The boat is approximately 515 feet away from the lighthouse.
To find the distance from the boat to the lighthouse, we can use trigonometry. The angle of depression from the person to the boat is 28°, and the height of the lighthouse is 200 feet. Let's call the distance from the boat to the lighthouse x. Using the tangent function, we have
tan 28° = 200 / x.Solving for x, we have x = 200 / tan 28°. Approximating this value using a calculator, we have x ≈ 514.7 feet. Rounding to the nearest foot, the boat is approximately 515 feet away from the lighthouse.
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a faucet is turned on at 9:00am and water starts to flow into a tank at the rate of r(t)=7t√, where t is time in hours after 9:00am and the rate r(t) is in cubic feet per hour.
7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.
The equation r(t) = 7t √ represents the rate at which water is flowing into the tank, measured in cubic feet per hour, at time t after 9:00am. The expression 7t √ means that the rate of flow increases over time, starting at 0 cubic feet per hour at t = 0 and increasing as t increases.
To find the volume of water in the tank at a specific time t after 9:00am, we can integrate the rate of flow over the time interval from 9:00am to t. The volume of water in the tank at time t can be expressed as:
V(t) = ∫ r(t) dt from 9:00am to t
= ∫ 7t √ dt from 0 to t
= 7/3 t^(3/2) + C
where C is an arbitrary constant of integration. This equation represents the volume of water in the tank as a function of time t.
Therefore, 7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.
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for the matrices a = −3 2 1 4 and b = 5 1 0 −2 in m2,2, determine whether the given matrix is a linear combination of a and b. −19 4 3 16
The given matrix is non linear matrix combination of a and b matrix.
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
An equation in which the maximum degree of a term is 2 or more than two is called a nonlinear equation.
Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics.
Given that,
a = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right][/tex]
b = [tex]\left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex]
The given matrix is a linear combination of a and b
a - b = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right] - \left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
a - b = [tex]\left[\begin{array}{ccc}-3-5&2-1\\1-1&4-0\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
Therefore,
The given matrix is non linear matrix combination of a and b matrix.
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
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Bob buys some apples for $16.50. If bob buys 4.4 pounds of apples, what is the price per pound
Answer: The price per pound of apples is $3.75.
Step-by-step explanation:
A cell phone plan costs $19.80 per mouth for 500 minutes of talk time. It costs an additional $0.09 per minute for each minute over 500 minutes. To get e-mail access, it costs 20% of the price for 500 minutes of talk time. Your bill, which includes e-mail, is the same each mouth for 7 mouths. The total cost for all 7 mouths is $212.31. Write and solve an equation to find the number of minutes of talk time you use each mouth.
So you use 73.02 minutes of talk time each month.
What is a cell phone?Cell phone is a portable electronic device that allows you to make calls, send messages, and perform various tasks such as browsing the internet.
Let x be the number of minutes of talk time you use each month.
The cost for the talk time each month is 19.80 + 0.09(x - 500), and the cost for e-mail is 0.2 * 19.80 = 3.96.
So, the total cost each month is 19.80 + 0.09(x - 500) + 3.96 = 23.76 + 0.09x - 46.04.
The total cost for 7 months is 7 * (23.76 + 0.09x - 46.04) = 166.32 + 0.63x.
We want to find the value of x that makes the total cost equal to $212.31, so we write:
166.32 + 0.63x = 212.31
Solving for x, we have:
0.63x = 45.99
x = 73.02
So you use 73.02 minutes of talk time each month
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Explain how to ue a table to write an equation that repreent the relationhip in the table
A table can be used to write an equation that represents the relationship in the table by using the values in the table to determine the coefficients of the equation.
Here's how you can use a table to write an equation:
1. Identify the dependent and independent variables in the table. The dependent variable is the value that depends on the independent variable.
2. Choose one of the variables as the dependent variable and write the equation in terms of the dependent variable.
3. Use the values in the table to find the coefficients of the equation. For example, if the independent variable is x and the dependent variable is y, you can use the values in the first column for x and the values in the second column for y to find the coefficients.
4. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for a unit change in x, and the y-intercept represents the value of y when x is 0.
5. Substitute the coefficients from step 3 into the equation from step 4.
6. Check your equation by plugging in the values from the table and verifying that they match the corresponding values in the dependent variable column.
By using a table to write an equation, you can easily find the mathematical relationship between the variables and make predictions for new values of the independent variable.
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A table can be used to write an equation that represents the relationship in the table by using the values in the table to determine the coefficients of the equation.
Here's how you can use a table to write an equation:
1. Identify the dependent and independent variables in the table. The dependent variable is the value that depends on the independent variable.
2. Choose one of the variables as the dependent variable and write the equation in terms of the dependent variable.
3. Use the values in the table to find the coefficients of the equation. For example, if the independent variable is x and the dependent variable is y, you can use the values in the first column for x and the values in the second column for y to find the coefficients.
4. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for a unit change in x, and the y-intercept represents the value of y when x is 0.
5. Substitute the coefficients from step 3 into the equation from step 4.
6. Check your equation by plugging in the values from the table and verifying that they match the corresponding values in the dependent variable column.
By using a table to write an equation, you can easily find the mathematical relationship between the variables and make predictions for new values of the independent variable.
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determine if the subset of consisting of vectors of the form , where is a subspace.
The subset of consisting of vectors of the form is indeed a subspace.
A subspace is a special type of set within a vector space that has the same properties as the larger vector space.
In order to determine if a subset of a vector space is a subspace, we must check if it satisfies certain conditions.
The first condition is that the subset must contain the zero vector.
The second condition is that the subset must be closed under addition.
The third condition is that the subset must be closed under scalar multiplication.
Now, let's apply these conditions to the subset of consisting of vectors of the form . It is clear that the zero vector satisfies this condition, as.
The subset is also closed under addition, as adding two vectors of the form and will result in a vector of the form.
Finally, the subset is closed under scalar multiplication, as multiplying a vector of the form by a scalar will result in a vector of the form .
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Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x))
The x-intercept of the composition is x = -1/2.
How to find the x-intercept of the composition?Remember that a linear function can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If a liear function passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
For g(x) we can use (-1, 2) and (1, 6), the slope is:
a = (6 - 2)/(1 + 1) = 2
Then the function is something like:
g(x)= 2x + b
To find the value of b, we use again the point (1, 6)
g(1) = 6 = 2*1 + b
6 - 2 = b
4 = b
So:
g(x) = 2x + 4
Now the same for h(x), we can use the points (-1, -1) and (1, 7), we will get:
a = (7 + 1)/(1 + 1) = 4
h(x) = 4x + b
Using the point (1, 7)
h(1) = 7 = 4*1 + b
7 - 4 = b
3 = b
h(x) = 4x + 3
The composition is:
g( h(x)) = 2*h(x) + 4
= 2*(4x + 3) + 4
= 8x + 10
The x-intercept is the value of x such that:
0 = 8x + 4
-4 = 8x
-4/8 = x
-1/2 = x
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The table below shows the cost of renting a bicycle at Ike's Bikes. Based on the rate in the table, what is the cost for 9 hours?
The cost of renting a bicycle for 9 hours is $72. The result is obtained by multiplying the rate and time duration.
How to calculate the cost of rent?The cost of rent related to time of rent. It could be cost per hour or cost per day.
The table is in the attachment to complete question.
We have the cost of renting a bicycle at Ike's Bikes.
$16 for 2 hours.$32 for 4 hours.$48 for 6 hours.Find the cost for 9 hours!
We take a sample of the data to find the rate.
The rate is
= $16/2 hours
= $8 per hour
Another sample will have the same result.
To rent for 9 hours, the cost will be
= $8 × 9
= $72
Hence, to rent a bicycle for 9 hours, it will cost $72.
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Which graph do you create if you plot the function on a coordinate plane?
Answer:
B
Step-by-step explanation:
B..................
Zack's biology lab group is studying how quickly bacteria grow when exposed to sunlight. At the beginning of the experiment, Zack looked at the sample under a microscope and counted 5 bacteria. After the sample was exposed to sunlight for one hour, Zack looked again and counted 35 bacteria.
Answer: 5(7) over x
Step-by-step explanation:
carbon-14 has a half-life of 5,730 years. if a sample contains 80 mg originally, how much is left after 17,190 years?
Answer:
After 17,190 years, the amount of carbon-14 left would be approximately 5 mg.
The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the remaining carbon-14 decays. To calculate the amount of carbon-14 remaining after 17,190 years, we can use the formula:
A = A0 * (1/2)^(t/T)
where:
A0 is the initial amount (80 mg)
t is the time elapsed (17,190 years)
T is the half-life (5,730 years)
A = 80 * (1/2)^(17,190/5,730)
A = 80 * (1/2)^3
A = 80 * (1/8)
A = 10 mg * 1/2
A = 5 mg
a team played 7 games. In those games the team won by 7points,lostby10,won by 8, won by 11,lostby2 and won by 10. What was the mean difference in game scores in the six games
The mean difference in game scores over the six games is 12
What is mean difference?The mean difference, or difference in means, measures the absolute difference between the mean value in two different groups.
Given the points by which a basketball team either won or lost 6 games.
- Won by 7 points = +7
- Lost by 10 points = -10
- Won by 8 points = +8
- Won by 11 points = +11
- Lost by 2 points = -2
- Won by 10 points = +10
Thus;
Mean difference of the 6 games is;
= (+7 - 10 + 8 + 11 - 2 + 10)/6
= 24/6
= 12
Hence, the mean difference in game scores over the six games is 12
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Balance of payments For each transaction in the table, indicate the current account component, cash flow position, and type of entry on the balance-of-payments account. US Cash Flow Position Entry on US Balance-of- Payments Account Component Transaction Consumers in Japan purchase baseball jerseys from their favorite US baseball teams. The jerseys are produced in the United States. An American investor owns stock in a Spanish company and receives a dividend payment from that company. The United States government provides foreign aid to another country after a natural disaster. Consider the case where a company in Spain purchases stock in a US-based company. This component of the financial account is known as 7. Factors affecting international capital flows A decrease in the tax rate on dividends in a country is likely to decrease portfolio investment in that country. An increase in the tax rate on corporate earnings in a country is likely to direct foreign investment (DFI) in that country.
For each transaction in the table, the current account component, cash flow position, and type of entry on the balance-of-payments account are as follows:
1. Consumers in Japan purchasing baseball jerseys from their favorite US baseball teams: Current account component: Imports; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.
2. An American-based subsidiary remitting earnings to the parent company in Canada: Current account component: Investment income; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.
3. France providing funds to the United States as a gift to be used for the construction of a large monument: Current account component: Gifts; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.
4. A US-based company purchasing stock in a French company: This component of the financial account is known as Foreign Direct Investment (FDI). It is defined as an investment made to acquire lasting interest in enterprises operating outside of the economy of the investor.
With regards to the balance of payments, FDI is considered a capital account item, so there will be no entry on the balance of payments account. This is because FDI does not involve any money entering or leaving the economy.
In conclusion, when a transaction is made, it is important to be aware of the current account component, cash flow position, and type of entry on the balance-of-payments account that is associated with it.
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Complete question is shown in figure.
Anissa is considering buying her first home. The house she is interested in buying is priced at $125,000. Anissa qualifies for a 30-year mortgage at 6%. What will her monthly mortgage payment be?
A) $629. 53
B) $697. 87
C) $805. 23
D) $749. 44
Anissa's monthly mortgage payment will be $749.44.
The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also gets additional income in terms of the recipient, known as interest, taking into account the time value of money.
In this case, we need to find the EMI - Equated Monthly Installments, Anissa has paid.
EMI = P*(1+r)^n / [(1+r)^n -1]
The Principal amount is P = $125,000.
The interest rate is, r = 6% p.a. = 0.005 per month.
The number of periods is, n = 30 × 12 = 360
The monthly payment is:
EMI = P*(1+r)^n / [(1+r)^n -1] = 3764.11/5.023 = 749.4381 = 749.44(approximately)
Thus, Anissa's monthly mortgage payment will be $749.44.
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The circumference of a circular garden is 75.36 feet. What is the diameter of the garden?
Answer:
24.12 feet.
Step-by-step explanation:
The formula to find the diameter of a circle from its circumference is:
diameter = circumference / π
Plugging in the given values:
diameter = 75.36 feet / π
diameter = 75.36 / 3.14
diameter ≈ 24.12 feet
So, the diameter of the circular garden is approximately 24.12 feet.
Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 25(1.071)^x
Answer:
Step-by-step explanation:
The given exponential function will grow at 6.1%
Given,
y =
To find,
identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
Solution,
We have,
y =
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is:
y(x)= a(1-r)^x such that r is the growth percent.
==> 1+r = 1.061
==> r = 0.061 = 6.1%
Enter the correct answer in the box.
Write the inverse of the cube root function used to represent the situation in
Model 2:
"Jack owns a company that manufactures a product that we’ll call product A. After producing and selling x units of product A, the profit his company made is represented by the cube root function [tex]f (x) = \sqrt[3]{(x+4)^{2} }[/tex]"
The inverse of the cube root function used to act for the situation in model is f⁻¹(x) = √x³ - 4
Inverse of the cube root function f(x)
f(x) = ∛ (x + 4) ²
To find the inverse function, let f(x) = y
So, y = ∛ (x + 4) ²
Taking the cube of both sides, we have
y³ = [∛ (x + 4) ²] ³
y³ = (x + 4) ²
Taking square root of both sides, we have
√y³ = √ (x + 4) ²
√y³ = (x + 4)
Subtracting 4 from both sides, we have
√y³ - 4 = x + 4 - 4
√y³ - 4 = x
change y with x, we have
√x³ - 4 = y
Replacing y with f⁻¹(x), we have
f⁻¹(x) = √x³ - 4
So, the inverse of the cube root function used to represent the situation in model is f⁻¹(x) = √x³ - 4
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Natalie has $300 in a savings account that earns 15% interest per year. How much interest will she earn in 4 years?
Answer: 480
Step-by-step explanation:
300 In Account
15% of 300 = 45
45x4= 180
300+180= 480
Answer:
If Natalie had simple interest: $180
If Natalie had compound interest: $224.70
Step-by-step explanation:
Simple Interest.
P(1 +rt)
300(1 + 0.15 x 4) = 480
480 - 300 = 180
Compound interest.
P(1 + r/n)^nt
300(1 + 0.15)^4 = 524.70
524.70 - 300 = 224.70
Consider two binary variables X and Y having the following joint probability distribution: XlY 1/3 1/3 1/3 Evaluate the following entropies: H(X), H(Y), H(XIY), H(YIX); H(X,Y), and the mutual informa- tion Im(X,Y).
The following entropies are evaluated as H(X, Y ) = ∑p(x, y) log p(x, y), H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y)) .
We have the following joint probability distribution:
X/Y 0 1
0 1/3 1/3
1 0 1/3
The entropy of X is given by
H(X) = −p log p − (1 − p) log(1 − p) = H(p)
The entropy does not depend on the values that the random variable takes (0 and 1 in this case), but only depends on the probability distribution p(x).
The joint entropy is given by
H(X, Y ) = ∑p(x, y) log p(x, y).
The joint entropy measures how much uncertainty there is in the two random variables X and Y
taken together.
The conditional entropy of X given Y is
H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y))
The conditional entropy is a measure of how much uncertainty remains about the random variable
X when we know the value of Y.
For two variables, the chain rule becomes:
H(X, Y ) = H(X|Y ) + H(Y ) = = H(Y |X) + H(X).
Thus, the following entropies are evaluated as H(X, Y ) = ∑p(x, y) log p(x, y), H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y)) .
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please help!
A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are shown.
10 gumballs are red
8 gumballs are blue
5 gumballs are green
2 gumballs are white
Based on the random sample results, complete the prediction statements for the entire machine of 200 gumballs.
Move the answers to the correct boxes.
There are
red gumballs in the machine.
There are
more green gumballs than white gumballs in the machine.
There are
gumballs that are either blue or green in the machine.
Based on the random sample results, the prediction statements for the entire machine of 200 gumballs is completed below;
There are 10 red gumballs in the machine.There are 3 more green gumballs than white gumballs in the machine.There are 13 gumballs that are either blue or green in the machine.Complete the prediction statement using the random sample?Total gumballs in the gumball machine= 200 gumballs
Result from the random sample= 25 gumballs
From the random sample selected:
10 gumballs are red
8 gumballs are blue
5 gumballs are green
2 gumballs are white
There are 10 red gumballs in the machine.
There are 3 more green gumballs than white gumballs in the machine.
= Green gumballs - red gumballs
= 5 - 2
= 3 gumballs
There are 13 gumballs that are either blue or green in the machine.
= Blue gumballs + green gumballs
= 8 + 5
= 13 gumballs
Ultimately, the prediction statement is completed using 10, 3 and 13 respectively.
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Stuck on homework please help
1 x 103 + 3 x 102 + 9 x 101 + 2
Answer:
1320
MDAS Method
Answer:
Your answer is 1320
Step-by-step explanation:
hope this is what you were looking for
Sandy ha 26 meter of brown wire and 20 meter of red wire. She need to cut both wire into maller piece o that all of the maller piece are the ame length and there i no wire leftover. The length of each piece mut be a whole number of meter. What i the longet he can make each maller piece of wire? Give your anwer in meter
Each malleable piece of wire he can produce has a length of 2 metres.
How to calculate length?When given an area A and a width w, the length w is calculated using the formula h = A/w. Its length can be calculated using h = P/²w if you know its perimeter (P) and width (W). Its length is h = (d²w²) if you have a diagonal d and a width w.The definition of length is the distance or measurement between two points. In other terms, the largest two or highest three dimensions of a geometric shape or item. As an illustration, the length and width of a rectangle are its dimensions.The number of digits in the base-numerical for, as determined by the formula, determines a number's base length. A vector's magnitude (length), which is a scalar and determined by the square root of the sum of the squares of its components, is called a scalar vector. This is an exception to the general rule that the Euclidean distance in n-space between any two places is equal to the square root of the sum of the squares of the elemental differences.Prime factorization
26 = 2 × 13
20 = 2² × 5
HCF = 2
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Write the product using exponents.
(-4) x (-4) x (-4) x Y x Y
Using exponents, the product is _.
The product of the expression (-4) x (-4) x (-4) x y x y is -64y²
What are expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression, (-4) x (-4) x (-4) x y x y
We need to find its product,
(-4) x (-4) x (-4) x y x y
= -4³ × y²
= -64 × y²
= -64y²
Hence, the product of the expression (-4) x (-4) x (-4) x y x y is -64y²
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Rectangle PQRS is dilated by a scale factor of 5 to form rectangle '. Side QR measures 5. What is the measure of Q'R'?
The length of Q'R' is 5 * 5 = 25.
Dilating Rectangle MeasurementThe steps to find the measure of Q'R' are:
Start with the length of QR, which is given as 5.Apply the dilation factor of 5 to find the length of Q'R'.The length of Q'R' is obtained by multiplying the length of QR by the scale factor: 5 * 5 = 25.So, the measure of Q'R' is 25.
This method is applicable for finding the length or width of a dilated figure when the original length or width and the scale factor are given. The formula to find the length (or width) of a dilated figure is: length (or width) of dilated figure = scale factor * length (or width) of original figure. The formula for finding the length or width of a dilated figure is a basic concept in geometry and is widely used in solving related problems.
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find the value of the integral ∫ (∇ × a® ).® if the vector a® = eˆ eˆ eˆ and is the surface defined by the paraboloid = 1 − 2 − 2 , where ≥ 0.
The integral is equal to zero, since the divergence of a constant vector is always zero.
The integral ∫ (∇ × a® ).® is equal to zero. This is due to the fact that the curl of a constant vector is always zero. The vector a® is given to be eˆ eˆ eˆ, therefore it is a constant vector. Since the divergence of a constant vector is always zero, the integral is equal to zero.
To further illustrate this point, we can expand the integral in terms of its components. ∇ × a® is equal to 0 as it is the curl of a constant vector. Similarly, a® .® is equal to 0 since the inner product of two constant vectors is always zero. Therefore, the integral is equal to 0.
The surface defined by the paraboloid is not used in this calculation, as the surface does not affect the value of the integral. The surface is used to define the range of the integral, but not to calculate the value of the integral itself.
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It costs $12. 50 to enter an amusement park and $1. 50 to play each game. Solve an inequality to find the number of games, g, Cole can play if he has $35 to spend at the park
The number of games cole can play $12.5 to enter and $1.5 to play each game by subtracting and dividing with $35 is 15 games.
The total money cole have is $35
To enter an amusement parks it costs around $12.5
so, remaining money by subtracting = 35-12.5 = $22.5
so, by dividing the remaining money with $1.5 paid per each game gives how many games does cole can play.The number of games cole can play $12.5 to enter and $1.5 to play each game by subtracting and dividing with $35 is 15 games. By dividing the remaining money with $1.5 paid per each game gives how many games does cole can play. Total number of games does cole can play is 22.5/1.5 = 14 games.
Therefore , the number of games cole can play are 14 games exactly.
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What is the equation of the line that passes through the point (-1, 1) and has a
slope of -1?
The equation of the line that passes through the point (-1, 1) and has a slope of -1 is y = -x.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-1, 1), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -1(x - (-1))
y - 1 = -1(x + 1)
y = -x -1 + 1
y = -x.
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The equation of the line is y = -x
How to determine the equation of the lineThe general formula for the equation of a line is expressed with the equation;
y = mx + c
Given that the parameters are;
y is a point on the y-axis of the linem is the slope of the line of graphx is a point on the x-axis of the line of graphc is the intercept of the line on the y-axisFrom the information given, we have that;
slope, m =-1
The points are (-1, 1)
Now, let's substitute the values
1 = -1(-1) + c
expand the bracket
1 = 1 + c
collect like terms
c = 0
The equation of the line is y = -x
Hence, the equation is y = -x
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Determine whether the system of equations
is consistent or inconsistent and if it is
independent or dependent.
3x + 5y = -5
6y +15=-15x
Unresolved problems are referred to be inconsistent systems.
How to find the Equation?Find the solution to the system of equations by attempting to remove one of the variables to see whether there is a single solution, no solution, or never-ending options (If these two equations' lines all fall on the same line, then
By adding -2 to the first equation
-4x - 6y = -22
the second equation after that, adding it.
5x + 6y = 14
getting x = -8
Returning to either equation, plug in the following: the first one,
2(-8) + 3y = 11
-16 +3y = 11
3y = 27
y = 9
These two lines come together at one point since there is only one possible answer. They remain dependable.
The graphs of the equations yield two distinct lines, proving the independence of this system. Should the equations result in
In a same vein, they are interdependent.
They would have produced a constant equation, such as 0 = 0, if they had been the same line and had been solved for one variable.
Thus, (D) is still true because they are reliable and separate.
The Complete Question is :
Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.
2x + 3y = 11
5x + 6y = 14
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Could the lengths 6 8 and 15 represent the sides of the triangle?
The lengths 6, 8 and 15 cannot represent the sides of the triangle. The solution has been obtained by using the triangle inequality theorem.
What is the triangle inequality theorem?
The triangle inequality theorem outlines the relationships between a triangle's three sides. According to this theorem, the lengths of any triangle's two shorter sides add up to be longer than the triangle's third side. In other terms, this theorem states that the shortest path between any two places is always a straight line.
We are given the lengths to be 6, 8 and 15.
Using the triangle inequality theorem,
⇒ 6 + 15 > 8
⇒ 21 > 8
Also,
⇒ 8 + 15 > 6
⇒ 23 > 8
Also,
⇒ 6 + 8 > 15
But,
⇒ 14 < 15
Hence, the lengths 6, 8 and 15 cannot represent the sides of the triangle.
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