(a) The critical points of the given system of equations are (0,0), (2,2), and (-2,-2).
(b) Near the critical point (0,0), the linear system is: [tex]\frac{dx}{dt} = 2y, \frac{dy}{dt} = -2x[/tex]. Near the critical point (2,2), the linear system is: [tex]\frac{dx}{dt} = -2y, \frac{dy}{dt} = 2x[/tex] Near the critical point (-2,-2), the linear system is: [tex]\frac{dx}{dt} = 2y, \frac{dy}{dt} = -2x[/tex]
(c) The eigenvalues of the linear system near (0,0) are: ±2i. The eigenvalues of the linear system near (2,2) are: ±2i. The eigenvalues of the linear system near (-2,-2) are: ±2i. These eigenvalues indicate that the nonlinear system is stable near each of the critical points.
(d) The phase portrait of the nonlinear system will be a series of circles centered at each of the critical points and will show that the system is stable near each of the critical points.
A critical point of a system of equations is a point at which the derivative of the system is equal to zero.
To find the critical points of the given system, we can set the derivative of each equation equal to zero and solve for x and y. For the first equation, this gives us:
[tex]\frac{dx}{dt}[/tex] = (2 + x)(y - x) = 0
If we set the derivative equal to zero, then either (2 + x) = 0 or (y - x) = 0. If (2 + x) = 0, then x = -2. If (y - x) = 0, then y = x.
For the second equation, setting the derivative equal to zero gives us:
dy/dt = (4 - x)(y + x) = 0
If we set the derivative equal to zero, then either (4 - x) = 0 or (y + x) = 0. If (4 - x) = 0, then x = 4. If (y + x) = 0, then y = -x.
Therefore, the critical points of the given system are (-2,0), (4,0), and (0,0).
Next, we can find the corresponding linear system near each critical point by finding the Jacobian matrix of the given system at each critical point. The Jacobian matrix is a matrix of the partial derivatives of the system with respect to x and y.
At the critical point (-2,0), the Jacobian matrix is:
[(2 + x)(y - x) (2 + x)(y - x)]
[(4 - x)(y + x) (4 - x)(y + x)]
Evaluating this matrix at the point (-2,0) gives us:
[(-2)(0 - (-2)) (-2)(0 - (-2))]
[(-2)(0 + (-2)) (-2)(0 + (-2))]
= [4 4]
[-4 -4]
At the critical point (4,0), the Jacobian matrix is:
[(2 + x)(y - x) (2 + x)(y - x)]
[(4 - x)(y + x) (4 - x)(y + x)]
Evaluating this matrix at the point (4,0) gives us:
[(4)(0 - 4) (4)(0 - 4)]
[(4 - 4)(0 + 4) (4 - 4)(0 + 4)]
= [-8 -8]
[0 0]
At the critical point (0,0), the Jacobian matrix is:
[(2 + x)(y - x) (2 + x)(y - x)]
[(4 - x)(y + x) (4 - x)(y + x)]
Evaluating this matrix at the point (0,0) gives us:
[(2)(0 - 0) (2)(0 - 0)]
[(4 - 0)(0 + 0) (4 - 0)(0 + 0)]
= [0 0]
[0 0]
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A battery producer claimed that the mean lifetime of a battery produced by his factory was 30 hours. A competitor thought that the figure was too high and took 8 batteries at random and the lifetime of each is as follows:
a) Can the claim by the battery producer be accepted at the 5% significant level? b) Can the claim by the battery producer be accepted at the 20% significant level?
The claim of the producer can be accepted at 5% significant level since the 30 hours is within 21.8118 < X < 30.932
The claim of the producer cannot be accepted at 20% significant level since the 30 hours is not within 23.648 < X < 29.102
How to check the claim of the producerThe claim is done using t score as the sample is less than 30. the formula for t scores is as follows
= x-bar ± t(s/√n)
from the given data the mean is calculated
sample mean, x-bar = (15 + 28 + 33 + 24 + 28 + 25 + 31 + 27) / 8
= 211/8
= 26.375
sample standard deviation, s
variance = (15 - 26.375)² + (28 - 26.375)² + (33 - 26.375)² + (24 - 26.375)² + (28 - 26.375)² + (25 - 26.375)² + (31 - 26.375)² + (27 - 26.375)²) / (8 - 1)
= 207.875 / 7
= 29.696
standard deviation = √variance
= √29.6964
= 5.45
Definition of variables
mean, x-bar = 26.375
standard deviation, s = 5.45
sample size, n = 8
significance level = 5%
confidence level = 1 - significance level = 1 - 0.05 = 0.95 = 95%
z score, z
For sample size less than 30, n < 30. t scores are used
degree of freedom, df = n - 1 = 8 - 1 =7
t score for 95% confidence level and df of 7 = 2.365
substituting into the formula
= x-bar ± t(s/√n)
= 26.375 ± 2.365 (5.45 / √8)
= 26.375 ± 4.557
= 21.8118 < X < 30.932
t score for 20% significant level and df of 7 = 1.415
substituting into the formula
= x-bar ± t(s/√n)
= 26.375 ± 1.415 (5.45 / √8)
= 26.375 ± 2.727
= 23.648 < X < 29.102
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I NEED HELPPPPPPPPPPPPPPPPPP
Answer:
[tex]x = -2[/tex]
Step-by-step explanation:
[tex]\textsf {Square both sides:}\\\\(\sqrt{3x+12} )^2 = 3x + 12\\\\(\sqrt{x+8} )^2 = x + 8[/tex]
(The square of the square root of a value is the value itself
[tex](\sqrt{x} )^2 \;is\;x[/tex])
The original identity then becomes
[tex]3x + 12 = x + 8\\\\3x - x = 8 - 12\\\\2x = -4\\\\x = -4/2\\\\x = -2[/tex]
in three to five sentences explain your understanding of the algorithm express the algorithm in either detailed pseudocode or in program code establish the running time complexity of the algorithm by explaining how you arrived at it.
An algorithm for navigating or searching through tree or graph data structures is called depth-first search. The algorithm begins at the root node (choosing an arbitrary node to serve as the root node in the case of a graph) and proceeds to investigate each branch as far as it can go before turning around.
Thus, the basic concept is to begin at the root or any other random node, mark that node, then advance to the next nearby node that is not marked. This process is repeated until there are no more adjacent nodes that are unmarked. Then go back and look for more unmarked nodes to cross. Print the path's nodes lastly.
To solve the issue, adhere to the instructions listed below:
Make a recursive function that accepts a visited array and the node's index.
STEP -1
// C++ program to print DFS traversal from
// a given vertex in a given graph
#include <bits/stdc++.h>
using namespace std;
// Graph class represents a directed graph
// using adjacency list representation
class Graph {
public:
map<int, bool> visited;
map<int, list<int> > adj;
// function to add an edge to graph
void addEdge(int v, int w);
// DFS traversal of the vertices
// reachable from v
void DFS(int v);
};
void Graph::addEdge(int v, int w){
adj[v].push_back(w); // Add w to v’s list.}
void Graph::DFS(int v)
{
// Mark the current node as visited and
// print it
visited[v] = true;
cout << v << " ";
// Recur for all the vertices adjacent
// to this vertex
list<int>::iterator i;
for (i = adj[v].begin(); i != adj[v].end(); ++i)
if (!visited[*i])
DFS(*i);
}
// Driver's code
int main()
{
// Create a graph given in the above diagram
Graph g;
g.addEdge(0, 1);
g.addEdge(0, 2);
g.addEdge(1, 2);
g.addEdge(2, 0);
g.addEdge(2, 3);
g.addEdge(3, 3);
cout << "Following is Depth First Traversal"
" (starting from vertex 2) \n";
// Function call
g.DFS(2);
return 0;
STEP- 2
Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.
Auxiliary Space: O(V), since an extra visited array of size V is required.
Pseudocode:
Depth_First_Search(matrix[ ][ ] ,source_node, visited, value)
{
If ( sourcce_node == value)
return true // we found the value
visited[source_node] = True
for node in matrix[source_node]:
If visited [ node ] == false
Depth_first_search ( matrix, node, visited)
end if
end for
return false //If it gets to this point, it means that all nodes have been explored.
//And we haven't located the value yet.
}
final answer-
A tree data structure or a graph's vertices can be searched using a recursive technique called t. Beginning with the first node of graph G, the depth-first search (DFS) algorithm digs down until it reaches the target node, also known as the node with no children.
The DFS method can be implemented using a stack data structure due to its recursive nature. The DFS algorithm implementation procedure is comparable to that of the BFS algorithm.
The following describes how to implement DFS traversal step-by-step. -
Create a stack with all of the graph's vertices in it first.
Select whatever vertex you want to use as the first vertex in the traverse, and add it to the stack.
uses for the DFS algorithm
The following list of uses for the DFS algorithm includes:
The topological sorting can be implemented using the DFS algorithm.
It can be applied to determine the routes connecting two vertices.
It can also be used to find graph cycles.
DFS technique is also applied to puzzles with a single solution.
If a graph is bipartite or not, it can be determined using DFS.
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use the following information to determine the value of river gardens' common stock: a. expected dividend payout ratio is 45%. b. expected dividend growth rate is 6.5%. c. river gardens' required return is 12.4%. d. expected earnings per share next year are $3.25.
The value of river garden's common stock is $24.79.
What is the value of the common stock?In order to determine the value of the common stock, the constant dividend model would be used.
According to this model, the value of a common stock is determined by its dividend, the growth rate and the required return.
Value of the stock = Dividend / (required return - growth rate)
The first step is to determine the dividend of the common stock.
Dividend = pay out ratio x expected earnings
Dividend = 0.45 x $3.25
Dividend = $1.46250
Value of the stock = $1.46250 / (0.124 - 0.065)
Value of the stock = $24.79
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Your friend asks for help on the following question:
Solve the system of equations using substitution:
x+7 y=0
2 x-8 y=22
Your friend says they want to rearrange the first equation for x and get x=-7 y, but now they are stuck. What needs to be done next?________
After doing this, you will now have______________
You tell your friend to remember that substitution means to replace. So we are replacing _____ with_________
Final answer is________
Answer:
(7,-1)
Step-by-step explanation:
x + 7y = 0
x = -7y Substitute -7y for x
2x -8y = 22
2(-7y) - 8y = 22
-14y - 8y = 22
-22y = 22 Divide both sides by -1
y = -1
Solve for x:
x - -7y
x = -7(-1)
x = 7
(7,-1)
solve the equation 1/3(x+6) = 1/2 (x-3) Show work pleaseee i need this now please help meeeee!!!!!!!!!!
Answer:
x = –24
[tex] \frac{1}{3(x + 6)} = \frac{1}{2(x - 3)} \\ \\ ⇒ \frac{1}{3x + 18} = \frac{1}{2x - 6} \\ \\ ⇒3x + 18 = 2x - 6 \: \\ \\ ⇒3x - 2x = - 6 - 18 \\ \\ ⇒x = - 24 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
Hope it helps you
Answer:
21.
Step-by-step explanation:
[tex]\frac{1}{3} (x+6)=\frac{1}{2} (x-3);\\\\6*\frac{1}{3} (x+6)=6*\frac{1}{2} (x-3);\\2(x+6)=3(x-3);\\2x+12=3x-9;\\x=21.[/tex]
if there are too many categories of statistics to present clearly on a graph, what is the next best option?
If there are too many categories of statistics to present clearly on a graph, then the next best option is a Chart.
Hence, option (a) is the correct choice.
A chart displays data that can be shown as a table, graph, or diagram. It includes a variety of information presentation techniques.
Various Graph and Chart Formats for Data are the following:
Bar Graph: When one data label is lengthy or if there are more than ten things to compare, a bar graph should be used to reduce clutter.
Column Chart.
Line Graph.
Dual Axis Chart.
Area Chart.
Stacked Bar Chart.
Mekko Chart.
Pie Chart.
The chart is one of the most effective ways to categorise the data.
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May be the complete questions should be as follow:
if there are too many categories of statistics to present clearly on a graph, what is the next best option?
Bar graph
Column Chart.
Line Graph.
Stacked Bar Chart.
Mekko Chart.
Find x to the nearest tenth.
After using trigonometric function the value of to the nearest tenth digit is 11.11
What is Trigonometric function ?
Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.
Function of Sine
The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA
Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.
Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11
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Suppose that the supply of x units of a product at price p dollars per unit is given by the following. 30 +90 In(4x +5) p (a) Find the rate of change of supply price with respect to the number of units supplied. dp dx (b) Find the rate of change of supply price when the number of units is 30. $ (c) Approximate the price increase associated with the number of units supplied changing from 30 to 31. $ Need Help? Talk to a Tutor Rea Watch It Read It
For part (a), we need to find the derivative of the supply equation with respect to the number of units, x.
The supply equation is given by:
S(x) = 30 + 90p * In(4x + 5)
To find the derivative of S(x) with respect to x, we can use the chain rule:
[tex]\frac{dS(x)}{dx} =\frac{dS(x)}{dp}*\frac{dp}{dx}[/tex]
Since the derivative of S(x) with respect to p is 90 * In(4x + 5), we can substitute this into the equation above:
[tex]\frac{dS}{dx}=(90*ln(4x+5))*(\frac{dp}{dx} )[/tex]
This gives us the expression for the rate of change of supply price with respect to the number of units supplied.
For part (b), we need to find the rate of change of supply price when the number of units is 30. Substituting x = 30 into the equation above gives us:
[tex]\frac{Ds(30)}{dx} = (90*ln(4*30+5))*\frac{dp}{dx}[/tex]
For part (c), we need to approximate the price increase associated with the number of units supplied changing from 30 to 31. To do this, we can use the equation from part (a) to find the rate of change of supply price with respect to the number of units supplied and then multiply this rate by the change in the number of units (from 30 to 31).
The approximate price increase is given by:
[tex]\frac{dS(x)}{dx} *(x2-x1)=\frac{dS(x)}{dx}*(31-30)[/tex]
Substituting the appropriate values into this equation will give us the approximate price increase associated with the number of units changing from 30 to 31.
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Biologists estimate that a baby elk has a 44% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers choose 7 baby elk at random to monitor. Let X = the number who survive to adulthood. Use the binomial probability formula to find P(X = 4). Interpret this result in context.
Using the binomial probability formula the value of P ( X = 4 ) = 23.04 %.
Given :
Biologists estimate that a baby elk has a 44% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers choose 7 baby elk at random to monitor. Let X = the number who survive to adulthood. Use the binomial probability formula to find P ( X = 4 ).
here ,
p = 0.44
q = 0.56
Number of trials n = 7
P ( X = 4 ) = C ( n , r ) * p^r * q^n - r
= C ( 7 , 4 ) * 0.44^4 * 0.56^7 - 4
= 35 * 0.44^4 * 0.56^3
= 0.23037
≈ 0.2304
= 0.2304 * 100%
= 23.04 %
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Which value of $x$ satisfies this inequality? -3 x-2>10
a. -2
b. -3
c. -4
d. -5
The value of x that satisfies the given inequality -3 x-2 > 10 is -5.
What is inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here, we have
Given: the inequality -3 x-2 > 10
We have to find the value of x that satisfies the given inequality.
For, x = -2
-3(-2) -2 > 10
4 > 10
x = -2 doesn't satisfy the given inequality.
For, x = -3
-3(-3) -2 > 10
7 > 10
x = -3 doesn't satisfy the given inequality.
For, x = -4
-3(-4) -2 > 10
10 > 10
x = -4 doesn't satisfy the given inequality.
For, x = -5
-3(-5) -2 > 10
13 > 10
Hence, the value of x that satisfies the given inequality is x = -5.
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P1.Suppose that the US population is growing by 0.94% each year and continues to grow at this rate everyyear.a. What is the overall growth factor for 30 years of population growth? (Round to 4 decimalplaces.) By what overall percentage will the US population grow over the next 30 years? (Roundto 2 decimal places.)
Answer:
Below
Step-by-step explanation:
.94 % is .0094 in decimal
this exponential growth is like a bank account compounded yearly
factor = ( 1+.0094)^30 = 1.3240
which would represent 32.40% growth
A line passes through point (-6, 1) and has a slope of 4/3 write an equation in Ax+By=C
The equation in the form Ax+ By=C is 4x-3y=27 if the line passes through the point (-6, 1) and slope is 4/3.
What is meant by an equation?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. The word equation and its translations in several languages might have slightly different meanings. For instance, in French, an equation is defined as including one or more variables, whereas in English, an equation is defined as any properly expressed formula that consists of two expressions joined by the equals sign.
The values of the variables that must fulfill the equality to make up the solution are referred to as the unknowns, together with the variables for which the equation must be solved.
Given point is (-6, 1)
Slope m=4/3
The equation of the line is:
y-y₁=m(x-x₁)
y-1=(4/3)(x+6)
3y-3=4x+24
4x-3y=27
Therefore, the equation in the form Ax+ By=C is 4x-3y=27
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Please help me with this and show work!! I’ll give brainliest
Answer:
The original price of the tie was 20 dollars
Step-by-step explanation:
The price of the t-shirt was originally 24, but because he bought it on sale, he would have payed 12 because 24x.5=12. This means we can subtract the value payed for the shirt from the total money payed. 22(total)-12(shirt)=. 10 (tie). However, 10 is the price he payed for the tie, not its original value. We can find this by multiplying 10x2, which gives us our answer.
Answer:
20 dollars is the original price
A rally car race course covers 631.95 miles. The winning car completed the course in 7.5 hours. What was the average speed of the winning car?
The average speed of the winning car is 79.38 miles per hour.
Given : Distance covered by rally car race course = 515.97 miles
Time taken to complete the course by winning car = 6.5 hours
The average speed of the winning car = ( Distance covered by rally car race course) ÷ (Time taken to complete the course by winning car)
= (515.97)÷ (6.5) miles per hour
= 79.38 miles per hour
Hence, the average speed of the winning car = 79.38 miles per hour.
What is average speed?Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.Average speed combines two ideas in two words: average, meaning a mean derived from a lot of individual data points, and speed, which is a change in position.You can calculate the average speed for any type of motion if you can time the motion and measure the distance.To learn more about Average speed refer to:
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Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 56% of students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA exam until the first pass.
(Assume the trials are independent.)
(a) What is the probability that Cathy passes the CPA on the first try? (Use 2 decimal places.)
(b) What is the probability that Cathy passes the CPA exam on the second or third try? (Use 4 decimal places.)
a) The probability that Cathy passes the CPA on the first try is of: 0.56 = 56%.
b) The probability that Cathy passes the CPA exam on the second or third try is of: 0.3548 = 35.48%.
How to calculate the probabilities?A probability is the division of the number of desired outcomes by the number of total outcomes.
56% of students who graduated pass the CPA exam, hence the probability of passing on each test, including the first, is of:
0.56 = 56%.
Then the probabilities for the second or the third test are given as follows:
Second: fails with 0.44 probability then passes with 0.56 probability.Third: fails the first two, each with 0.44 probability, then passes with 0.56 probability.Then the probability that Cathy passes the CPA exam on the second or third try is calculated as follows:
p = 0.44 x 0.56 + 0.44² x 0.56 = 0.3548 = 35.48%.
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The floor of Demetri’s house is rectangular in shape and is 20 feet longer than it is wide. A scale model of the floor has a length of 15 inches and a width of 10 inches. What is the width, in feet, of the floor of Demetri’s house?
Solving a system of equations we will see that the width is 40 feet.
What is the width of the floor?
We know that the floor has a rectangular shape, and the length is 20 feet longer than the width, so we can write the relation:
L = 20ft + W
Also, we know that a scale model of the floor has a length of 15 inches and a width of 10 inches, the same scale factor k is applied to the two of these, then we can write:
15 in = k*L
10in = k*W
So we have a system of equations:
L = 20ft + W
15 in = k*L
10in = k*W
Taking the quotient between the second and third equations we will get:
15in/10in = (k*L)/(k*W)
15/10 = L/W
1.5*W = L
Now we have two equations:
L = 20ft + W
1.5*W = L
We can substitute the second equation into the first one, so we will get:
1.5*W = 20ft+ W
1.5*W - W = 20ft
0.5*W =20ft
W = 20ft/0.5
W = 40ft
The width is 40 feet.
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What is the greatest common factor of 18, 24, and 40?
2
3
4
8
Answer:
(a) 2
Step-by-step explanation:
You want the greatest common factor of 18, 24, 40.
FactorsThe prime factorization of these numbers is ...
18 = 2 · 3²24 = 2³ · 340 = 2³ · 5The only common factor is 2.
2 is the greatest common factor of 18, 24, and 40.
North Pole 3. Write an equation of a line that is parallel to the line y = 4x + 7 and
passes through point (3, 2)
A person's body mass index, B, is directly proportional their weight, w, and inversely proportional to the square of their height, h. a. (6 points) Write a single equation to express the proportionality relationship, using k as the constant of proportionality. b. (6 points) A 70 inch tall person who weighs 198 pounds has a body mass index of 28.4
The proportionality constant, k, in this case is 0.00043.
a. The proportionality relationship between body mass index (B), weight (w), and height (h) can be expressed as follows:
B ∝ w * [tex]h^{-2[/tex]
where k is the constant of proportionality.
b. To find the value of the constant of proportionality, k, we can substitute the known values into the equation and solve for k.
28.4 = k * 198 * [tex]70^{-2[/tex]
Solving for k gives:
k = 0.00043
Therefore, the proportionality constant, k, in this case is 0.00043.
A proportionality constant is a number that is used to indicate the ratio of two different variables that are proportional to each other. It is also known as a scaling factor or a constant of proportionality. It is usually represented by the letter k.
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13. A particular amusement park ride will make 156 revolutions in 180 seconds. At this rate, how many revolutions will it make in 2 minutes?
14. The costume designer for the school play uses 4 feet of fabric to make 8 costumes. At the same rate, how many costumes can the designer make with 4 yards of fabric?
15. Nina can type 45 words per minute. Write the ordered pairs (number of minutes, number of words) Nina can type for 0, 1, 2, and 3 minutes.
PLEASE answer quick! It is due tomorrow and I am so tired..
a population grows exponential. if it was 3190 initially and after 4 years grew to 3605 what is formula?
The exponential formula that shows population is y = y₀ (1.031)ˣ.
What is an exponential function?An exponential function is a function which can be defined as y = y₀ aˣ, Where 'x' is a variable and 'a' is a constant.
Given that,
The growth of population is exponential.
Also,
The initial population y₀ = 3190.
And after 4 year the population y = 3605.
Use exponential formula
y = y₀ aˣ (1)
Where x = time
Substitute the values in the formula,
3605 = 3190 a⁴
3605/3190 = a⁴
1.13009 = a⁴
a = 1.031
Substitute the value of a in equation (1),
y = y₀ (1.031)ˣ
The required formula is y = y₀ (1.031)ˣ.
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I need the answer
2x+3y+7x+4y
Answer:
The correct answer to this expression is 9x + 7y. To find this answer, you need to combine like terms. This means that you need to add together any terms that have the same variable and coefficient. In this case, the expression has two terms with the variable x and two terms with the variable y. The coefficients of the x terms are 2 and 7, and the coefficients of the y terms are 3 and 4. To combine these terms, you need to add the coefficients of the x terms together to get 9, and add the coefficients of the y terms together to get 7. Therefore, the combined expression is 9x + 7y.
Please help!! Will give brainliestttt
Solve
3=7^x
Solve
-4=7^x
[tex]3=7^x[/tex]
Flip:
[tex]7^x=3[/tex]
Take logarithm:
[tex]log(7^x)=log(3)[/tex]
[tex]x\times(log(7))=log(3)[/tex]
[tex]x=\dfrac{log(3)}{log(7)}[/tex]
[tex]\fbox{x = 0.564575}[/tex]
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[tex]-4=7^x[/tex]
Flip:
[tex]7^x=-4[/tex]
Take logarithm:
[tex]log(7^x)=log(-4)[/tex]
[tex]x\times(log(7))=log(-4)[/tex]
[tex]x=\dfrac{log(-4)}{log(7)}[/tex]
[tex]\fbox{Not a Number}[/tex]
14=6+z over -2 whats the answer please i need help
Answer:
Hi!
If you're trying to solve for z, the answer would be -34.
I hope this helps you :)
in the equation y = 75 - 6x, what is the slope and what is the y-intercept ?
The slope and y intercept of the equation are -6 and 75 respectively.
What is slope?The slope of a line is a number that describes both the direction and the steepness of the line.
Given that, the equation of a line is y = 75 - 6x
Comparing to the standard equation of the line, y = mx+c
m = slope and c is the y intercept.
In the equation, we can see,
The slope (m) = -6
The y intercept (put x = 0) = y = 75 - 6x0
y = 75
Hence, the slope is -6 and y intercept is 75.
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Use the function below to find each value:
f(x)= 4x-2 if x≤-1
1/2x+9 if x>1
f(-4)=
f(-2)=
f(6)=
f(-1)=
Value of the function given below is f(-4)= -18 , f(-2)= -10 , f(6)= 12 , f(-1)= -6
What is a function?
An algebraic function in mathematics is a function that may be described as the solution to a polynomial problem. Algebraic expressions with a finite number of terms and solely the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power make up algebraic functions rather frequently.
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.
f(-4) means x =-4 which is less than -1
so the 4x-2 expression will be used
f(-4)= 4(-4)-2
f(-4)= -18
f(-2) means x =-2 which is less than -1
so the 4x-2 expression will be used
f(-2)= 4(-2)-2
f(-2)= -10
f(6) means x =6 which is greater than -1
so the x/2 +9 expression will be used
f(6)= 6/2 +9
f(6)= 12
f(-1) means x =-1
so the 4x-2 expression will be used for x = -1
f(-1)= 4(-1)-2
f(-1)= -6
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Question 1
Two months ago, a car dealership sold 30 red cars and 120 cars that were not red. Last
month the car dealership sold a total of 200 cars. Tarik predicts that the dealership sold
45 red cars last month. Do you think this is a reasonable prediction? Explain.
Answer:
Yes this is a resendable prediction
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST
Solve the equation.
log base (3) of (81) = 3x+5
there you go i think
25%498.60 how much in total
