Answers
So H satisfies the three conditions of the subgroup test, and is a subgroup of G.
Let H represent the collection of all G products of X elements and their inverses. We will demonstrate that H meets the three aforementioned requirements, demonstrating that H is a subgroup of G.
The group operation "let a and b be arbitrary elements of H" declares that H is closed. There are then finite sequences of X's elements and their inverses, such as a₁, a₂,..., a and b₁, b₂,..., bm, where a = a₁a₂...an and b = b₁b₂...bm. The result of concatenating the two sequences, a₁a₂...anb₁b₂...bm, is the product ab. As each of these products must belong to X or its inverse because X is closed under the group operation, the product ab must belong to H.
The empty product, which is the product of 0 components from X, is the identity element of H and hence contains the identity element of G.
Let a be an element of H and let a₁, a₂,..., a be a finite sequence of elements from X and their inverses such that a = a₁a₂...an. This proves that H is closed under taking inverses. If these elements are written in reverse order, then a-1 is the product of their inverses: a-1 = an-₁...a₂-1a₁-1. as we know that each of these inverses belongs to X or its inverse because X is closed under taking inverses, Thus H owns a-1
H is a subgroup of G as a result of meeting all three requirements of the subgroup test. In addition, H is the smallest subgroup of G that contains X because it is the set of all products in G of the elements of X and their inverses.
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Related Questions
put equation in conic form
Answers
Answer:
I'm happy to help you put an equation in conic form, but you haven't provided an equation to work with. Please provide the equation and I'll do my best to assist you.
A Ferris wheel is 30 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h(t) gives a person's height in meters above the ground t minutes after the wheel begins to turn. a. Find the amplitude, midline, and period of h(t). Amplitude: meters Period: Midline: h - minutes meters b. How high off the ground is a person after 5 minutes? meters
Answers
Answer:
a. The Ferris wheel has a diameter of 30 meters, which means the radius is 15 meters. Since the wheel is boarded from a platform that is 2 meters above the ground, the center of the Ferris wheel is 2 + 15 = 17 meters above the ground.
The function h(t) gives a person's height in meters above the ground t minutes after the wheel begins to turn. Since the Ferris wheel completes one revolution in 10 minutes, the period of h(t) is 10 minutes.
The midline is the average value of the function h(t) over one period, and it is equal to the vertical displacement of the graph from the x-axis. Since the center of the Ferris wheel is 17 meters above the ground, the midline is h = 17 meters.
The amplitude of the function h(t) is the distance between the midline and the maximum or minimum value of the function. The maximum height a person can reach on the Ferris wheel is when they are at the very top of the wheel, which is 17 + 15 = 32 meters above the ground. The minimum height a person can reach on the Ferris wheel is when they are at the very bottom of the wheel, which is 17 - 15 = 2 meters above the ground. So the amplitude of h(t) is 15 meters.
Therefore, the amplitude is 15 meters, the midline is h = 17 meters, and the period is 10 minutes.
b. To find the height of a person after 5 minutes, we can plug t = 5 into the function h(t):
h(5) = 15 sin(2π/10 * 5) + 17
h(5) = 15 sin(π) + 17
h(5) = 2 meters
Therefore, a person is 2 meters above the ground after 5 minutes on the Ferris wheel.
Step-by-step explanation:
You have just been approved for a 30 year 6.0% fixed home mortgage. The monthly payment that you qualify for is $1112.10. Use the table provided to determine the price of a home that can be purchased. Round your answer to the nearest cent. A 5-column table with 4 rows titled Monthly Payments per 1000 dollars of mortgage. Column 1 is labeled Interest Rate (percent) with entries 5, 5.5, 6, 6.5. Column 2 is labeled 10 Years with entries 10.61, 10.86, 11.11, 11.36. Column 3 is labeled 20 years with entries 6.60, 6.88, 7.17, 7.46. Column 4 is labeled 30 years with entries 5.37, 5.68, 6.00, 6.33. Column 5 is labeled 40 years with entries 4.83, 5.16, 5.51, 5.86. a. $183,147 c. $185,350 b. $184,789 d. $186,523
Answers
The price of a home that can be purchased is $185,350.
What is interest rate?The supply and demand for credit, the rate of inflation, and the state of the economy as a whole all influence interest rates.
To determine the price of a home that can be purchased, we need to use the given monthly payment of $1112.10 and the interest rate of 6.0% for a 30-year fixed mortgage.
From the table, we can see that the monthly payment per $1000 of mortgage for a 30-year fixed mortgage with a 6% interest rate is $6.00.
So, the mortgage amount can be calculated as:
Mortgage amount = Monthly payment / Monthly payment per $1000 of mortgage
Mortgage amount = $1112.10 / $6.00 = $185,350 (rounded to the nearest cent)
Therefore, the price of a home that can be purchased is $185,350.
Therefore, the answer is (c) $185,350.
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A square has a diagonal length 9m. What is the side length of the square, to the nearest centimeter?
Answers
Since the square has a diagonal length 9 m, the side length of the square is equal to 636 centimeters.
How to calculate the area of a square?In Mathematics and Geometry, the area of a square can be calculated by using this mathematical equation (formula);
A = x²
Where:
A represents the area of a square.x represents the side length of a square.In Mathematics and Geometry, the side length of a square can be calculated by using this mathematical equation (formula);
Diagonal, d = √2x
Solving for x, we have:
x = d/√2
x = 9/√2
x = 6.3640 meters.
Conversion:
1 meter = 100 centimeters
6.3640 meters = 636.4 ≈ 636 centimeters.
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In the past few years, many small businesses have been faced with difficulty keeping their doors open, and in many cases large corporations with cash on hand have come in to take over the companies and their real estate. In such case, a large restaurant chain purchased a small corner tavern with plans to use the name to build a local franchise. The cost of buying the franchise naming rights was four times the cost of buying the physical property. If the total purchase price was $1,250,000, how much did the restaurant chain pay for each individual element of the sale ( naming rights and physical property)?
Answers
The restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.
What is sale?Sale refers to the transfer of ownership of goods or services from one person to another in exchange for money or other consideration.
The total purchase price of the franchise naming rights and physical property was $1,250,000.
To calculate the amount paid for each individual element of the sale, the total purchase price must be divided by the two elements.
The total purchase price of $1,250,000 divided by two elements equals $625,000.
This means that the restaurant chain paid $625,000 for the franchise naming rights and $625,000 for the physical property.
The amount of money paid for the franchise naming rights (four times the cost of buying the physical property) can be calculated by multiplying the cost of the physical property, which is
$625,000/4 .
When the cost of the physical property is multiplied by four, the result is $2,500,000.
This means that the restaurant chain paid $2,500,000 for the franchise naming rights.
In summary, the restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.
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Solve the following maximization problem graphically.
P(x,y)=82x+50y
subject to
2x+2y≥10
3x+6y≤54
x≥0
y≥0
x≤10
y≤8
Answers
Answer:
Step-by-step explanation:
To solve the maximization problem graphically, we first need to graph the constraints and find the feasible region. Then we can find the corner points of the feasible region and evaluate the objective function at each corner point to find the maximum value.
Graphing the constraint 2x + 2y ≥ 10, we get the following line:
2x + 2y = 10
y = 5 - x
Graphing the constraint 3x + 6y ≤ 54, we get the following line:
3x + 6y = 54
y = 9 - 0.5x
We also need to graph the non-negative constraints x ≥ 0 and y ≥ 0, as well as the constraints x ≤ 10 and y ≤ 8, which limit the values of x and y.
The feasible region is the shaded region in the graph. To find the corner points of the feasible region, we can find the points where the lines intersect. There are four corner points: (0, 5), (0, 9), (6, 4), and (10, 0).
Now we can evaluate the objective function at each corner point to find the maximum value:
P(0, 5) = 82(0) + 50(5) = 250
P(0, 9) = 82(0) + 50(9) = 450
P(6, 4) = 82(6) + 50(4) = 652
P(10, 0) = 82(10) + 50(0) = 820
Therefore, the maximum value of the objective function is 820, which occurs at the point (10, 0).
Therefore, the maximum value of P(x,y)=82x+50y subject to the given constraints is 820, and it occurs at the point (10,0).
a certain water filtration system can remove 70% of the contaminants each time a simple of water is passed through it. if the water is passed through the system four times, what percent of the original contaminants will be removed from the water sample?
Answers
after four passes through the filtration system, 99.19% of the original contaminants will have been removed from the water sample
How to solve the question?
Each time the water passes through the filtration system, 70% of the contaminants are removed, which means that 30% of the contaminants remain in the water. After the first pass, 30% of the original contaminants are left in the water. After the second pass, 30% of the remaining 30% is left, which is equivalent to 9% of the original contaminants. After the third pass, 30% of the remaining 9% is left, which is equivalent to 2.7% of the original contaminants. Finally, after the fourth pass, 30% of the remaining 2.7% is left, which is equivalent to 0.81% of the original contaminants.
Therefore, after four passes through the filtration system, 99.19% of the original contaminants will have been removed from the water sample. This calculation can be obtained by subtracting the final percentage of contaminants left (0.81%) from 100%.
It's important to note that while passing the water through the filtration system multiple times increases the overall percentage of contaminants removed, it's not a substitute for regular maintenance and replacement of the filtration system's components. Over time, the filtration system's effectiveness can diminish, and it's crucial to follow the manufacturer's instructions for proper maintenance and replacement to ensure that the system continues to function optimally.
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What is the exponential regression equation to best fit the data where the y values were rounded to the nearest integer?
x y
0 12
1 21
2 40
3 73
4 135
Answers
y = 2.04. (2.51)ˣ is the exponential regression equation that fits the data to the precision of two decimal places the best.
What is an exponential regression equation?When the input variable x appears as an exponent in the formula f(x) = aˣ, an exponential function is indicated.
The exponential curve is influenced by both the exponential function and the value of x.
y=abˣ is the exponential equation.
Let's examine some of this equation's characteristics: 'b' must not be equal to one and must be bigger than zero; b>0, b1.
So, the given table is as follows:
x y
0 2
1 5
2 12
3 40
4 76
5 19
Put the values for x into one list and y into the other list at this point.
The scatter plot should now be graphed as seen in the attachment below.
We arrive at the exponent equation:
y = 2.035e⁰°⁹²⁰⁴ˣ
y = 2.035. (e⁰°⁹²⁰⁴)ˣ = 2.04.(2.51)ˣ
As a result, y = 2.04. (2.51)ˣ is the exponential regression equation that fits the data to the precision of two decimal places the best.
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Correct question:
What is the exponential regression equation to best fit the data? Round each value in your equation to two decimal places. Enter the answer in the box
x y
0 2
1 5
2 12
3 40
4 76
5 193
A farmer watered 3/8 of a felid. what percentage is equivalent to the fraction of the felid the farmer wanted?
Answers
The fraction 3/8 is equivalent to 37.5% as a percentage.
Define percentageA percentage can be used to represent a number as a portion of 100.. It is frequently employed to convey ratios, rates, and proportions in a more intelligible manner. One part in one hundred is represented by the percentage sign, which is %.
Define fractionA fraction is a measure of a ratio between two numbers or a portion of an entire. It has a horizontal line between the numerator and denominator. The denominator reflects the total number of pieces in the whole, whereas the numerator specifies how many parts are being taken into account.
To convert the fraction 3/8 to a percentage, we need to multiply it by 100.
So,
3/8 x 100 = 37.5%
Therefore, the fraction 3/8 is equivalent to 37.5% as a percentage.
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PLEASE
Describe one difference between the graph of y = nx^2 and the graph of
y = nx^3 for any rational number n.
Answers
Answer:
One difference between the graph of y = nx^2 and y = nx^3 is that the graph of y = nx^3 is steeper than the graph of y = nx^2 near the origin. This is because the power of x is one greater in the equation y = nx^3 than it is in the equation y = nx^2, which means that the rate of change of y with respect to x is increasing more rapidly in the former. As a result, the curve of y = nx^3 will be more curved and will have a steeper slope at the origin than the curve of y = nx^2.
Another difference is that the graph of y = nx^3 will have both positive and negative values for x and y, whereas the graph of y = nx^2 will only have positive values of y for positive values of x. This is because the exponent of x in y = nx^3 is odd, which means that the graph will pass through the origin and change signs as it crosses the x-axis. On the other hand, the exponent of x in y = nx^2 is even, so the graph will only have positive values for y when x is positive.
Step-by-step explanation:
Perimeter and area of
Answers
The perimeter and area of the rectangle are 14xy² + 20x² units and 70x³y² square units respectively.
The perimeter and area of the triangle are respectively.
The area of the trapezoid is 18x³y square units.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + B)
Where:
P represent the perimeter of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a perimeter of a rectangle, we have the following;
P = 2(L + B)
P = 2(7xy² + 10x²)
P = 14xy² + 20x² units.
For the area of rectangle, we have:
Area = LB
Area = 7xy² × 10x²
Area = 70x³y² square units.
For the perimeter and area of the triangle, we have:
Perimeter = 2a³b + 6a³b + 4ab = 8a³b + 4ab units.
Area = 1/2 × base × height
Area = 1/2 × 4ab × 2a³b
Area = 4a⁴b² square units.
For the area of trapezoid, we have;
Area of trapezoid, A = ½ × (a + b) × h
Area of trapezoid, A = ½ × (4xy + 8xy) × 3x²
Area of trapezoid, A = 6xy × 3x²
Area of trapezoid, A = 18x³y square units.
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A sign in a bakery gives these options:
12 cupcakes for $29
24 cupcakes for $56
50 cupcakes for $129
a. Find each unit price to the nearest cent.
Answers
The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.
Define unitary methοd.Tο cοmplete the assignment, use the tried-and-true straightfοrward methοdοlοgy, the real variables, and any pertinent details frοm the preliminary and specialized questiοns. In respοnse, custοmers might be given anοther οppοrtunity tο range sample the prοducts. In the absence οf such changes, majοr advances in οur knοwledge οf prοgrammes will be lοst.
Here,
We must divide the tοtal cοst by the quantity οf cupcakes in οrder tο determine the unit cοst οf each οptiοn:
Twelve cupcakes:
Unit cοst is calculated as Tοtal Cοst / Cupcakes.
=> Unit cοst: $29 fοr 12 cupcakes.
=> $2.42 is the unit cοst per cupcake.
Tο make 24 cupcakes:
Unit cοst is calculated as Tοtal Cοst / Cupcakes.
=> 24 cupcakes equals $56 fοr the unit.
=> $2.33 is the unit cοst per cupcake.
50 cupcakes =
Unit cοst is calculated as Tοtal Cοst / Cupcakes.
=> $129 fοr a unit οf 50 cupcakes.
=> Unit cοst: $2.58 fοr each cupcake
As a result, 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.
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A 2-column table with 6 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 9, negative 8, negative 7, 0, 19, 56.
What is the x-intercept of the continuous function shown in the table?
(0, –8)
(0, 2)
(–8, 0)
(2, 0)
Which interval contains a local minimum for this function?
Answers
In the given situation the required x-intercept is (2,0).
What is the x-intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Alternatively, we may state that the x-intercept is the value of the x coordinate of a position where the value of the y coordinate equals zero.
It is the value of the x-coordinate of the point where the graph intersects the x-axis.
So, the software displays a table of values for x and their corresponding values for the function f(x):
x f(x)
1 -9
0 -8
1 -7
2 0
3 19
4 56
The term "x-intercept" in the question refers to the value of x when f(x)=0.
When f(x) = 0, x equals 2 when analyzing the table.
To sum up, the x-intercept is (2,0)
Therefore, in the given situation the required x-intercept is (2,0).
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Correct question:
A 2-column table with 6 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 9, negative 8, negative 7, 0, 19, 56. What is the x-intercept of the continuous function shown in the table?
a. (0, –8)
b. (0, 2)
c. (–8, 0)
d. (2, 0)
what is 3(5x^2 - 9x) evaluated for x = -3
Answers
Answer:
216
Step-by-step explanation:
Answer:
216
Step-by-step explanation:
3(5x² - 9x)
3(5(-3)² - 9(-3))
3(5(9) - 9(-3))
3(45 + 27)
3(72)
216
help me it is asking to write this in a simplified fractions!
Answers
Answer:
[tex]-\frac{12}{35}[/tex]
Step-by-step explanation:
[tex]\frac{1}{15}[/tex] ÷ [tex]\frac{1}{12}[/tex] · -[tex]\frac{3}{7}[/tex]
[tex]\frac{1}{15}[/tex] ÷ [tex]\frac{1}{12}[/tex] = [tex]\frac{1}{15}[/tex] · 12 = [tex]\frac{12}{15}[/tex] = [tex]\frac{4}{5}[/tex]
[tex]\frac{4}{5}[/tex] · -[tex]\frac{3}{7}[/tex] = [tex]-\frac{12}{35}[/tex]
So, the answer is [tex]-\frac{12}{35}[/tex]
Yellowstone National park has an area of about 2.22 million acres. The table shows the estimated park populations for several animals. Find the population density in animals per square acres for each animal. Sounds your anger to the nearest ten thousand.
Answers
Using density, we can find the following:
There are about 0.00032 grizzly bears per acre.
There are about 0.0090 elks per acre.
There are about 0.00085 mule deer per acre.
There are about 0.0015 bighorn sheep per acre.
Define density?A measurement of the amount of data stored on a medium (tape or disk). The amount of data stored on magnetic tape is measured in bits per inch or millimetre; for discs, it is measured in a defined number of bits per sector, sectors per track and tracks per disc.
Density is calculated mathematically by dividing mass by volume.
Here in the question,
The national park is 2.22 million acres.
= 2,220,000 acres.
Now given,
Grizzly bears population = 728.
Elks' population = 20,000
Mule deer's population = 1900
Bighorn sheep's population = 345.
Now, to find density:
Density of Grizzly bears = 728/2220000
= 0.00032
Density of elk = 20,000/2220000
= 0.0090
Density of mule deer = 1900/2220000
= 0.00085
Density of bighorn sheep = 345/2220000
= 0.0015
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can someone pls help me with this and explain thanks!
Answers
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{37}\\ a=\stackrel{adjacent}{35}\\ o=\stackrel{opposite}{BD} \end{cases} \\\\\\ BD=\sqrt{ 37^2 - 35^2} \implies BD=\sqrt{ 144 }\implies BD=12 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{AD}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ AD=\sqrt{ 13^2 - 12^2}\implies AD=\sqrt{ 169 - 144 } \implies AD=\sqrt{ 25 }\implies \boxed{AD=5}[/tex]
Above are two different models of the same rectangular patio. If the area of the model on the left is 4 sq cm, what is the area of the model on the right? A. 29 sq cm B. 100 sq cm C. 20 sq cm D. 40 sq cm
Answers
the area of the model on the right is 100 sq cm.So, the answer is (B) 100 sq cm.in order to solve this use area of rectangle formula
what is area of rectangle ?
The area of a rectangle is the amount of space that is enclosed within its boundaries. It is the product of the length and width of the rectangle. The formula for the area of a rectangle is:
Area = length x width
In the given question,
Since the two models are of the same rectangular patio, they have the same length and width. Let the length of the rectangle be L and the width be W.
The area of a rectangle is given by the formula A = L x W.
For the model on the left, we are given that the area is 4 sq cm.
A = L x W = 4
For the model on the right, the length and width are both increased by a factor of 5. Therefore, the new length is 5L and the new width is 5W.
The area of the new rectangle is:
A = (5L) x (5W) = 25LW
We know that LW = 4 from the model on the left. Therefore:
A = 25LW = 25(4) = 100
Therefore, the area of the model on the right is 100 sq cm.
So, the answer is (B) 100 sq cm.
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Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 10 red pieces of candy out of 51 pieces
of candy total.
=
Choose the correct answer below.
(Round to three decimal places as needed.)
A. The individual events are dependent. The probability of the combined event is_____?
Or
B. The individual events are independent. The probability of the combined event is _____?
This question: 1 point(s)
possible
√i
Vi
Submit quiz
Answers
Answer:
Step-by-step explanation:
A. The individual events are dependent. The probability of the combined event is:
The probability of drawing a red piece of candy on the first draw is 10/51. Since we do not replace the candy after the first draw, the probability of drawing another red piece of candy on the second draw depends on what happened on the first draw. If a red piece of candy was drawn on the first draw, then there are 9 red pieces of candy left out of 50 total pieces of candy for the second draw. If a non-red piece of candy was drawn on the first draw, then there are still 10 red pieces of candy left out of 50 total pieces of candy for the second draw. Therefore, the probability of drawing two red pieces of candy in a row is:
(10/51) x (9/50) + (41/51) x (10/50) = 0.0698
Rounded to three decimal places, the probability of the combined event is 0.070.
1) Find the future value of $460 in 8 months, if the annual interest rate is 12%.
2) If you can earn 6% interest, what lump sum must be deposited now so that its value will be $3500 after 9 months? (Always convert time to years
3) Zach buys $2800 worth of furniture. He pays $400 down and agrees to pay the balance at 6% add-on interest for 2 years.
Find
a) the total amount to be repaid and
b) the monthly payment
Answers
1) The future value of $460 in 8 months, with an annual interest rate of 12% is $496.10.
2) The present value that must be deposited now so that its value will be $3,500 after 9 months is $3,350.34.
3a) The total amount to be repaid, including accumulated interest, for Zach's purchase of furniture worth $2,800 with a $400 down payment, is $2,552.87.
3b) The monthly payment is $106.37.
How the future value, present value, and monthly payments are determined:An online finance calculator can be used to determine the future value, present value, and monthly payments for 1), 2), and 3).
The future value is the present value compounded into the future at an interest rate.
The present value is the future value discounted to the present period at an interest rate.
1) Future Value:N (# of periods) = 0.6667 years (8/12 months)
I/Y (Interest per year) = 12%
PV (Present Value) = $460
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $496.10
Total Interest = $36.10
2) Present Value:N (# of periods) = 0.75 years (9/12 years)
I/Y (Interest per year) = 6%
PMT (Periodic Payment) = $0
FV (Future Value) = $3,500
Results:
Present Value (PV) = $3,350.34
Total Interest = $149.66
3) Down Payment:The cost of furniture bought by Zach = $2,800
Down payment = $400
Loan amount - $2,400 ($2,800 - $400)
Interest rate = 6%
Loan period = 2 years.
N (# of periods) = 24 months (2 years x 12)
I/Y (Interest per year) = %6
PV (Present Value) = $2,400
FV (Future Value) = $0
Results:
Monthly Payment (PMT) = $106.37
Sum of all periodic payments = $2,552.87
Total Interest = $152.87
The total amount to be repaid = Loan amount + Accumulated Interest
= $2,552.87
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Solve and explain the following: if F(x) = -5 - 7x, find F(-2).
Answers
The value of the function as f(-2) is 9
What are functions?Functions are simply described as those equations, expressions, or laws that explains or shows the relationship between two variables.
These two variables are namely;
The dependent variableThe independent variableFrom the information given, we have that;
f(x) = -5 - 7(x)
substitute the values of x as -2
Then, we have;
f(-2) = -5 - 7(-2)
expand the bracket
f(-2) = -5 + 14
Add the values, we have;
f(-2) = 9
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I need help with this sequence to find an explicit equation or formula.
the sequence is 800 600 450 and I think 337.1 I may be incorrect since I am basing that off in class and had trouble solving it.
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The next term in the sequence is approximately 337.50.
The explicit equation or formula for this sequence is:
an = 800 × (0.75)n-1
What is the explicit equation for the sequence?To find the explicit equation or formula for this sequence, we need to determine the pattern or rule that generates the sequence.
If we look at the first three terms of the sequence, we can see that each term is obtained by multiplying the previous term by a certain fraction or ratio:
To get from 800 to 600, we divide by 1.3333... (or multiply by 0.75)To get from 600 to 450, we divide by 1.3333... (or multiply by 0.75)Therefore, we can assume that the next term in the sequence is obtained by dividing the previous term by 1.3333... (or multiplying by 0.75):
To get the next term, we divide 450 by 1.3333... (or multiply by 0.75):
450 ÷ 1.3333... ≈ 337.50
So the next term in the sequence is approximately 337.50.
Therefore, the explicit equation or formula for this sequence is:
an = 800 × (0.75)n-1
Where;
n is the position of the term in the sequence (starting with n = 1 for the first term), and an is the value of the nth term in the sequence.Learn more about sequence here: https://brainly.com/question/6561461
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Need help
Solve for angle A
A°= 117+ ?
———
2
Answers
The solved answer for a is 125
What is a chord in mathematicsIn mathematics, a chord is a line segment that connects two points on the circumference of a circle. Specifically, a chord is any line segment that has its endpoints on the circle.
The length of a chord can be found using the Pythagorean theorem, given the length of the radius of the circle and the distance between the endpoints of the chord. The chord is also an important concept in geometry and trigonometry, as it forms the basis of many geometric shapes and formulas.
The formula says that a = b + c / 2
a = 117 + 133 / 2
a = 250 / 2
a = 125
The measure of a = 125
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The following figure is made of 1 triangle and 1 rectangle 5,6,9
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The area of the triangle is 12 square units. The area of the rectangle is 30 square units. The area of the whole figure is 42 square units,
What is area?A two-dimensional surface's area, such as the surface of a shape or item, can be measured. Typically, it is expressed in terms of square measurements, such as square metres (m2) or square feet (ft2). The length and width of a rectangle can be multiplied to determine the area of a shape, or alternative formulas, like base times height divided by two for a triangle, can be used for other shapes.
The area of triangle is:
A = 1/2*b*h
A= 1/2*4*6=12 square units
A = 12 square units
The area of rectangle is:
B = 6(5) = 30 sq. units,
The area of the whole figure is:
A + B = 12 + 30 = 42 square units.
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The complete question is:
I really really really need someone help
Answers
Answer:
[tex]m = \frac{13.0 - 11.2}{14 - 4} = \frac{1.8}{10} = \frac{9}{50} [/tex]
[tex]13 = \frac{9}{50} (14) + b[/tex]
[tex] \frac{650}{50} = \frac{126}{50} + b[/tex]
[tex]b = \frac{524}{50} [/tex]
[tex]y = \frac{9}{50} x + \frac{524}{50} [/tex]
Today Ian wants to run less than 7/12 mile. Write a fraction with a denominator of 4 to respresent a distance that is less than 7/12 miles.(HELP PLEASE ANSWER THISSSS)
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A certain forest covers an area of 4900 km². Suppose that each year this area decreases by 3.5%. What will the area be after 10 years?
round your answer to the nearest square kilometer.
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Answer:
Below
Step-by-step explanation:
The formula to calculate the final area after a certain percentage of decrease for a given number of years is:
Final area = Initial area x (1 - percentage decrease)^number of years
In this case, the initial area is 4900 km² and the percentage decrease is 3.5%.
We need to calculate the final area after 10 years.
First, we need to convert the percentage decrease to a decimal:
3.5% = 0.035
Substituting the values into the formula, we get:
Final area = 4900 km² x (1 - 0.035)^10
Final area = 4900 km² x 0.6657
Final area = 3260.93 km²Rounding to the nearest square kilometer, the area of the forest after 10 years will be 3261 km².
Factor the following polynomial.
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After applying the difference of squares procedure , the factors we get =(7y + 5z)(7y - 5z)
Describe factor?Finding the factors of a given statement is a procedure known as factoring.
For instance, the factors of 12 are 1, 2, 3, 4, 6, and 12 are. The components of x²+ 5x + 6 are (x + 2) and (x + 3), respectively.
What is the square formula difference?Factorization of polynomials is a specific instance of the difference of squares formula. It claims that the product of two squares' sum and differences may be calculated using their difference.
A difference of squares expression is, for instance, a² - b² = (a + b)(a - b).
the phrase 49y² - 25z² can be factored, where
a² - b² = (a + b).(a - b).
Where a=49 , b = 25
After applying the difference of squares procedure, the phrase 49y² - 25z² can be factored, where a² - b² = (a + b).(a - b).
Consequently, 49y - 25z
= 7y + 5z(7y - 5z).
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you are running in the 100 meter dash. from the starting line, you sprint up to 42m/sec at the accelertion rate of 2 m/s/s/ down the track to win the race How long did it take you to win the race.
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it took the runner 21 seconds to win the race
What are Distance and velocity ?
velocity is a unit of measurement for the Distance an object travels in a
the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by
dividing the total Distance traveled by the journey time.
We want to find t, so we can rearrange the equation to isolate t:
t = (v - u) / a
Substituting the values we have:
t = (42 m/s - 0 m/s) / (-2 m/s^2)
t = -21 s
Wait a minute, why is the time negative? That's because we chose a coordinate system where positive is in the direction of motion, and negative is opposite to it. In other words, the runner is going in the negative direction of the x-axis, so the displacement (100 meters) is negative. Therefore, the time is negative as well. However, we can take the absolute value of time to get the magnitude:
|t| = |-21 s| = 21 s
So it took the runner 21 seconds to win the race (assuming constant acceleration, which may not be realistic for human sprinters).
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I forgot my angles. I’ll please help.
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The name of types of angles shown in the diagram is straight angles, right angle, and supplementary angles.
What are supplementary angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if you have two angles, and the sum of those angles is 180 degrees, then those two angles are supplementary. For example, if one angle is 60 degrees, then the other angle would be 120 degrees in order for them to be supplementary. Supplementary angles can be adjacent (share a common vertex and side) or non-adjacent (do not share a common vertex or side).
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