6958x = 222776
Divide both sides of the equation by 6958:
x = 222776 / 6958
x = 32
Now that we have the value of 'x', we can substitute it back into either Equation 1 or Equation 2 to solve for 'y'. Let's substitute it into Equation 1:
7(32) + 87y = 8315
224 + 87y = 8315
87y = 8315 - 224
87y = 8091
Divide both sides of the equation by 87:
y = 8091 / 87
y ≈ 93
Therefore, the cost of one share in the software company (x) is $32, and the cost of one share in the biotech company (y) is approximately $93.
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If the manager of a bottled water distributor wants to estimate, 95% confidence, the mean amount of water in a 1-gallon bottle to within ±0.006 gallons and also assumes that the standard deviation is 0.003 gallons, what sample size is needed?
If a light bulb manufacturing company wants to estimate, with 95% confidence, the mean life of compact fluorescent light bulbs to within ±250 hours and also assumes that the population standard deviation is 900 hours, how many compact fluorescent light bulbs need to be selected?
If the inspection division of a county weighs and measures department wants to estimate the mean amount of soft drink fill in 2-liter bottles to within ± 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.08 liters, what sample size is needed?
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 52 minutes. What sample size is needed if the executive wants to be 95% confident of being correct to within ±5 minutes?
Answers
n = (Z * σ / E)^2
where:
n = required sample size
Z = Z-value for the desired confidence level (for 95% confidence, Z ≈ 1.96)
σ = standard deviation
E = desired margin of error
Let's calculate the sample sizes for each scenario:
1. Bottled Water:
Z ≈ 1.96, σ = 0.003 gallons, E = 0.006 gallons
n = (1.96 * 0.003 / 0.006)^2 ≈ 384.16
Since we can't have a fraction of a sample, we round up to the nearest whole number. Therefore, a sample size of 385 bottles is needed.
2. Compact Fluorescent Light Bulbs:
Z ≈ 1.96, σ = 900 hours, E = 250 hours
n = (1.96 * 900 / 250)^2 ≈ 49.96
Again, rounding up to the nearest whole number, a sample size of 50 light bulbs is needed.
3. Soft Drink Fill:
Z ≈ 1.96, σ = 0.08 liters, E = 0.01 liters
n = (1.96 * 0.08 / 0.01)^2 ≈ 122.76
Rounding up, a sample size of 123 bottles is needed.
4. Digital Media Consumption:
Z ≈ 1.96, σ = 52 minutes, E = 5 minutes
n = (1.96 * 52 / 5)^2 ≈ 384.16
Rounding up, a sample size of 385 consumers is needed.
Please note that the sample sizes calculated here assume a simple random sampling method and certain assumptions about the population.
```
n = (Z^2 * σ^2) / E^2
```
where:
- Z is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence)
- σ is the population standard deviation
- E is the desired margin of error
Substituting the given values, we get:
```
n = (1.96^2 * 52^2) / 5^2
n ≈ 385.07
```
Rounding up, we get a required sample size of 386.
Therefore, the advertising executive should sample at least 386 individuals to estimate the mean time that consumers spend with digital media with a margin of error of ±5 minutes and 95% confidence level.
The new corporate logo created by the design engineers at Magic Motors is shown in the accompanying diagram. If the measure of arc AC = 80°, what is the mLB?
Answers
The measure of angle LB is 40°.
To find the measure of angle LB, we can use the fact that the measure of an inscribed angle is half the measure of its intercepted arc.
In this case, we are given that the measure of arc AC is 80°, so we can conclude that the measure of angle LB is half of that.
Since angle LB is an inscribed angle that intercepts arc AC, we can write the equation:
mLB = 1/2 [tex]\times[/tex] mAC
Substituting the given value, we have:
mLB = 1/2 [tex]\times[/tex] 80°
mLB = 40°
Therefore, the measure of angle LB is 40°.
In the context of the corporate logo, angle LB represents a portion of the circular shape of the logo.
By knowing the measure of arc AC, we can determine the measure of angle LB, which helps in accurately representing the logo in terms of angles and proportions.
This information is crucial for design and branding purposes, as it ensures consistency and precision in the presentation of the logo across various media and materials.
Overall, understanding the measures of angles and arcs in the logo design allows for effective communication and replication of the logo's visual elements, ensuring brand recognition and consistency in its representation.
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If the left-hand limit of is equal to the right-hand limit of as x approaches 10, the limit of as x approaches 10 is and the value of k is .
Answers
The limit of f(x) as x approaches 10 is 315 and The value of k is 250.
The function f(x) is a piecewise function, so we need to evaluate it separately for x < 10 and x >= 10.
[tex]f(x)= { \frac{(0.1x(2)+20x+15,x < 10)}{(0.25x(3)+k,x > 10)}[/tex]
For x < 10, the function is equal to 0.1x^2 + 20x + 15. So the left-hand limit of f(x) as x approaches 10 is equal to 0.1(10)^2 + 20(10) + 15 = 315.
For x >= 10, the function is equal to 0.25x^3 + k. So the right-hand limit of f(x) as x approaches 10 is equal to 0.25(10)^3 + k = 250 + k.
Since the left-hand limit and the right-hand limit are equal, the limit of f(x) as x approaches 10 is also equal to 315, and the value of k is equal to 250.
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Escriba el tipo de variable y nivel de medición para la siguiente grupo de variables : A) tipo de medallas a prueba olímpica. B) Volumen de agua en un tanque
Answers
The type of medals is a categorical nominal variable, while the volume of water is a numerical continuous variable.
How can these variables be classified?Type of medals in an Olympic event: This is a categorical nominal variable as there are fixed categories for the medals such as gold and silver and they do not have an inherent order The volume of water in a tank: This is a numerical and continuous variable which means it is measured with numbers. Moreover, it is continuous as it is obtained by measuring.Note: This question is in Spanish, here is the question in English:
Write the type of variable and level of measurement for the following group of variables: A) type of medals at Olympic test. B) Volume of water in a tank
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witch of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it
a. length(time)
b.Time(race)
c.time(length)
d.cost(time)
Answers
The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".
When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.
In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.
a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.
b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.
c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.
d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.
Therefore, "time(length)" is the most suitable and appropriate name for the function.
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The height of a rectangular box is 7 ft. The length is 1 ft longer than thrice the width x. The volume is 798 ft³.
(a) Write an equation in terms of x that represents the given relationship.
The equation is
Answers
The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)
Let's break down the information given:
Height of the rectangular box = 7 ft
Length of the rectangular box = 1 ft longer than thrice the width (x)
Volume of the rectangular box = 798 ft³
To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.
The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.
Given that the height is 7 ft, we can substitute this value into the equation.
Volume = (Length) * (Width) * (7)
Now, let's focus on the length. It is described as 1 ft longer than thrice the width.
Length = 1 + (3x)
Substituting this value into the equation, we have:
Volume = (1 + (3x)) * (Width) * (7)
Since the volume is given as 798 ft³, we can set up the equation as follows:
798 = (1 + (3x)) * (Width) * 7
Simplifying further, we get:
798 = 7 * (1 + 3x) * (Width)
Dividing both sides of the equation by 7, we have:
114 = (1 + 3x) * (Width)
Therefore, the equation in terms of x that represents the given relationship is:
114 = (1 + 3x) * (Width)
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Which of the following graphs shows a pair of lines that represents the equations with the solution (4, −1)?
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 1 unit to the right and 4 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 4 units to the right and 1 unit down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 4 units to the left and 1 unit up.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 1 unit to the left and 4 units up.
Answers
The graph that shows a pair of lines representing the equations with the solution (4, -1) is option D.
To determine which graph represents the equations with the solution (4, -1), we need to check if the given point lies on the lines represented by each graph.
Let's examine each option:
A) The lines intersect 1 unit to the right and 4 units down. This does not match the given solution of (4, -1), so option A can be eliminated.
B) The lines intersect 4 units to the right and 1 unit down. Again, this does not match the given solution of (4, -1), so option B can be eliminated.
C) The lines intersect 4 units to the left and 1 unit up. This is the exact opposite of the given solution (4, -1), so option C can be eliminated.
D) The lines intersect 1 unit to the left and 4 units up. This matches the given solution of (4, -1), where the x-coordinate is 1 unit to the left and the y-coordinate is 4 units up. Therefore, option D represents the equations with the solution (4, -1).
In conclusion, the graph that shows a pair of lines representing the equations with the solution (4, -1) is option D.
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A bag of marbles contains 2 blue marbles, 4 red marbles 6 green marbles
Answers
Answer:
We start with 17 marbles, 4 of which are red. So P(first marble is red) = 4/17. Since the red marble is not replaced, there are now 16 marbles, 3 of which are red. So P(second marble is red) = 3/16.
The correct calculation is
P(red, then red) = 4/17 × 3/16
Question #3
Solve for x
OOO
O 10
07
5
8
6x+8
N
p
U
K
122°
L
M
194°
Answers
The calculated value o x in the circle is 7
How to determine the solution for xFrom the question, we have the following parameters that can be used in our computation:
The circle
The value of x can be calculated using teh equation of the intersection of chords
So, we have
122 = 1/2(6x + 8 + 194)
Evaluate
244 = 6x + 202
So, we have
6x = 42
Divide by 6
x = 7
Hence, the solution for x is 7
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What are the values of x and y?
A) x = 18√3; y = 9√3
B) x = 9; y = 9√3
C) x = 9√3; y = 9
D) x = 9√2; y = 9
Answers
The values of x and y are 9√3 and 9. Thus, option C is the answer.
From the figure, we know that angle A = 60°, angle C = 30° and side AC =18 units.
We have to use trigonometric ratios to find the values of x and y.
sin30° = Opposite side/Hypotenuse
But, we also know that sin30° = 1/2
Substituting the value in the above equation, we get
1/2 = y/18
Thus, the value of y = 18/2 = 9.
Now, sin60° = Opposite Side/ Hypotenuse
sin60° = √3/2
Substituting the value, we get
√3/2 = x/18
Thus, x = 9√3.
Therefore, the values of x and y in the given triangle are 9√3 and 9.
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williams has 32 coins that are all either quarter or dimes the coins have a value of $5 how many dimes does williams have
Answers
Answer:
20 dimes
Step-by-step explanation:
1 dime = $0.1
1 quarter = $0.25
Let there be x dimes
Then the number of quarters is 32-x
Also, $5 = 0.1x + 0.25(32-x)
⇒ 5 = 0.1x + 8 - 0.25x
⇒ 0.25x - 0.1x = 8 - 5
⇒ 0.15x = 3
⇒ x = 3/0.15
⇒ x = 20
Currency exchange rates are based on______.
A.each country’s economy
B. The gold standard
C.current bartering
D.one-for-one exchange
Answers
Currency exchange rates are primarily based on each country's economy.
The exchange rate of a currency is influenced by various factors, such as inflation rates, interest rates, political stability, economic performance, trade balances, and market supply and demand.
These factors reflect the overall strength or weakness of a country's economy and play a significant role in determining the value of its currency relative to other currencies in the foreign exchange market.
While historical exchange rate systems, such as the gold standard, had an impact on currency values in the past, the modern exchange rate regime is primarily determined by market forces and economic fundamentals.
Bartering and one-for-one exchange are not directly related to currency exchange rates in the context of global currency markets, as exchange rates involve the relative value of one currency against another.
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The area of the figure is square units.
3 units, 8 units, 3 units, 9 units, 3 units, 21 units
Answers
The area of the figure is 114 square units.
To determine the area of the figure, we need to identify its shape.
From the given dimensions, it appears that we have three rectangular sections.
The first section has a length of 3 units and a width of 8 units, giving us an area of 3 [tex]\times[/tex] 8 = 24 square units.
The second section has a length of 3 units and a width of 9 units, resulting in an area of 3 [tex]\times[/tex] 9 = 27 square units
The third section has a length of 3 units and a width of 21 units, yielding an area of 3 [tex]\times[/tex] 21 = 63 square units.
To find the total area of the figure, we need to sum up the areas of the individual sections:
Total area = 24 + 27 + 63 = 114 square units.
Therefore, the area of the figure is 114 square units.
It's important to note that without a clear description or diagram of the figure, it's challenging to provide an accurate interpretation.
The given dimensions could represent various arrangements, and the resulting area would vary accordingly.
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The following pie chart shows the number of rabbits, sheep, cattle, pigs on a farm
sheep
700
cattle
300
Pig
500
a. How many animals are on the farm? b.What represents the number of sheep on the farm
c. what percentage of the total number of animals are rabbits
d. Calculate the angle that represents number of pigs
Answers
B) 700/1500 sheep
C) I don’t see a number of rabbits or pie chart so I can’t tell
D) 1/3 animals are pigs
Solve the proportion for the missing values 5/12 = x/20
Answers
Answer:
x = 5
Step-by-step explanation:
We can solve for x in this proportion, or an equation of ratios, by multiplying both sides by 20.
[tex]{/}\!\!\!\!\!{20}\cdot \dfrac{5}{{/}\!\!\!\!\!20}=\dfrac{x}{{/}\!\!\!\!\!20} \cdot {/}\!\!\!\!\!20[/tex]
We can see that the 20s cancel in the numerator and denominator in both sides, and the equation is solved for x:
[tex]x = 5[/tex]
Step-by-step explanation:
We can solve for x in this proportion, or an equation of ratios, by multiplying both sides by 20.
5
⅔⅜=
2020
We can see that the 20s cancel in the numerator and denominator in both sides, and the equation is solved for x:
7 = 5
Two roll of electric wire contain 80m 20cm and 86m 56cm of wire respectively. what is the total length of electric wire of both the roll? Express the Result in metres
Answers
The total length of electric wire in both rolls is 166.76 meters.
To find the total length of electric wire in both rolls, we need to add the lengths of the two rolls together.
The first roll contains 80m 20cm of wire. We can convert this to meters by noting that 1 meter is equal to 100 centimeters. Therefore, the length of the first roll is:
80m 20cm = 80 meters + (20 centimeters / 100) meters
= 80 meters + 0.20 meters
= 80.20 meters
Similarly, the second roll contains 86m 56cm of wire. Converting this to meters:
86m 56cm = 86 meters + (56 centimeters / 100) meters
= 86 meters + 0.56 meters
= 86.56 meters
To find the total length, we add the lengths of both rolls:
Total length = 80.20 meters + 86.56 meters
= 166.76 meters
Therefore, the total length of electric wire in both rolls is 166.76 meters.
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find the inverse of each function
Answers
Answer:
c
Step-by-step explanation:
assume base 10
-logy = x
[tex] \frac{1}{ log(y) } = x[/tex]
log base x y = 5 turns into the format x^ 5 = y
implement that to get c
Ian took out a $19,000 personal loan to pay for his home renovations. He will not make a payment for 5 years and there is a 15% interest rate. How much will be owed in 5 years with monthly compounding?
Round your answer to the nearest cent.
Do NOT round until your final answer.
Answers
The amount owed in 5 years with monthly compounding, considering a $19,000 personal loan with a 15% interest rate, will be $34,558.52.
1. Convert the interest rate to a decimal: 15% = 0.15.
2. Determine the number of compounding periods: Since the loan compounds monthly, multiply the number of years by 12. In this case, 5 years * 12 months/year = 60 months.
3. Calculate the monthly interest rate: Divide the annual interest rate by 12. In this case, 0.15 / 12 = 0.0125.
4. Use the compound interest formula to calculate the future value:
Future Value = Principal * (1 + Monthly Interest Rate)^(Number of Compounding Periods)
Future Value = $19,000 * (1 + 0.0[tex]125)^{(60[/tex])
5. Evaluate the expression inside the parentheses: (1 + 0.0[tex]125)^{(60[/tex]) ≈ 1.954503.
6. Multiply the principal by the evaluated expression: $19,000 * 1.954503 = $37,133.57 (unrounded).
7. Round the final answer to the nearest cent: $34,558.52.
Therefore, in 5 years with monthly compounding, the amount owed on the $19,000 personal loan will be approximately $34,558.52.
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CAN SOMEONE HELPPPPPP
Answers
Answer:
∠1 = 100
∠2 = 110
Step-by-step explanation:
∠1 + 80 = 180(angles on a straight line add to 180)
∠1 = 180 - 80
∠1 = 100
∠2 = 110 (vertically opposite angles are equal)
Please answer ASAP I will brainlist
Answers
Answer:
Step-by-step explanation:
The given augmented matrix is already in reduced row echelon form. We can interpret it as a system of equations as follows:
1x + 0y + 0z + (4/5)w = 0
0x + 1y + 0z + 5w = 0
0x + 0y + 1z - 4w = 0
0x + 0y + 0z + w = -4
From the last row, we can see that w = -4. Substituting this value back into the previous rows, we get:
1x + 0y + 0z + (4/5)(-4) = 0
0x + 1y + 0z + 5(-4) = 0
0x + 0y + 1z - 4(-4) = 0
Simplifying these equations, we have:
x - (16/5) = 0
y - 20 = 0
z + 16 = 0
From the second equation, y = 20. From the third equation, z = -16. Substituting these values into the first equation, we get x - (16/5) = 0, which implies x = 16/5.
Therefore, the solution of the system is (16/5, 20, -16, -4).
So, the correct choice is:
A. The system has exactly one solution. The solution is
(16/5, 20, -16, -4)
Find the perimeter of a sector whose radius is 4 unit and arc length is 16π
Answers
Answer:
perimeter ≈ 58.3 units
Step-by-step explanation:
the perimeter of the sector includes 2 radii and the arc
perimeter = 4 + 4 + 16π = 8 + 16π ≈ 58.3 ( to 1 decimal place )
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Answers
There is just one solution to this system. The answer is (460/7), (-13/7), and (-24/7). The correct answer is option A.
Given the system of equations as X+ y- z=63x- y+ z=2x- 4y+ 2z-34.We have to use row operations to solve this system of equations. Let us start by writing down the augmented matrix of the given system of equations. [1, 1, -1 | 6][3, -1, 1 | 2][1, -4, 2 | -34]
The first step is to change the first element of the second row to zero. For that, we subtract three times the first row from the second row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][1, -4, 2 | -34]
Now, we need to change the first element of the third row to zero. For that, we subtract the first row from the third-row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][0, -5, 3 | -40]
The next step is to change the second element of the third row to zero. For that, we add 5/4 times the second row to the third row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][0, 0, 7 | -24]
Now, we solve the system of equations using back-substitution. We have 7z = -24 ⇒ z = -24/7
Substituting this value of z in the second equation, we get -4y = 4 - z = 4 + 24/7 = 52/7⇒ y = -13/7
Substituting these values of y and z in the first equation, we get x = 63 - y + z = 63 + 13/7 - 24/7 = 460/7Thus, the solution of the given system of equations is (x, y, z) = (460/7, -13/7, -24/7). Therefore, the correct choice is A. This system has exactly one solution. The solution is (460/7, -13/7, -24/7).
The given system of equations is solved using row operations. It is found that this system has exactly one solution which is (460/7, -13/7, -24/7). Therefore, the correct choice is A. This system has exactly one solution. The solution is (460/7, -13/7, -24/7).
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Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
The dependent variable is t.
When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155."
The dependent variable is f(t).
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t.
The independent variable
Answers
The correct statements are
The dependent variable is t.
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t. Option A,D,E,F.
Let's analyze each statement to understand why it is true:
A) The dependent variable is t: In the given function, f(t), the value of f depends on the value of t. Therefore, t is the independent variable, and f is the dependent variable.
D) When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced": Here, the value of t is 2, representing the year 2002, and the value of f(t) is 1,323, representing the amount of garbage produced in tons.
E) When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced": Similar to statement D, the value of t is 4, representing the year 2004, and the value of f(t) is 1,458.6, representing the amount of garbage produced in tons.
F) The independent variable is t: As mentioned in statement A, t is the independent variable in the given function. It is the variable that we can change or manipulate, and the value of f depends on the value of t.
Statements B, C, and G are incorrect:
B) When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155": This statement is incorrect because in the given function, t represents the time in years after 2000, not the amount of garbage produced.
C) The dependent variable is f(t): This statement is incorrect because, as mentioned earlier, t is the independent variable, and f is the dependent variable.
G) The independent variable f(t): This statement is incorrect because f(t) represents the amount of garbage produced, which is the dependent variable in the given function.
So Option A,D.E.F. Are correct.
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Note the complete question is
Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
A.) The dependent variable is t.
B.) When f(12) = 2,155, 12 represents "12 tons of garbage produced," and 2,155 represents "the year 2155."
C.) The dependent variable is f(t).
D.) When f(2) = 1,323, 2 represents "the year 2002," and 1,323 represents "1,323 tons of garbage produced."
E.) When f(4) = 1,458.6, 4 represents "the year 2004," and 1,458.6 represents "1,458.6 tons of garbage produced."
F.) The independent variable is t.
G.) The independent variable f(t)
on #5
Find the measure of the indicated are.
90°
80°
100°
70°
H
40°
Answers
The measure of the Intercepted arc having an inscribed angle of 40 degrees is 80 degrees.
What is the measure of the intercepted arc?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the figure:
Inscribed angle = 40 degrees
Intercepted arc = ?
Plug the given value into the above formula and solve for the arc:
Inscribed angle = 1/2 × intercepted arc.
40 = 1/2 × intercepted arc
Multiply both sides by 2:
40 × 2 = 2 × 1/2 × intercepted arc
40 × 2 = intercepted arc
Intercepted arc = 80°
Therefoore, the Intercepted arc is 80 degrees.
Option B) 80° is the correct answer.
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A box contains 240 lumps of sugar. Five lumps are fitted across the box and there were three layers. How many lumps are fitted along the box?
Answers
Number of lumps across each layer = 5
Number of layers = 3
Total number of lumps = Number of lumps across each layer × Number of layers
Total number of lumps = 5 × 3 = 15
Therefore, 15 lumps of sugar are fitted along the box.
If it’s possible, please mark me brainliest!
Please answer ASAP I will brainlist
Answers
Answer:
-x + 20(8) = 147 -x + 10(8) = 67
-x + 160 = 147 -x + 80 = 67
x = 13 x = 13
A. The system has exactly one solution. The solution is (13, 8).
B. All three colonies had a population of 8 thousand people in 2013.
determine the value of x
Answers
The hypotenuse (x) of the right triangle is 10 units
Finding the hypotenuse of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse (x) of the right triangle can be calculated using the following sine equation
sin(30) = 5/x
Using the above as a guide, we have the following:
x = 5/sin(30)
Evaluate
x = 10
Hence, the hypotenuse of the right triangle is 10
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NO LINKS!! URGENT HELP PLEASE PLEASE!!!
Answers
Answer:
[tex]\textsf{12)} \quad \text{a.}\;\;m \angle 1 = 107^{\circ}, \quad \text{b.}\;\;m \angle 2 = 107^{\circ}, \quad \text{c.}\;\;m \angle 3 = 73^{\circ}[/tex]
[tex]\textsf{13)} \quad EC = 6[/tex]
[tex]\textf{14)}\quad \text{a.}\;\;x = 33, \quad \text{b.}\;\; x = 8[/tex]
Step-by-step explanation:
Question 12As the base angles of an isosceles trapezoid are congruent, the measures of angles E and J are the same. Therefore:
[tex]m\angle 3 = 73^{\circ}[/tex]
The opposite angles of an isosceles trapezoid sum to 180°. Therefore:
[tex]\implies m\angle 1 + m\angle 3 = 180^{\circ}[/tex]
[tex]\implies m\angle 1 + 73^{\circ} = 180^{\circ}[/tex]
[tex]\implies m\angle 1 = 107^{\circ}[/tex]
Since the base angles of an isosceles trapezoid are congruent, the measures of angles A and N are the same. Therefore:
[tex]m\angle 2 = 107^{\circ}[/tex]
[tex]\hrulefill[/tex]
Question 13The diagonals of isosceles trapezoid ABCD are AC and BD.
Point E is the point of intersection of the diagonals. Therefore:
[tex]BE + ED = BD[/tex]
[tex]AE + EC = AC[/tex]
As the diagonals of an isosceles trapezoid are the same length, BD = AC. Therefore:
[tex]AE + EC = BD[/tex]
Given BD = 20 and AE = 14:
[tex]\implies AE + EC = BD[/tex]
[tex]\implies 14 + EC = 20[/tex]
[tex]\implies 14 + EC - 14 = 20 - 14[/tex]
[tex]\implies EC = 6[/tex]
[tex]\hrulefill[/tex]
Question 14The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides (legs) of the trapezoid.
The formula for the midsegment of a trapezoid is:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Midsegment of a trapezoid}\\\\$M=\dfrac{1}{2}(a+b)$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the midsegment.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides.\\\end{minipage}}[/tex]
a) From inspection of the given trapezoid:
M = xa = 18b = 48Substitute these values into the midsegment formula and solve for x:
[tex]x=\dfrac{1}{2}(18+48)[/tex]
[tex]x=\dfrac{1}{2}(66)[/tex]
[tex]x=33[/tex]
Therefore, the value of x is 33.
b) From inspection of the given trapezoid:
M = 15a = 22b = xSubstitute these values into the midsegment formula and solve for x:
[tex]15=\dfrac{1}{2}(22+x)[/tex]
[tex]30=22+x[/tex]
[tex]x=8[/tex]
Therefore, the value of x is 8.