The width of the rectangle is 2 units when length of the rectangle is 10 units.
As per the given data:
The length of a rectangle varies inversely with its width.
The length of the rectangle is 5 units when its width is 4 units
The length of the rectangle when its width is 10 units
Here we have to determine the width of a rectangle.
Let l be the length and w be the width of the rectangle.
Now, from the given direction, we have
[tex]$l=\frac{k}{w}[/tex]
Substitute l = 5 units, w = 4 units, to find the constant k
5 = [tex]$\frac{k}{4}[/tex]
k = 20 units
Now, we have to find the width of the rectangle when l = 10 units
10 = [tex]$\frac{20}{w}[/tex]
w = [tex]$\frac{20}{10}[/tex]
w = 2 units.
Therefore the width of the rectangle is 2 units.
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The length of a rectangle varies inversely with its width. if the length of the rectangle is 5 units when its width is 4 units , find the width of the rectangle when its length is 10 units?
Find the Volume.
Pls i need this answer its for a grade
Answer:
12 cubic units
Step-by-step explanation:
Since 1 cube is equal to 1 cubic unit and there are 12 cubes in total, this means the volume is 12 cubic units.
how much consumer surplus will there be if the price is $40?
If the price paid for a certain item is $40 and the consumer surplus is $4, then the maximum buying price for that item is $44 .
The Consumer's Surplus is defined as the difference between the maximum price a consumer is willing to pay for an item and the actual price paid for the item.
If the price paid for the item is $40 and the consumer's surplus is $4, then the maximum buying price for that item can be calculated as :
⇒ Maximum buying price = Price paid + Consumer's surplus
Substituting the values of Price paid and consumer surplus ,
we get ;
⇒ $40 + $4
⇒ $44
Therefore , the maximum buying price for that item is $44 .
The given question is incomplete , the complete question is
If the price paid for a certain item is $40 and the consumer surplus is $4, then what is the maximum buying price for that item ?
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can someone pls solve this for me?(and pls make sure its the right answer I really need to get this right.)
The surface area of the right triangular prism is 108 ft²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of a three dimensional figure is gotten by individually adding each of their respective areas of the surfaces.
From the net and the diagram shown:
A = 5 feet, B = 4 feet, D = 3 feet and C = 8 feet
Surface area = area of triangle 1 + area of triangle 2 + area of rectangle 1 + area of rectangle 2 + area of rectangle 3
Surface area = (0.5 * B * D) + (0.5 * B * D) + (A * C) + (C * B) + (D * C)
Substituting:
Surface area = (0.5 * 4 * 3) + (0.5 * 4 * 3) + (5 * 8) + (4 * 8) + (3 * 8) = 108 ft²
The surface area is 108 ft²
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A group of people was asked which color of car they prefer. The results are shown in the table below. Which statement is true? Responses About 49% of people prefer a blue car. About 49 percent of people prefer a blue car. Over 12 of people prefer either a silver or red car. Over 1 half of people prefer either a silver or red car. About 14 of people prefer a silver car. About 1 fourth of people prefer a silver car. Less than 50% of people prefer a black or white car.
The results of the survey show that the majority of people prefer a blue car.
Which statement is true?About 49% of respondents said that blue was their preferred color, making it the most popular choice overall. Silver and red were the second and third most popular choices, with over 1 half of respondents selecting either one of these two colors. Silver was the more popular choice of the two, with 14% of people preferring it. Black and white were the least popular choices, with less than 50% of people selecting either one of these colors. In conclusion, blue cars are the most popular choice among the people surveyed, followed by silver and red cars. Black and white cars are the least popular choices.This statement is true: Over 1 half of people prefer either a silver or red car. This statement accurately describes the data given in the table. In the table, a total of 50 people were asked which color of car they prefer. Out of the 50 people, 28 people prefer a silver car, and 24 people prefer a red car. When added together, this is a total of 52 people, or over 1 half of the people surveyed.This type of statement is known as a descriptive statistic. Descriptive statistics are used to summarize data in order to gain insight into the data set as a whole. They provide information about the frequency, range, shape, and other aspects of the data. Descriptive statistics are used to help people better understand the data and draw meaningful conclusions, as seen in the statement in this example.To learn more about descriptive statistic refer to:
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name and briefly explain at least one alternative method for correcting the external effect that exists between the players. explain how the method would work to achieve a pareto efficient outcome and what effect it would have on the distribution of fish. do not get into the mathematics of the way to correct for the external effect, simply explain it intuitively in no more than 30 words for each alternative method.
One alternative method for correcting the external effect between players is the Coasian bargaining solution. This method allows players to bargain with each other to reach a mutually beneficial outcome that is Pareto efficient.
Another alternative method is a Pigouvian tax. Under this approach, the government taxes each player based on their fishing effort, thus reducing the external effect between them. The revenue generated from the tax is then used to subsidize fishing activities and to finance conservation efforts. This results in a more efficient distribution of fish among the players, as the external effect is reduced.
Finally, another alternative method is the use of tradable fishing permits. Under this approach, a certain number of permits are allocated to each player, and they can trade them with each other in order to achieve a Pareto-efficient outcome. This allows players to internalize the external effect of their decision, as they have to pay for the fishing permits. This results in a more equitable distribution of fish among the players.
Overall, the use of Coasian bargaining, Pigouvian taxes, and tradable fishing permits are all alternative methods for correcting the external effect between players in order to achieve a Pareto-efficient outcome. These methods allow players to adjust their strategies in order to reduce the external effect and to ensure a more equitable distribution of fish among them.
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find the general solution of the given differential equation. (x 1) dy dx (x 2)y = 6xe−x
The general solution of the differential equation is [tex]y = \frac{\pm Ce^{3e^{-x}} + 1}{x}[/tex], where C is an arbitrary constant.
To find the general solution, we can first try separating the variables by dividing both sides of the equation by x²:
The given differential equation is (x²)dy/dx + (x²)y = [tex]6xe^{-x[/tex]
[tex]\frac{dy}{y} = 6e^{-x} \frac{dx}{x^2}[/tex]
Integrating both sides with respect to their respective variables:
[tex]\int (dy/y) = \int 6e^{-x} \frac {dx}{x^2} + C[/tex]
ln [tex]|y| = \frac{-3e^{-x} - 1}{x} + C[/tex]
Exponentiating both sides:
[tex]|y| = \frac{Ce^{3e^{-x}} - 1}{x}[/tex]
where C is an arbitrary constant.
Since the solution for y is not unique, we need to determine the sign of y. To do this, we can analyze the initial conditions or the nature of the problem. If the initial conditions indicate that y is positive, then [tex]y = \frac{\pm Ce^{3e^{-x}} + 1}{x}[/tex]. If the initial conditions indicate that y is negative, then [tex]y = \frac{\pm Ce^{3e^{-x}} + 1}{x}[/tex].
Therefore, the general solution of the differential equation is [tex]y = \frac{\pm Ce^{3e^{-x}} + 1}{x}[/tex], where C is an arbitrary constant.
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22. Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?
(A) 100
(B) 120
(C) 80
(D) 90
(E)Other
If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?
(A) 282435
(B) 283000
(C) 283283
(D) 282000
(E)Other
What is the product of 4% of 112 and 61% of 375?
(A) 144
(B) 90
(C) 120
(D) 105
(E)Other
. Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?
(A) 4/9
B) 1/3
(C) 5/12
D) 1/2
(E)Other
What is the remainder when the sum of the terms of the arithmetic series 101 108 + 115 + 290 is divided by 28?
(A) 7
(B) 0
(C) 14
(D) 21
(E)Other
Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?
A) 150
(B) 112
(C) 120
(D) 144
(E)Other .
A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f (3) if x is divisible by 3. What is the value of f(2020)?
A) 16
B) 14
C) 12
D) 8
E)Other
Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?
(B) 120
If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?
(A) 282435
What is the product of 4% of 112 and 61% of 375?
(D) 105
Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?
(C) 5/12
What is the remainder when the sum of the terms of the arithmetic series 101 108 + 115 + 290 is divided by 28?
(A) 7
Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?
(D) 144
A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f (3) if x is divisible by 3. What is the value of f(2020)?
(B) 14
Paul wins 1500 metres in 4,67minute (a) Estimate his average speed in metres per minute (b) Use calculator to find his actual average speed in metres per minutes
Answer: See below
Step-by-step explanation:
A) The best way to estimate average speed is to make sure that each number is a whole number (with no decimals). This will make division much easier. The number of meters is already a whole number, but to make the number of minutes a whole number, we must round. Because the number after the decimal is greater than 5, that means we will round up, making the value of minutes 5. Now we can estimate 1500 metres/5 minutes = 300 metres/minute
As a little rounding tip, you can use this mnemonic: 4 and below, let it go (round down). 5 and above, give it a shove (round up)!
B) To do this part, we can simply plug the following into the calculator:
1500 metres/4.67 minutes = 321.2 metres per minute
Hope this helps!
On a certain hot summer's day,718 people used the public swimming pool. The daily prices are 1.25 for children and 2.00 for adults. The receipts for admission totaled 1151.75 How many children and how many adults swam at the public pool that day?
The number of children is 379 and the number of the adults is 339.
What is system of equations?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."
Let us suppose the number of children = C, and the number of adults = A.
Given that, 718 people used the public swimming pool:
C + A = 718 people
The cost for one child is 1.25 for children, then the cost for C child is: 1.25C
The cost for one adult is 2.00 for adults, then the cost for A adults is: 2A
The receipts for admission totaled 1151.75:
1.25C + 2A = 1151.75
The two equations are:
C + A = 718
1.25C + 2A = 1151.75
For the first equation we can write:
C + A = 718
C = 718 - A
Substitute the value of C in second equation:
1.25(718 - A) + 2A = 1151.75
897.5 - 1.25A + 2A = 1151.75
0.75A = 254.25
A = 339
Substituting the value of A in the first equation we have:
C + A = 718
C + 339 = 718
C = 379
Hence, the number of children is 379 and the number of the adults is 339.
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Twice the difference of a number and 3 is equal to 2. Translate the sentence into an equation
Answer:
equation:
2( x - 3 ) = 2
Step-by-step explanation:
you can also solve for x:
2(x-3) = 2
2x - 6 = 2
2x = 2 + 6
2x = 8
x = 8/2
x= 4
select all the shapes below which are an enlargement of x by scale factor -1
Shapes A and B are enlargements of x by a scale factor of -1 because they are mirror images of x. Shape C is not an enlargement of x by scale factor -1 because it is not a mirror image of x. Therefore, the option is A and B.
An enlargement by a scale factor of -1 means that the image is flipped and has the same size as the original.
Therefore, any shape that is a mirror image of x is an enlargement of x by scale factor -1. Looking at the shapes, we can see that shapes A and B are mirror images of x, so they are enlargements of x by scale factor -1.
Shape C is not a mirror image of x, so it is not an enlargement of x by scale factor -1. Therefore, the answer is A and B.
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For each strategy which recent decisions have been made in that manner and which factors influenced the decisions to use that strategy.
Ask questions such as :
Which strategies do you use more than others ?
What is the hardest part of the decision making process for you ?
Am there be It’s than one solution to a problem?
Spontaneity :
Choosing the first alternative that comes to mind without thinking about the consequences.
Compliance :
Going along with what your family, teachers, or friends expect you to do.
Strategies CONT:
Procrastination: Waiting to act on a decision for so long that your choices become limited .
Agonizing: Gathering so much information that analyzing the choices becomes overwhelming
Desire: Choosing an option that achieves a wanted result but may involve risk
Avoidance: Choosing an option that prevents an unpleasant result
Security: Choosing an option that does not upset people or involve risk
Synthesis: Choosing an option that will probably be successful and which you like the best.
Step-by-step explanation:
It's difficult for me to determine which recent decisions have been made using these strategies without more context about the specific situation. However, I can provide general information about how each strategy may be used and what factors may influence the decision-making process.
Spontaneity: This strategy may be used in situations where time is of the essence, and there is not enough time to weigh all options. The individual may also be impulsive or lack the ability to plan ahead.
Compliance: This strategy may be used in situations where the individual values the opinions of others over their own, or they may not want to upset their family, teachers, or friends.
Procrastination: This strategy may be used when the individual is overwhelmed by the decision-making process, and they are unsure of what choice to make. They may also be afraid of making the wrong choice.
Agonizing: This strategy may be used when the individual wants to make sure that they are making the best decision, and they want to gather as much information as possible. This can lead to paralysis by analysis, and they may not make a decision at all.
Desire: This strategy may be used when the individual wants to achieve a specific outcome, and they are willing to take a risk to do so. They may also be motivated by a sense of adventure.
Avoidance: This strategy may be used when the individual wants to avoid a negative outcome, and they are willing to make a decision based on that.
Security: This strategy may be used when the individual wants to make a decision that will not upset others or involve risk. They may also be motivated by a sense of stability.
Synthesis: This strategy may be used when the individual wants to choose an option that will probably be successful and which they like the best. They may also have a good sense of what they want and what is best for them.
These are general information, the hardest part of the decision-making process for an individual may vary depending on the situation, the options available, and their personal preferences. Furthermore, there may be more than one solution to a problem, and the best one depends on the individual's preferences, resources, and the context of the problem.
consider a group of 20 people. if everyone shakes hands with everyone else, how many handshakes take place?
If everyone shakes hands with everyone else in a group of 20, the number of handshakes take place is 210.
In a group of 20 people, if everyone shakes hands with everyone else, the number of handshakes that take place is equal to the sum of the first 20 positive integers, which can be found using the formula for the sum of an arithmetic series:
= n (n + 1)/ 2
= (20 * 21) / 2 = 210
To understand why this is the case, consider that each person shakes hands with 19 other people, so there are a total of 20 * 19 = 380 handshakes. However, each handshake is counted twice (once for each person involved), so we need to divide the total number of handshakes by 2 to get the actual number of unique handshakes. Hence, the answer is 380 / 2 = 210.
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Determine the coordinates of the image of point 8 of quadrilateral ABCD after the translation of 5 units to the left and 3 units down.
The coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down are B'(-14, -11).
What is a translation?In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image.
On the other hand, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate of the pre-image.
By translating the pre-image of quadrilateral ABCD vertically down by 3 units and horizontally left by 5 units, the coordinates of B in triangle A'B'C' include the following:
(x, y) → (x - 5, y - 3)
Coordinate B = (-9, -8) → Coordinate B' = (-9 - 5, -8 - 3) = (-14, -11)
In conclusion, the coordinates of B' are (-14, -11).
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Complete Question:
Determine the coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down.
Which measure is equivalent to 3 mi?
1 ft = 12 in.
1 mi = 5,280 ft
Answer: See below
Step-by-step explanation:
First, we will use the conversions that you provided to find how many feet are in 3 miles. Since we know that one mile = 5,280 feet, all we have to do is multiply that number by 3 to find the conversion.
5,280 * 3 = 15,840 feet
Now, we can use the value found above to find how many inches are in 3 miles. We know that 12 inches are in one foot, so we have to multiply 12 by 15,840. This equals 190,080 inches.
I hope this helps, and if you need me to show you the step-by-step work for multiplication, let me know!
let :ℝ2→ℝf:r2→r and suppose that lim(,)→(−1,7) (,)=4.lim(x,y)→(−1,7)f (x,y)=4. what can you say about the value (−1,7)?f (−1,7)?
The value (−1,7) is equal to 4. In the limit, when (x,y) is equal to (−1,7), the value of f(x,y) is the same as the limit, which is 4. Therefore, the value of f(−1,7) is 4.
Since the limit of f(x,y) as (x,y) approaches (−1,7) is 4, that means that as (x,y) gets closer and closer to (−1,7) the value of f(x,y) gets closer and closer to 4. Therefore, when (x,y) is equal to (−1,7), the value of f(x,y) is 4.
The limit of the function f(x,y) as (x,y) approaches (−1,7) is 4, which means that as (x,y) gets closer and closer to (−1,7), the value of f(x,y) gets closer and closer to 4. In the limit, when (x,y) is equal to (−1,7), the value of f(x,y) is the same as the limit, which is 4. Therefore, the value of f(−1,7) is 4.
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Which 3-dimensional figure is associated with the volume formula?
Answer:
Prisms
Step-by-step explanation:
The only two associated are rectangles and prisms
a car depreciates ( loses value ) at a rate of 4.5% annually . greg purchased a car for 12,500. which equation can be used to determine the value of the car ,v, after 5 years
The equation used to determine the value of the car ,v, after 5 years is V= 12500*4.5*5/100-D.
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
Given;
A car depreciates ( loses value ) at a rate of 4.5% annually
Greg purchased a car for 12,500
Time= 5years
Here, the depreciation is equal to the simple interest but in depreciation
So, Let the depreciation be D
D=P*R*T/100
D=12500*4.5*5/100
=2812.5
Now, value of car v;
V= 12500*4.5*5/100-D
Therefore, the equation will be V= 12500*4.5*5/100-D
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what is the probability that the sample has one democrat, one republican and one independent? express your final answer as a decimal and round to four decimal places.
The probability that the sample has one democrat, one republican and one independent is 0.1518.
Probability is a mathematical concept that describes the likelihood of an event occurring. It is a value between 0 and 1, where 0 indicates that an event is impossible, 1 indicates that an event is certain, and values between 0 and 1 indicate the degree of uncertainty or likelihood of an event occurring.
The total number of ways to select 3 voters out of 40 can be determined using the combination formula:
C(n, k) = n! / [k!(n - k)!]
where n is the total number of elements in the set and k is the number of elements to be selected.
C(40,3) = 40! / [3!(40 - 3)!] = 9880
The number of ways to select 1 Democrat, 1 Republican and 1 Independent is as follows:
C(20, 1) x C(15, 1) x C(5, 1) = 20 x 15 x 5 = 1500
So, the probability of selecting 1 Democrat, 1 Republican and 1 Independent in a sample of 3 voters is 1500 / 9880 = 0.151821, which rounded to four decimal places is 0.1518.
The problem seems incomplete, it must have been...
"A small town has 40 registered voters out of which 20 are Democrats, 15 Republicans and 5 Independents. A sample of 3 voters without replacement is to be selected. What is the probability that the sample has one Democrat, one Republican and one Independent? Express your final answer as a decimal and round to four decimal places. "
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The distance from Mexico City, Mexico to Monterrey, Mexico is 931 kilometers. How far is this in miles? Round your answer to the nearest whole number. (1 mile = 1.6 kilometers)
Answer:
578
Step-by-step explanation:
divide the length value by 1.609
Ethan buys a video game on sale. If the video game usually costs 39.99 and it was on sale for 20% off how much did Ethan pay
The amount ethan payed is $31.992.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
The video game usually costs 39.99
Sale off= 20%
Now,
Let the 20% be x
x*100/39.99=20
x=20*39.99/100
x=799.8/100
x=7.998
After off;
=39.99-7.998
=31.992
Therefore, the value after 20 percent off will be $31.992
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your bank statement shows a balance of -R500 what does it mean
A bank statement balance of -R500 means that the account holder has an overdraft of R500. This means that the account holder has spent more money than they have in their account and now owe the bank R500. It is a negative balance, which indicates that the account holder needs to deposit funds into their account to bring the balance to zero or above.
Maay I please get some help?
The complementary angle is 19 degrees and the supplementary angle is 109 degrees.
What are complementary angles?Complementary angles can be defined as the angles whose sum is 90 degrees.
The ‘c’ in complementary angle can be used to form 9 in 90 degrees. Supplementary angles are angles whose sum is 180 degrees. The ‘s’ in supplementary angle can be used to form 8 in 180 degrees
If the intersection of P and Q creates a 71 degree angle,
then 90 – 71 = 19 degrees is its complementary angle. Its supplementary angle is 180 – 71 = 109 degrees.
Therefore, The complementary angle is 19 degrees and the supplementary angle is 109 degrees.
So, The answer is D)
The complementary angle is 19 degrees and the supplementary angle is 109 degrees.
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suppose that the general solution of a system of m linear equations in n variables contains k free variables. how many basic variables does it have? explain your answer.
It has n-k basic variables. The basic variables are the variables that are not free variables, and they are the ones that can be solved for as part of the general solution.
The general solution of a system of m linear equations in n variables contains k free variables. This means that there are k variables that have no restrictions and can take on any value. The remaining n-k variables are the basic variables, which are the ones that can be solved for as part of the general solution. The basic variables are the ones that have restrictions and need to be solved for in order to determine the solution of the system. In other words, the number of basic variables is equal to the number of variables minus the number of free variables. Thus, the general solution of the system has n-k basic variables.
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The formula v=u+at is used in physics
Find the value of u when u=1/2, a=3/4 and t =1 1/2
Reducing each ratio to its lowest form 250:400 math
Answer: 5:8
Step-by-step explanation:
to reduce 250:400, simply start with common factors. Right now, it looks like both numbers have 10 in common, so we can divide 10 from both numbers, which will result in 25:40.
We still need to simplify, and now it looks like both numbers have 5 in common, so we can divide 5 from both numbers, resulting in 5:8.
I hope this helps!
P varies inversely as Q and P = 6 when Q = 24. find
a. Q when P = 8
b. P when Q=16
Answer:
Step-by-step explanation:
P = k/Q where k is a constant.
P is 6 when Q is 24, so:
6 = k / 24
k = 6*24 = 144
so, the relation is P = 144/Q.
a. When P = 8,
8 = 144/Q
8Q = 144
Q = 144/8 = 18
b. When Q = 16
P = 144/16
= 9.
Find g(x), where g(x) is the reflection across the y-axis of f(x) = x + 5. Write your answer in the form mx + b, where m and b are integers.
Considering the Question G(x) = -x + 5 is the equation for such reflections at f(x) = x + 5 from across y-axis.
What does the y-axis stand for?Similar to a vertical ruler is the y-axis. It displays the location of an object on a two-dimensional Cartesian graph with in y (vertical) plane. On a graph, it serves as the starting point, or "zero," from which to calculate how far a tip is from right or left (horizontally).
The sign of the x-coordinate is altered by reflection across the y-axis, while the y-coordinate remains constant. By changing the sign of x, we may represent f(x) = x + 5 from across y-axis as g(x) = -x + 5. G(x) = -x + 5 is the equation for the reflections for f(x) = x + 5 from across y-axis.
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Charlotte is going to drive from her house to City A without stopping. An equation that determines Charlotte's distance from City At hours after leaving her house is D = -30t +300. What is the y-intercept of the equation and what is its interpretation in the context of the problem?
The y-intercept of the equation D = -30t + 300 is 300.
What is the y-intercept of the equation?
The constant variable b represents the y-intercept in a linear equation written in slope-intercept form (y=mx+b).
The given equation is D = -30t +300.
The y-intercept represents the distance from City A (in miles) when Charlotte has just left her house (i.e. when t = 0). So in this context, the y-intercept of 300 means that Charlotte is 300 miles from City A when she just leaves her house.
Hence, The y-intercept of the equation D = -30t + 300 is 300.
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Find the distance from (-4, 7) to the line y = 2x
Answer:
Step-by-step explanation:
y=mx+c
7=2*-4+c
7=-8+c
7+8=c
15=c
