To make the polynomial monic, divide even by leading term first.
Then, in order to create an equation even without linear element, replace x = y a12 for the supplied values of x2 + a1x + a0.
A monic polynomial is what?A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.
x3=y3 and y2=x2+xy+y2.
Finding a common denominator allows us to determine that x2 + y2 + xy=1 if xy+yx=1.
By multiplying by xy:
x2+y2=−xy
move every term to the left:
x2+xy+y2=0
Consequently, x3y3=(xy)(x2+xy+y2)=(xy)
x/y+y/x+1=0
=>(x²+y²+xy)/xy=0/1
=>x²+xy+ y²=0——(1)
Now, Since,x³-y³=(x-y)(x²+xy+y²)
=>x³ -y³=(x-y)(0). [from equation (1)]
=>x³ -y³=0,Ans.
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What is the condition for a triangle whose two sides are 6cm 8cm then the third side is?
Answer:
10cm
Step-by-step explanation:
Pythagoras
(6×6) + (8×8) = □×□
36 + 64 = 100
square root of 100 = 10
Answer:
Step-by-step explanation:
The condition for a triangle whose two sides are 6cm and 8cm is the triangle should be right angled triangle.
so by this condition,
=> (hypotenuse)^2 = (base)^2 + (perpendicular)^2
=> (hypotenuse)^2 = (6)^2 + (8)^2
=> hypotenuse = 10 cm
so the thisrd side of triangle is 10cm.
in a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). the probability of rolling doubles with one roll of two fair six-sided dice is 16 . what is the probability that it takes three rolls until the player rolls doubles?
The probability of rolling doubles with three rolls of two fair six-sided dice is 0.512.
How do you calculate probability?
Probability is the likelihood that something will happen. Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes.
The probability of rolling doubles with one roll of two fair six-sided dice is 16/36, or 1/6. This means that the probability of not rolling doubles with a single roll is 5/6.
The probability of not rolling doubles with two rolls is (5/6)^2, or 25/36.
The probability of not rolling doubles with three rolls is (5/6)^3, or 125/216.
Therefore, the probability of rolling doubles with three rolls of two fair six-sided dice is (216-125)/216, or 91/216, or 0.512.
P(doubles on 1 roll) = 1/6
P(not doubles on 2 rolls) = (5/6)^2 = 25/36
P(not doubles on 3 rolls) = (5/6)^3 = 125/216
P(doubles on 3 rolls) = 1 - (125/216) = 91/216 = 0.512
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two components of a minicomputer have the following joint pdf for their useful lifetimes x and y. what is the probability that the lifetime x of the first component exceeds 3?
Therefore , the solution of the given problem of probability comes out to be 1/ ( 1+ y)x².
What precisely is involved in the probability process?Evaluating the chance that a claim is true or that a particular event will happen is the focus of the mathematical field known as probability theory. A chance can be represented by any number between 0 and 1, with 1 denoting certainty and 0 typically expressing the possibility of occurrence. The possibility or possibility that a happening will occur is represented diagrammatically as probability. Figures 0 and 1, percentage ranging 0% - 100%, and some other characters can be used to represent probabilities. the percentage of times, out of all possible possibilities, that an incidence occurred within a good set with equally likely options.
Here,
Probability for X (for x≥0)
=> [tex]\int\limits^{ \infty}_{ 0}[/tex]x e⁻ˣ⁽¹⁺ⁿ⁾ dy
=> -e⁻ˣ [tex]\int\limits^{ \infty}_{ 0}[/tex]de⁻ˣⁿ
=>e⁻ˣ
Probability for X exceed 3
=> [tex]\int\limits^{ \infty}_{ 3}[/tex]f(x)dx
=> [tex]\int\limits^{ \infty}_{ 3}[/tex]e⁻³dx
=> e⁻³
Probability for y ≥ 0
=> [tex]\int\limits^{ \infty}_{ 3}[/tex]xe⁻ˣ⁽¹⁺ⁿ⁾ dy
=> [tex]\int\limits^{ \infty}_{ 3}[/tex]x/1 + y d e⁻ˣ⁽¹⁺ⁿ⁾ = 1/ ( 1+ y)x²
Therefore , the solution of the given problem of probability comes out to be 1/ ( 1+ y)x².
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6.50 and each adult ticket sells for $11.50. The drama club must make a minimum of $1300 from ticket sales to cover the show's costs. Write an inequality that could represent the possible values for the number of student tickets sold, ss, and the number of adult tickets sold, aa, that would satisfy the constraint.
The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The dramatization club is offering passes to their play to fund-raise for the show's costs. Every understudy ticket sells for $6.50 and every grown-up ticket sells for $11.50. The dramatization club should make at least $1300 from ticket deals to take care of the show's expenses.
Let 's' and 'a' be the number of tickets sold to students and adults, respectively. Then the inequality is given as,
6.5s + 11.5a ≥ 1300
The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.
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Find the slope of the line represented by the data below
Answer:
-4
Step-by-step explanation-
y2-y1
-------- = m = slope
x2-x1
8-12 -4
--------- = ---- = -4
-2-(-3) 1
How would I solve this?
The price of one slice of pizza is $3.5, and the price of one drink is $3.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x be the price of one slice of pizza and y be the price of one drink.
The system of equations can be written as:
3x + 2y = 16.50
4x + 4y = 26
To find the price of one slice of pizza and the price of one drink, we can use the substitution or elimination method.
After solving the equation for x and y we get the values as:
x = 3.5 and y = 3
So, the price of one slice of pizza is $3.5, and the price of one drink is $3.
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what is the largest possible quotient of a positive 3-digit number divided by the sum of its digits, if the 3 digits must be different
The largest possible quotient of a positive 3-digit number divided by the sum of its digits if the 3 digits must be different is 41
How to calculate for the largest possible quotientThe largest possible quotient of a positive 3-digit number divided by the sum of its digits is obtained when the 3 digits are as large as possible, subject to the constraint that they must be different.
The largest possible 3-digit number is 987, which has digits 9, 8, and 7.
The sum of its digits is 9 + 8 + 7 = 24.
The quotient of 987 divided by 24 is:
987/24 = 41.125
otherwise when expressed as a mixed number is read as 41 whole number 3/24
In conclusion, the largest possible quotient of a positive 3-digit number divided by the sum of its digits, when the 3 digits must be different, is 41.
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what refrence tool is uses to determine how the fiber is to be orientated for for a particular ply of fabric
A reference tool that is used to determine how the fiber is to be orientated for a particular ply of fabric is called a lay plan or lay direction.
A lay plan is a detailed diagram that shows the orientation of fibers in each layer of a fabric, and it is used as a guide for the manufacturing process. The lay plan indicates the direction in which the fibers should be oriented in each layer of the fabric, which is essential for achieving the desired strength, stretch, and durability of the final product.
The lay plan is also used to ensure that the fibers are aligned in the same direction in each layer, which helps to prevent warping or other issues that can occur during manufacturing.
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Expense Amount
Rent payment $953. 20/month
Auto payment $165. 87/month
Telephone $56. 98/month
Auto insurance $714. 36/six months
Once-a-week outing $35. 00/week
Using the table, what are your total monthly fixed expenses?
$ your answer goes here /month
Using the table your total monthly fixed expenses is 977.43.
Rent payment $953. 20/month
Auto payment $165. 87/month
Telephone $56. 98/month
Auto insurance $714. 36/six months
Once-a-week outing $35. 00/week
= 953.20 + 165.87 + 56.98 + 714.36/6 + (35*4)
= 1435.11
= 2412.54 - 1435.11
=977.43.
An expense is something that calls for the transfer of funds, or fortune in general, from one person or organization to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students. Purchasing anything like food, clothing, furniture, or a car is frequently referred to as a cost.
A cost that is "paid" or "remitted" usually in exchange for anything of value is referred to as an expense. "Expensive" refers to something that appears to be very expensive. "Inexpensive" refers to something that appears to be inexpensive. "Expenses of the table" include costs associated with eating, drinking, a feast, etc.
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at a local college, an admissions officer surveys the incoming class of 1,000 first-year students concerning their preference of major. the officer randomly selects 100 of them and asks if they intend to major in liberal arts. of the 100 first-year students, 62 state they intend on majoring in liberal arts. assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts?
The 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is estimated to be between 0.58 and 0.66.
To calculate the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts, we need to calculate the point estimate and margin of error. The point estimate is the proportion of first-year students who stated they intend on majoring in liberal arts
(62/100 = 0.62).
The margin of error is 1.96 times the standard error
(SE = √(p(1-p)/n) = √(0.62(1-0.62)/100) = 0.04).
The lower bound of the 95% confidence interval is the point estimate minus the margin of error
(0.62 - 0.04 = 0.58).
The upper bound of the 95% confidence interval is the point estimate plus the margin of error
(0.62 + 0.04 = 0.66).
Therefore, the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is estimated to be between 0.58 and 0.66.
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3. A mature blue whale may have a length of 28.0 m. How far from a con-
cave mirror with a focal length of 30.0 m must a 7.00-m-long baby blue
whale be placed to get a real image the size of a mature blue whale?
Answer:
2.00 m in front of the concave mirror with a focal length of 30.0 m
Step-by-step explanation:
To find the distance from a concave mirror with a focal length of 30.0 m at which a 7.00-m-long baby blue whale must be placed to get a real image the size of a mature blue whale, we can use the mirror equation:
1/u + 1/v = 1/f
Where u is the distance between the object and the mirror, v is the distance between the image and the mirror, and f is the focal length of the mirror.
We know that v is negative because the image is real, and the same size of the mature blue whale that is 28m.
So, we can substitute the values we know into the equation:
1/u - 1/28 = 1/30
We can solve for u by multiplying both sides by 30u and getting:
30 - 28u = u
So u = 2m
Therefore, the 7.00-m-long baby blue whale must be placed 2.00 m in front of the concave mirror with a focal length of 30.0 m to get a real image the size of a mature blue whale.
si A/4 = B/9 y A + B = 169; halle el valor de "A"
El número A = 52 es una solución del sistema de ecuaciones lineales.
¿Cómo resolver un sistema de ecuaciones lineales mediante métodos algebraicos?
En esta pregunta tenemos un sistema de dos ecuaciones lineales con dos incógnitas, de modo que existe la posibilidad de una solución única. Primero, escriba el sistema de ecuaciones descrito en el enunciado de la pregunta:
A / 4 = B / 9
A + B = 169
Segundo, despeje la variable A de la segunda ecuación del sistema de ecuaciones:
B = 169 - A
Tercero, elimine la variable B en la primera ecuación del sistema de ecuaciones y despeje la variable A:
A / 4 = (169 - A) / 9
9 · A = 4 · (169 - A)
9 · A = 676 - 4 · A
13 · A = 676
A = 52
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A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns. chosse from the below option.a)Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solutionAnswer: (Type an ordered pair here _____)x1=2, x2=4, x1+x2=6b) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solutionAnswer: (Type an ordered pair here _____)x1=2, x2=4, x1+x2=8c)No, overdetermined systems cannot be consistent because there are fewer free variables than equations. For example, the system of equations below has no solution.x1=2, x2=4, x1+x2=12d)No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.x1=2, x2=4, x1+x2=24
a) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (2,4)
x1=2, x2=4, x1+x2=6
An overdetermined system of linear equations can have infinitely many solutions if the equations are dependent, meaning they are linearly dependent and can be derived from one another by a linear combination. If a system of equations is dependent, it means that the equations are not providing new information.
b) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.
x1=2, x2=4, x1+x2=8
An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.
d) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.
x1=2, x2=4, x1+x2=24
An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.
c) is not a valid option as it contains a mix of concepts of dependent and independent systems and also the system of equations is inconsistent.
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How many edges does this polyhedron have?
The polyhedron with 10 vertices and 7 faces has 15 edges.
What is polyhedron?
A polyhedron is a three-dimensional object or solid that has flat faces, straight edges, and sharp corners or vertices. It is a geometric shape that is bounded by a finite number of polygons, which are shapes with straight sides.
Based on the Euler's formula for polyhedra, which states that the number of vertices plus the number of faces minus the number of edges is always equal to 2, we can solve for the number of edges:
10 (vertices) + 7 (faces) - E (edges) = 2
Simplifying the equation:
10 + 7 - E = 2
17 - E = 2
E = 17 - 2
E = 15
Therefore, the polyhedron with 10 vertices and 7 faces has 13 edges.
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the distance between Orlando and jacksonville
The distance between Orlando and Jacksonville is approximately 230 miles.
What is the distance?
Distance refers to the measurement of the separation between two points in space. It can be thought of as the length of the path between two points, and it can be measured in various units such as meters, feet, miles, kilometers, etc.
The distance between Orlando and Jacksonville is approximately 230 miles (370 km) if you take the most direct route by car. The driving distance between Orlando and Jacksonville is around 4 hours and 30 minutes. It could vary depending on the route taken and traffic conditions.
Hence, the distance between Orlando and Jacksonville is approximately 230 miles.
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Identify the true statements about the correlation coefficient, ????. if two variables are negatively correlated, when one variable increases, the other variable also increases. the correlation coefficient is not affected by outliers. a correlation coefficient of zero means that no relationship exists between the two variables. the sign of ???? describes the direction of the association between two variables. when the data points in a scatter plot are randomly scattered, the correlation between the two variables is weak. the value of ???? ranges from negative one to positive one.
a. Since both a strong-positive and weak-positive correlation are formally considered to be "growing," this is ambiguous (positive slope). In the same way, negative correlation. Speaking strictly in terms of truth or untrue, I would classify this as false
b. This is once more a little tricky. When "r" is zero, there isn't any evidence of a linear link. It doesn't necessarily follow that the variables don't correlate with one another. The answer is probably True if this is a course on statistics for beginners. If not, False.
c. This is simple to understand. Inverse relationships are indicated by negative coefficients. One grows while the other shrinks (or vice versa). False.
d. The range of the coefficient r is [0, 1] (inclusive), not (0,1). In this case, True if the text suggests [0,1].
e. Simple and accurate
f. Plain and simple, FALSE. Quite a high correlation coefficient
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Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter your answer using interval notation.)r(t)=8t^2i+7t^3j
The curve is smooth for [tex]t\neq 0[/tex] on the intervals (-∞, 0), (0, ∞)
We have to consider the curve
[tex]r(t) = 8t^{2}i + 7t^{3}j[/tex]
Now, the objective is to find the open intervals when on which the curve given by the vector valued function is smooth, using the result.
The parametrization of the curve represented by the vector valued function
[tex]r(t) = f(t)i + g(t)j + h(t)k[/tex]
This equation is smooth on an open interval when f'(t), g'(t), and h'(t) are continuous on [tex]l[/tex] and r'(t) [tex]\neq[/tex] 0 for any value of t in the interval.
Now, we know the vector equation:
[tex]r(t) = 8t^{2}i + 7t^{3}j[/tex]
Differentiating r(t) with respect to r,
[tex]r'(t) = 16t i + 21t^{2} j[/tex]
At t = 0, equate r'(t) = 0.
[tex]r'(0) = 16(0) + 21(0)^{2}[/tex]
Therefore, the curve is smooth for all values except 0, as we can see above.
Hence, the curve is smooth for [tex]t\neq 0[/tex] on the intervals (-∞, 0), (0, ∞).
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compute the linear correlation coefficient. round to three decimal places. x2 y2 10 8.14 8 7.14 13 7.74 9 7.77 11 8.26 14 7.10 6 5.13 4 2.10 12 8.13 7 6.26 5 3.47
The word "correlation" is made by join forces the words "co" and "relation". The word "co" means jointly, thus, correlation means the relationship between any set of data when examine together.
In Statistics, the correlation coefficient is a compute defined between the numbers -1 and +1 and act for the linear interdependence of the set of data.
This data is then divided by the product of standard deviations for these variables.
The equation given below recap the above concept:
ρxy=Cov(x, y)/σxσy
Cov(x,y)=covariance of variables x and y
σx=standard deviation of x.
σy=standard deviation of y.
1. For a positive correlation: the values increase together.
2. For a negative correlation: one value decreases as the other increases.
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Extending Voting Rights
Voting rights for various segments in the United States was extended in stages from the time the United States gained independence, to the late 1900s.
How have voting rights been extended in the United States ?In the late 1700s and early 1800s, voting rights were expanded to include more people, such as white men who owned property. The 15th Amendment was ratified in 1870, and prohibits the federal and state governments from denying a citizen the right to vote based on that citizen's "race, color, or previous condition of servitude."
The 19th Amendment was then ratified in 1920, and prohibits the federal and state governments from denying the right to vote to citizens of the United States on the basis of sex. Then the Voting Rights Act of 1965 was passed to overcome legal barriers at the state and local levels that denied African Americans the right to vote under the 15th Amendment. It was one of the most effective pieces of legislation passed during the Civil Rights Movement.
The 26th Amendment lowered the national voting age from 21 to 18 for all federal, state, and local elections.
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Full question is:
Extending Voting Rights; how have voting rights been extended in the United States since independence ?
a card is drawn at random from a standard $52$-card deck. what is the probability that it is an odd number ($3,$ $5,$ $7,$ $9$) or a $\spadesuit$ (or both)?
The probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.
Now, According to the question:
We are informed that a card is drawn at random from a standard 52-card deck.
We are asked the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit.
We assume the event of drawing an odd card from the random pick to be A, and the event of drawing a card of spade suit to be B.
The number of outcomes favorable to event A = 16 {4 odd cards of each of the 4 suits, that is, 4×4 = 16}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of event A, P(A) = 16/52.
The number of outcomes favorable to event B = 13 {The 13 cards of spade suit}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of event B, P(B) = 13/52.
The number of outcomes favorable to events A and B both = 4 {4 odd cards of the spade suit}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of events A and B both, P(A ∩ B) = 4/52.
The probability that the randomly drawn card is an odd number or of spade suit is represented by P(A ∪ B), which is calculated by the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 16/52 + 13/52 - 4/52 = 25/52.
Hence, the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.
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true/false. The expected result of the experiment would be for the markers to have shifted adjacently to each other. If the scientist sees no movement, the results could be interpreted as the markers were placed on plates moving similarly, which could cause little to no change in distance.
The experiment's predicted outcome is that the markers will either be farther apart or closer together, proving that the tectonic plates are in fact moving and not static.
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The likelihood that an event will occur increases with its probability.
A straightforward illustration is tossing a fair (impartial) coin.
The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).
Hence, The experiment's predicted outcome is that the markers will either be farther apart or closer together, proving that the tectonic plates are in fact moving and not static.
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Find the slope passing the line (3,4) and (8, -3)
Answer: -1 2/5 i think im not sure (check explaination)
Step-by-step explanation:
slope formula= y2-y1/x2-x1
-3-4/8-3=-7/5,-1 2/5
find the general solution of the given higher-order differential equation. y(4) + y''' + y'' = 0, y(x) =
The general solution of the given higher-order differential equation is y(x) = e2x + x2 + c4e3x + c5e-3x.
What is general solution?A general solution is an answer that can be applied to a wide range of problems. It is a broad-based approach that can be used to solve any problem, regardless of its complexity or specific details. General solutions take into account the overall goal of a problem, rather than its individual elements, and look for a way to achieve the desired result. Additionally, they are often easy to implement and can be applied to a variety of scenarios.
The general solution of the given higher-order differential equation, y(4) + y''' + y'' = 0, is given by
y(x) = c1e2x + c2e-2x + c3x2 + c4e3x + c5e-3x + c6x3.
Here, c1, c2, c3, c4, c5 and c6 are constants of integration.
To determine the values of these constants, we must use initial conditions. Suppose we are given y(0)=1 and y'(0)=2, then we can solve for the constants using this information.
Substituting y(0)=1 and y'(0)=2 into the equation, we get
1 = c1 + c2 + c3(0)2 + c4 + c5 + c6(0)3
2 = 2c3 + 3c6(0)2
Solving these equations, we get c1 = 1, c2 = 0, c3 = 1 and c6 = 0.
Therefore, the general solution of the given higher-order differential equation is
y(x) = e2x + x2 + c4e3x + c5e-3x.
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lin rides 6 miles on her bike in 48 minutes at a constant speed how many minutes per mile does she ride
The number of minutes per mile that Lin does ride will be 8 minutes per mile.
Lin rides at a speed of 6 miles / 48 minutes = 0.125 miles per minute. For us to convert this to minutes per mile, we have to take the reciprocal of this value, which is 1 / 0.125 = 8 minutes per mile.
To convert speed from miles per minute to minutes per mile, you can take the reciprocal of the value which means is the upside value and top. In this case, 0.125 miles per minute to minutes per mile is 8 minutes per mile.
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the length of the freeway is 600 miles. if 0.5 inch represents 50 miles, what is the length of the freeway on the map? a. 10 inches c. 12 inches b. 6 inches d. 3 inches
As per the ratio proportion, the length of 600 miles freeway is 6 inches on the map.
What is ratio proportion?
Ratio proportion is an equation where two sides of it are equal. A ratio or proportion maintains the equality between two fractions.
Given, 0.5 inches represent 50 miles.
Let, x inches represent 600 miles.
Therefore, as per the ratio proportion, we can write:
0.5 : 50 = x : 600
⇒ 0.5/50 = x/600
⇒ x = (600 × 0.5)/50 = 6.
Therefore, the length of 600 miles freeway is 6 inches on the map.
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A movie theater sends out a coupon for 35% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant. The equation is y=
The value of the equation is y = 0.75x , where y is the total cost of the ticket and x is the original cost of the ticket
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the original cost of the ticket be represented as x
Let the discounted price of the ticket be y
Now , the percentage of discount = 35 %
So , the discounted price of the ticket y = original cost of the ticket - ( 35/100 ) x original cost of the ticket
Substituting the values in the equation , we get
The discounted price of the ticket y = x - 0.35x
On simplifying the equation , we get
The discounted price of the ticket y = 0.75x
y = 0.75x be equation (1)
Now , the cost of the ticket cannot be a negative value so it should lie in the first quadrant
Hence , the equation is y = 0.75x
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The proportional relationship between the number of songs Nolan downloads, s, and the total cost in dollars and cents, c, can be represented by the equation c = 0. 35s. How much does it cost to download a single song?
Please I need help!!!
A single song may be downloaded for $0.35. Adjusting the solution c = 0.35s yields the answer because c/s = 0.35.
Equation: What is it?An equation is an mathematical statement that uses an equal sign to express the relationship across two or more objects, such as variables or integers. Equations can be used to represent relationships between physical, chemical, and other sorts of events as well as to solve mathematical problems. An equation in mathematics is a claim made regarding the equivalence of two expressions. A assertion claiming two expressions equal equal is what an equation is, in other words.
This indicates that each music download costs $0.35. Consequently, it costs $0.35 to buy a single song.
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(Graphing Linear Equations MC)
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $120, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Answer:
"going from the point 0 comma negative 120 through the point 2 comma negative 100"
Step-by-step explanation:
Let y be the total income from the homecoming dance, and x the number of students who purchase tickets (at $10 each). We are told that it costs $120 for the decorations.
The income from ticket sales would be:
1) the number of tickets sold times $10/ticket, or $10
2) Less the expenses of decorating (-$120)
We can write the total income as:
y = $10x - $120
The graph of this function would be a straight line that has a y-intercept of -$120. Before any ticket is sold, the cost of decorations must be considered. If no tickets are sold (x=0), the total income is -$120.
Using the equation, we can calculate the income when 2 tickets are sold (x=2):
y = $10x - $120
y = $10*(2) - $120 [two tickets sold]
y = -$100
Summary
y = $10x - $120
(0,-$120)
(2,-$100)
This matches the statement "going from the point 0 comma negative 120 through the point 2 comma negative 100" provided in the answer options.
See the attached graph.
Given the function f(x)=3x^5 and g(x)=7*4^x, Which statement is true
A. f(5)>g(5)
B.f(5)
C.f(5)=g(5)
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
What is a function?The process of evaluating a function is typically straightforward when we have the function in the form of a formula. For instance, it is possible to evaluate the function f(x)=53x2 by first squaring the input number, multiplying by 3, and then subtracting the result from 5.
The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x.
To determine the outcome, simplify the values. The abscissa is the x value of the point (x, y). It shows how far a point is from the origin or from the x-axis' horizontal axis.
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Solve the problem. Express your answer to the correct number of significant figures. 6.221 x 7.11 - 13.7
The answer in the correct number of significant figures is 30.5.
What is the significant figure?
Significant figures are the number of digits in a value, often a measurement, that contributes to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.
We have given,
6.221 × 7.11 − 13.7
first, we determine the product of 6.221 and 7.11 and round the value to a minimum number of significant figures which is "3" since 7.11 has "3" significant figures and 6.221 has "4" significant figures
so Product = 6.221 × 7.11 = 44.2
now we do the subtraction and round the answer to a minimum decimal number
44.2 - 13.7
30.5
Hence, the answer in the correct number of significant figures is 30.5.
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