This answer states that when graphing a linear relationship (y = 2x) on a coordinate plane, the points form a straight line, indicating that the relationship is proportional. However, when graphing a non-linear relationship (y = x2) on a coordinate plane, the points form a parabolic curve, indicating that the relationship is not proportional.
A: Relationship 1:
The relationship between x and y is y = 2x.
When graphed on a coordinate plane, the points (0,0), (1,2), (2,4), (3,6), and (4,8) form a straight line, indicating that the relationship is proportional.
Relationship 2:
The relationship between x and y is y = x2.
When graphed on a coordinate plane, the points (0,0), (1,1), (2,4), (3,9), and (4,16) form a parabolic curve, indicating that the relationship is not proportional.
This answer states that when graphing a linear relationship (y = 2x) on a coordinate plane, the points form a straight line, indicating that the relationship is proportional. However, when graphing a non-linear relationship (y = x2) on a coordinate plane, the points form a parabolic curve, indicating that the relationship is not proportional.
Learn more about equation of the plane here
https://brainly.com/question/27190150
#SPJ4
What happens to the value of the expression m-10 as m decreases
During the hockey season, Elena
averaged 5.625 assists per game. What is
5.625 written in expanded form? How is
it written with number names?
Answer: five and six hundred-twenty-five
Step-by-step explanation:
the decimal point represents the and, and all you need to do is write out the numbers, then you are good to go
Could someone help me
Answer: g = 3 sqrt n/ n
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
35/k=7/3
help plesetank you
Answer:
15
Step-by-step explanation:
35/k=7/3
7k=35*3
7k=105
k=15
Descartes decides to plot the runways at the Regina airport on a grid. Runway AB passes through the points A(-5, -24) and B(6, 9). Being the father of analytic geometry, he notices right away that he can describe
Runway CD with the equation 2x + y - 11 = 0.
Find the intersection point of Runways AB and CD analytically.
To find the intersection point of Runways AB and CD, we need to find the point where the two lines intersect. The two lines can be described as follows:
What exactly is a math graph?
A math graph is a visual representation of mathematical data or concepts. It typically uses Cartesian coordinates (x, y) to plot points, lines, and shapes that help to illustrate mathematical relationships. Graphs can be used to represent many types of mathematical information, including functions, equations, data sets, and geometric shapes. They are commonly used in fields such as science, engineering, economics, and statistics to analyze and understand complex information. Graphs are also an important tool for conveying mathematical ideas and results in a clear and understandable way.
Line AB: y = mx + b, where m = (9-(-24))/(6-(-5)) = 33/11 and b = -24 - (33/11)(-5) = -24 + 165/11 = 141/11
Line CD: 2x + y - 11 = 0
Now we can substitute the equation of the line AB into the equation of the line CD:
2x + (33/11)x + 141/11 -11 = 0
Combining like terms we get:
(33/11+2)x + (141/11 - 11) = 0
35/11x + 130/11 = 0
35/11x = -130/11
x = -130/35 = -26/7
Now we can use this value of x to find the corresponding y value using the equation of the line AB
y = (33/11)x + 141/11 = (33/11)(-26/7) + 141/11 = -86/11
So the point of intersection of the two lines is (-26/7, -86/11)
So the intersection point of Runways AB and CD is (-26/7, -86/11)
Learn more about graph
brainly.com/question/19040584
#SPJ1
adam is going to a carnival that has games and rides. each game costs $1.50 and each ride costs $3. adam spent $15 altogether at the carnival and the number of games he played is 3 times the number of rides he went on. graphically solve a system of equations in order to determine the number of games adam played, x,x, and the number of rides adam went on, yy.
The number of games played is 6 and the number of rides is 2.
Here it is given that the number of games played was 3 times the number of rides. So, by this, we get the value of both is the ratio.
That is $15,
number of games played: number of rides = 3: 1
Let x be the common ratio. So, we have
Number of games played = 3x, and number of rides = x
It is given that the cost of each game is $1.50 and cost of each ride is $3 and the total cost is $15.
By this, we get an equation,
1.50 × 3x + 3 × x = 15
4.5x + 3x = 15
7.5x = 15
x = 2
Therefore the number of games= 3x = 3×2 = 6 and the number of rides = x = 2.
For more such questions on the ratio and proportion
https://brainly.com/question/29774220
#SPJ4
Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.
the longest interval in which the initial value problem is certain to have a unique twice differentiable solution is (-∞, ∞).
Initial value problem:
y'' + 4y' + 4y = 0, y(0)=1, y'(0)=2
The longest interval in which the initial value problem is certain to have a unique twice differentiable solution is the interval (-∞, ∞).
The given initial value problem is a second order linear homogeneous differential equation. This type of equation is known to have a unique twice differentiable solution on the interval (-∞, ∞). Therefore, the longest interval in which the initial value problem is certain to have a unique twice differentiable solution is (-∞, ∞).
Learn more about confidence interval here
https://brainly.com/question/24131141
#SPJ4
Julie is rolling two trick number cubes she got with a magic set she purchased. Both of her number cubes have the number 5 on three of the faces, 10 on two of the faces, and 15 on one of the faces. Which of the following tables is a probability model for the sum of the two number cubes?
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-third, one-third, one-third.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 20, 30. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 15, 20. Column 2 is labeled probability with entries one-fourth, one-third, StartFraction 5 Over 18 EndFraction.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 15, 20. Column 2 is labeled probability with entries one-fifth, one-fifth, one-fifth.
The probability of rolling two trick number cubes with the numbers 5, 10, and 15 on them can be calculated using the formula P(A) = n(A) / n(S), where P(A) is the probability of event A, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.
In this case, the total number of possible outcomes is 6, since there are six possible combinations of two number cubes. The number of favorable outcomes for a sum of 10 is 2, since there are two possible combinations (5 and 5, and 10 and 15). Therefore, the probability of rolling a sum of 10 is 2/6, or one-third. The probability of rolling a sum of 15 is also one-third, since there is only one possible combination (10 and 5). The probability of rolling a sum of 20 is one-sixth, since there is only one possible combination (10 and 10). Therefore, the probability model for the sum of the two number cubes is a 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ4
a(n)_____is a measure that describes a characteristic of the whole population. a(n)____ais a measure that describes a sample.
Statistic is a measure that describes a characteristic of the whole population.
Estimate is a measure that describes a sample.
A statistic is a measure of a characteristic of an entire population. This means that it is a measure that describes the entire population, such as the average age, number of people, etc.
An estimate is a measure of a characteristic of a sample. This means that it is a measure that describes a portion of the population, such as the average age of a group of people, number of people in a certain area, etc.
Learn more about population mean here
https://brainly.com/question/19538277
#SPJ4
Alexandra invested 40% of his money in mutual funds, 40% in real estate, and 20% in stocks. If the value of the money that he invested in mutual funds, real estate, and stocks grew by 2%, 7%, and 11% respectively, what was the average growth on his total investment?
What was the average growth on his total investment?
Answer:
5.8%
Step-by-step explanation:
To find the average growth on Alexandra's total investment, we need to calculate the weighted average of the growth in each of the three investments. The weighted average is calculated by multiplying the growth of each investment by its proportion of the total investment and then adding them together.
First, we need to calculate the total amount of money that Alexandra invested. Since he invested 40% in mutual funds, 40% in real estate, and 20% in stocks, we can assume he invested $100.
So the amount invested in mutual funds is 40/100 * $100 = $40
The amount invested in real estate is 40/100 * $100 = $40
The amount invested in stocks is 20/100 * $100 = $20
Then we can calculate the growth of each investment using the percentages provided:
The growth of mutual funds is 2/100 * $40 = $0.80
The growth of real estate is 7/100 * $40 = $2.80
The growth of stocks is 11/100 * $20 = $2.20
Now we can add up the growth of each investment and divide it by the total investment to find the average growth:
($0.80 + $2.80 + $2.20) / $100 = $5.80 / $100 = 0.058 or 5.8%
So the average growth on Alexandra's total investment is 5.8%.
The following equations define a system.
2x + y = 10
−x + 2y = 5
Which graph represents the system?
The graph shows a line that passes through negative 5 comma 0 and 0 comma 2.5. There is a second line that passes through 0 comma 10 and 5 comma 0. The lines intersect at 3 comma 4.
The graph shows a line that passes through negative 5 comma 0 and 0 comma 10. There is a second line that passes through 0 comma 2.5 and 5 comma 0. The lines intersect at negative 3 comma 4.
The graph shows a line that passes through negative 5 comma 0 and 0 comma negative 2.5. There is a second line that passes through 0 comma negative 10 and 5 comma 0. The lines intersect at 3 comma negative 4.
The graph shows a line that passes through negative 5 comma 0 and 0 comma negative 10. There is a second line that passes through 0 comma negative 2.5 and 5 comma 0. The lines intersect at negative 3 comma negative 4.
Option (a) is the correct answer i.e. the graph that shows a line that passes through negative 5 comma 0 and 0 comma 2.5, there is a second line that passes through 0 comma 10 and 5 comma 0 and the lines intersect at 3 comma 4, represents the system of given equations.
What is a system of equations?
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations.
Given equations : 2x + y = 10 .......equation 1
−x + 2y = 5 ......equation 2
Let's take the equation : 2x + y = 10
when x=0, y = 10 and when y=0, x=5
So, the first line passes through (0,10) and (5,0).
Now, If we look at second equation : −x + 2y = 5
when x=0, y = 2.5 and when y=0, x= -5
So, the second line passes through (0,2.5) and (-5,0).
Now, we've −x + 2y = 5
we'll use substitution method to find out the intersection point.
multiplying it by 2, we get -2x + 4y = 10 ......equation 3
Adding equation 1 and 3,
we get, 5y = 20
y = 4
Putting y = 4 in equation 3,
we get, x= 3.
Hence, The intersection point is (3,4).
Learn more about equations from the given link:
https://brainly.com/question/13729904
#SPJ1
a1=33
an=an–1–7
an=
find the explicit formula
The explicit formula of the arithmetic sequence in this problem is given as follows:
[tex]a_n = 40 - 7n[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The explicit formula of an arithmetic sequence is given as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
From the recursive formula, each term is the previous term subtracted by 7, hence the common difference is given as follows:
d = 7.
The first term of the sequence is given as follows:
[tex]a_1 = 33[/tex]
Hence the explicit formula is obtained as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]a_n = 33 - 7(n - 1)[/tex]
[tex]a_n = 40 - 7n[/tex]
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
#SPJ1
A certain bacteria grows according to the function P. Consider P a solution to the logistic dP 2Pl 3 differential equation dt 7000 where P is the population of bacteria and t is measured in days_ If P(0) = 2,400, solve for P(t). What is the largest rate of increase in the number of bacteria? What will be the maximum number of bacteria? Explain your reasoning:
The carrying capacity K for this equation be 33.33.
What is meant by carrying capacity?To determine how many people an ecosystem can support, carrying capacity is crucial. Without significant setbacks from environmental degradation, this is essential for sustainable growth.
The greatest population that may be supported in a given environment under a variety of restrictions is known as the carrying capacity. In the population vs. time graph, it is at the value K that the graph asymptotically approaches the graph y=K.
The population growth model is given by [tex]$\frac{d P}{d t}=0.01 P-0.0003 P^2$[/tex]
The population model can be re-written as:
[tex]$$\begin{aligned}\frac{d P}{d t} & =0.01 P-0.0003 P^2 \\& =0.01 P(1-0.03 P) \\& =\frac{1}{100} P\left(1-\frac{3 P}{100}\right)\end{aligned}$$[/tex]
Carrying capacity of the equation be
[tex]$$\begin{aligned}K & =\frac{P}{1-\frac{1}{r P} \frac{d P}{d t}} \\& =\frac{P}{1-\frac{100}{P} \cdot \frac{P}{100}\left(1-\frac{3 P}{100}\right)} \\& =\frac{P}{\frac{3 P}{100}} \\& =\frac{100}{3}=33.33\end{aligned}$$[/tex]
The complete question is:
Suppose that a population of bacteria grows according to the logistic differential equation [tex]$\mathrm{dP} / \mathrm{dt}=0.01 \mathrm{P}-0.0003 \mathrm{P}^2$[/tex] where P is the population measured in thousands and t is time measured in days.
a) Calculate the carrying capacity K for this equation? (You must justify your answer by showing how you derived K.)
b) What does the carrying capacity represent?
To learn more about carrying capacity refer to:
https://brainly.com/question/18111919
#SPJ4
1. Formulate a series and show a proof by PMI to validate.
2. Give at least one example each on the operations of functions.
3. In at least 50 words; What have you learned in GE4?
Series: 1 + 3 + 5 + 7 + 9 + ...
Proof by PMI:
P: The series starts with 1 and increases by 2 for each consecutive term.
M: The nth term of the series is 2n - 1.
I: The series is an arithmetic series with a common difference of 2.
Operations of functions:
Addition: (f + g)(x) = f(x) + g(x)
Example: f(x) = 2x + 1 and g(x) = 3x - 2, then (f + g)(x) = (2x + 1) + (3x - 2) = 5x - 1
Multiplication: (f * g)(x) = f(x) * g(x)
Example: f(x) = 2x + 1 and g(x) = 3x - 2, then (f * g)(x) = (2x + 1) * (3x - 2) = 6x^2 - 2x + 3x - 2 = 6x^2 + x - 2
GE4 is a mathematical modeling course, in which I have learned how to use mathematical methods and models to analyze and solve real-world problems. I learned how to use statistical analysis, optimization, and simulation to make predictions and decisions. I also learned how to use various tools and software to create and analyze models. I learned to use mathematical tools to solve problems in different fields such as finance, engineering, and science.
Solve the triangle. Round your answer to the new nearest tenth
Answer:
A = 44º
[tex]b \approx 28.99[/tex]
[tex]c \approx 40.31[/tex]
Step-by-step explanation:
In this problem we are tasked with "solving the triangle," which means we need to solve for each of the triangle's non-given dimensions.
We can first solve for angle A, since we are given the other two interior angles of the triangle (90º and 46º), and we know that the measures of the interior angles of a triangle add to 180º.
A + 90º + 46º = 180º
A = 180º - 90º - 46º
A = 44º
Now that we have angle A, we can use the Law of Sines to solve for side length b.
[tex]\dfrac{a}{\sin(A)} = \dfrac{b}{\sin(B)}[/tex]
[tex]\dfrac{28}{\sin(44\textdegree)} = \dfrac{b}{\sin(46\textdegree)}[/tex]
[tex]b = \dfrac{28\sin(46\textdegree)}{\sin(44\textdegree)}[/tex]
[tex]b \approx 28.99[/tex]
Finally, we can solve for c using the Pythagorean Theorem.
a² + b² = c²
28² + 28.99² ≈ c²
[tex]c \approx \sqrt{1624.70}[/tex]
[tex]c \approx 40.31[/tex]
if a plane travels 340 mph for 3.5 hr, find the distance traveled. The distance traveled is (blank) mi.
The distance traveled is 1190 m. We can evaluate using the speed and time formula.
What is speed?The pace that an object travels a certain distance is what is meant by the speed formula.The amount of distance a body moves in a certain amount of time is referred to as speed.The metric unit of speed is the m/s. For example, m/s, km/hr, miles/hr, and other quantities can be used to express speed.Given the distance and time needed to travel that distance, the speed formula can be used to determine the speed of objects.By replacing the unknown quantities, we can also use the speed formula to determine the distance or time.Given Speed = 30mph
Time = 3.5 hr
We know that
Speed = Distance / Time
340 = distance /3.5
Distance = 1190m
To learn more about the speed from the given link
https://brainly.com/question/7359669
#SPJ1
Which inequality best describes the range of the function shown on the graph?
The range of the function shown on the graph is, y ≥ 2.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The graph of function is shown in figure.
Now, We know that;
The range is the set of possible outputs values, which are shown on the y - axis.
Hence, By the graph;
The range of function is,
⇒ y ≥ 2
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ1
pamela decided to start a donut company that will focus on savory donuts. the cost of ingredients for each donut is $0.67. Pamela will sell each donut for $2.99. her goal by the ebd of the year is to make at least 4000. how many donuts will she need to sell in order to reach her goal
4000 donuts will Pamela need to sell in order to reach her goal.
What is the profit?
Profit is when the selling price is more than the cost price or revenue is more than the cost while loss is the opposite of profit.
To calculate the number of donuts Pamela needs to sell to reach her goal, you need to divide her desired profit by the profit per donut.
If the cost of ingredients for each donut is $0.67 and she plans to sell each donut for $2.99, the profit per donut would be $2.99 - $0.67 = $2.32.
To reach her goal of making at least 4000, she needs to make a profit of $2.32 x 4000 = $9280.
So she needs to sell $9280/$2.32 = 4000 donuts.
Hence, 4000 donuts will Pamela need to sell in order to reach her goal.
To learn more about the profit visit,
https://brainly.com/question/19104371
#SPJ1
a heat source is applied to a metal surface, causing the temperature of the metal to increase with respect to time at a rate that is proportional to the sum of the metal's instantaneous temperature, t, and the metal's original temperature, to. select the differential equation that represents the relationship.
Answer:
the answer is d t d T = c ( T + T 0 )
Step-by-step explanation:
Supóngase que el 2% de la población en promedio son zurdos. La probabilidad que en 100 personas haya 3 o más zurdos es
The probability of 3 or more deaf people in a sample of 100 is given as follows:
0.3633 = 36.33%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of the parameters for this problem are given as follows:
p = 0.02, n = 100.
The probability of 3 or more deaf people are given as follows:
P(X >= 3) = 1 - P(X < 3).
In which:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Hence:
P(X = 0) = 0.98^100 = 0.1326.P(X = 1) = 100 x 0.02 x 0.98^99 = 0.2707.P(X = 2) = 99 x 50 x 0.02² x 0.98^98 = 0.2334.Thus:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
P(X < 3) = 0.1326 + 0.2707 + 0.2334
P(X < 3) = 0.6367.
P(X >= 3) = 1 - P(X < 3).
P(X >= 3) = 1 - 0.6367.
P(X >= 3) = 0.3633.
TranslationWe suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.
More can be learned about the binomial distribution at https://brainly.com/question/24756209
#SPJ1
What is the area of a regular hexagon whose apothem is 12 in and sides are 8 in?
A) 288 [tex]in^{2}[/tex]
B) 36 [tex]in^{2}[/tex]
C) 576 [tex]in^{2}[/tex]
According to mathematics, a regular hexagon's area A is 288 sq units option -A is correct answer.
What is the method for calculating a regular hexagon's area?How to Locate a Hexagon's Area
A regular hexagon's side length can be determined in step 1.
Step 2: Calculate the area using the formula for the area of a hexagon (3√3 s²)/2, where s is the length of the hexagon's sides.
A regular hexagon whose side length is 8 in.
and the apothem is 12 in.
The equation for the area,
A=(3√3)/2 × a²
Therefore
A = 6×(0.5×8×12)
A = 288 sq units
In conclusion, a regular hexagon's surface area A is 288 square feet.
To know more about area visit:
https://brainly.com/question/4378368
#SPJ1
Answer:
Your answer is A) [tex]288in^{2}[/tex]
Step-by-step explanation:
the quotient of 2 and 9
Answer: The quotient of 2 and 9 is 0.2222 (approximately) or 2/9
Step-by-step explanation:
Quotient is a mathematical term that refers to the result of dividing one number by another. In this case, the quotient of 2 and 9 is found by dividing 2 by 9, which results in 0.2222 (approximately) or 2/9.
It's important to note that the quotient is a decimal number because 9 doesn't divide into 2 exactly, so there is a remainder of 0.2222. The quotient represents the number of times 9 can be divided into 2, which is a fraction of a time. In this case, 9 can be divided into 2 only 0.2222 times.
I hope this helps :)
The quotient of 2 and 9 is the result of the division of 2 by 9 which is approximately 0.2222.
Explanation:The question is asking for the quotient of 2 and 9. The quotient is the result of division. So, to find the quotient of 2 and 9, you need to divide two by nine.
The calculation is as follows: 2 ÷ 9 = 0.2222 (rounded to the fourth decimal place).
So, the quotient of 2 and 9 is approximately 0.2222.
Always remember, that when the divider (the number we divide by) is larger than the dividend (the number to be divided), we get a quotient less than one.
Learn more about Quotient here:https://brainly.com/question/21942308
#SPJ2
(PLEASE ANSWER BY TODAY) A car service charges $2.50 to pick you up and charges c cents for each mile of your trip.
Write an equation in the form y=mc+b that could represent the cost of a car based on the number of miles driven.
The linear equation for the given situation is y= cx + 2.50.
What is a linear equation?
A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.
We are given that a car service charges $2.50 to pick us up and charges c cents for each mile of our trip.
So, the equation that represent the cost of a car based on the number of miles driven is given by:
y= cx + 2.50
Hence, the linear equation for the given situation is y= cx + 2.50.
Learn more about linear equation from the given link
https://brainly.com/question/2030026
#SPJ1
Find x round to the nearest tenth
Answer:
[tex]x \approx 31.6\textdegree[/tex]
Step-by-step explanation:
Apply the Law of Sines.
[tex]\dfrac{\sin(A)}{a} = \dfrac{\sin(B)}{b}[/tex]
↓ plug in given side lengths and angle measures
[tex]\dfrac{\sin(74\textdegree)}{22} = \dfrac{\sin(x)}{12}[/tex]
↓ multiply both sides by 12
[tex]\dfrac{12\sin(74\textdegree)}{22} = \sin(x)[/tex]
↓ take the inverse sine of both sides
[tex]\sin^{-1}\left(\dfrac{6\sin(74\textdegree)}{11}\right) = x[/tex]
↓ evaluate using a calculator and round to tenths place
[tex]x \approx 31.6\textdegree[/tex]
- 4(x - 2) = 2 - 2x
What is x?
Answer:
x=3
Step-by-step explanation:
-4(x-2)=2-2x
-4x+8=2-2x
-4x+8=-2x+2
-4x=-2x+2-8
-4x=2x-6
-2x=-6
x=3
Let's solve your equation step-by-step.
-4(x-2)=2-2x
Step 1: Simplify both sides of the
equation.
-4(x-2)=2-2x
Simplify:
(-4)(x)+(-4)(-2) = 2+ -2x
(Distribute)
-4x+8=2+ -2x
-4x+8=-2x+2
Step 2: Add 2x to both sides.
-4x+8 + 2x = -2x+2+2x
-2x+8=2
Step 3: Subtract 8 from both sides.
-2x+8-82-8
-2x=-6
Step 4: Divide both sides by -2.
-2x -6 = -2 -2
x=3
Write an equation of the line that passes through point P and is
perpendicular to the line with the given equation.
P(1, 3), y = 2x - 1
Y is 1/3x +5 an equation of the line that passes through point P.
How the perpendicular lines calculated?The slope of parallel lines is the same. The slopes of perpendicular lines are opposing reciprocals. To put it another way, if m=ab, then m=ba. Use the provided information to calculate the slope before attempting to discover a line's equation.The need for determining the perpendicular line is coordinates and a line equation. Think about a line with the equation axe + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. The slopes should add up to -1 if one line is perpendicular to this one.The slope of the new line will be equal to (1/3) = 1/3because perpendicular lines have slopes that are the negative reciprocals of one another.
X and Y are represented by X and Y, (x,y) is the pair of coordinates for the point, and m is the slope in this equation, which reads: Y - y = m(X-x).
Y-4 = 1/3(X-1), which leads to Y = 1/3X +1 +4 and Y = 1/3X +5.
To learn more about slope refer to:
https://brainly.com/question/22057368
#SPJ1
It is easy to check that for any value of c, the function
y = ce^{-2x} + e^{-x}
is solution of equation
y' + 2y = e^{-x}.
Find the value of c for which the solution satisfies the initial condition y(2)= 9.
The value of c for which the solution satisfies the initial condition y(2)= 9 is c = 9 - e^{-2}.
Let us solve this problem step by step.
For the given equation: y' + 2y = e^{-x}
We have the solution as: y = ce^{-2x} + e^{-x}
We have to find the value of c for which the solution satisfies the initial condition y(2)= 9.
Substituting x = 2 in the above equation, we get:
9 = c + e^{-2}.
Therefore, we can solve for c as:
c = 9 - e^{-2}
Hence, the value of c for which the solution satisfies the initial condition y(2)= 9 is c = 9 - e^{-2}.
Learn more about initial condition here:
https://brainly.com/question/13243199
#SPJ4
my last question hurry CMON
Answer:
44
Step-by-step explanation:
Because of similar triangles we have
VN/UN = VL/UM
11/8 = VL/24
Cross multiply.
8VL = 11 × 24
VL = 11 × 3
VL = 33
LN = VL + VN
LN = 33 + 11
LN = 44
Given vectors t=⟨−3,−3,−4⟩, u=⟨−3,−3,3⟩, and v=⟨−6,−8,4⟩, find t(u⋅v).
Answer:
Answer in attached photo.
Step-by-step explanation:
SolutionSteps are in the attached photo, do note that t(u) is different from t·u, t(u) is multiplying vectors together, while t·u is the dot product of 2 vectors.
Expresión de la suma 3x,x,2y y-5y
Therefore , the solution of the given problem of expression comes out to be 4x -2y is the sum of given expression.
Expression : what is it?Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.
Here,
Given :
expressions are : 3x,x,2y and y-5y
To find the sum of the expression ,
We add them:
=> 3x+ x+2y+y-5y
=> 4x+3y-5y
=>4x -2y
Therefore , the solution of the given problem of expression comes out to be 4x -2y is the sum of given expression.
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
