In the diagram below of triangle ABC, D is a midpoint of AB and E is a midpoint of BC. If DE =9x-20, and AC =5x+12, what is the measure of AC?

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.

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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Answer:

  B.  False

Step-by-step explanation:

You want to know if it is true that a tessellation can be created from circles.

A tessellation is the covering of a plane, using one or more geometric shapes with no overlaps and no gaps.

As the attachment shows, it is not possible to cover a plane with circles, leaving no gaps.

A tessellation cannot be created using circles. The proposition is False.

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]

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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Answer:

  (a)  2

Step-by-step explanation:

You want the greatest common factor of 18, 24, 40.

The prime factorization of these numbers is ...

The only common factor is 2.

2 is the greatest common factor of 18, 24, and 40.

The balance of the loan (not made any payments yet) of the bank

be after one year charges 3.8% interest each year is; $7785

There are mainly two types of interest. One which works only on principal(or say initial) amount, and one which works on amount plus interest to be paid till date.

For 1 year case, if interest is applied annually, both interests are same since there is no interest before first year.

For 1 year, interest with R% rate for principal amount P is just R% of P which is; (P/100) * R

We are given that R = 3.8% each year

Since P = $7500, thus, interest for 1 year is 3.8% of $7500 is;

I = 7500/100 * 3.8

I = $285

Thus, total payable amount = Principal amount + interest

Total amount = $7500 + $285 = $7785

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Answer:

Hi!

If you're trying to solve for z, the answer would be -34.

I hope this helps you :)

The inequality which represents the possible number of hours , x, the salesperson works this week is 20x + 800 ≥ 1400 where x ≥ 30,

using equation formation steps.

What is an equation ?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation.

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

In given que,

minimum earning = $1400

The possible number of hours = x

No. of cars sold = 8

Price earned by sold cars = $800

Price earned per hour =$20

Price earned for x hours = $20x

So, the total amount = 20x + 800

The equation become 20x + 800 ≥ 1400

Solving inequality que,

20x >= 600

x ≥ 30

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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

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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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

The 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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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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2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).

Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.

Given

Polynomial

(2x³ + 4x² − 5x)(x³ + 2x - 1)

Multiplying by distributive method,

2x³(x³ + 2x - 1) + 4x²(x³ + 2x - 1) - 5x(x³ + 2x -1)

2x⁶ + 4x⁴ - 2x³ + 4x⁵ + 2x³ - 4x² - 5x⁴ + 10x² - 5x

Adding polynomials with same powers

2x⁶ + 4x⁵ + 4x⁴ - 5x⁴ - 2x³ + 2x³ - 4x² + 10x² - 5x

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).

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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%.

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:

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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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.

The value of river garden's common stock is $24.79.

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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The growth of the mass of the sample of a bacteria is represented by the exponential model m(x) = 5 · 1.02ˣ.

In this problem we find the case of mass of a sample of a bacteria (m(x)), in miligrams growing in time (x), in days. This growth is done exponentially, the exponential model is shown below:

m(x) = m' · (1 + r / 100)ˣ

Where:

We have that the mass of the sample was initially 5 miligrams and grows at a rate of 2 % during 10 days. If we know that m' = 5 mg and r = 2, then the exponential model for the sample is:

m(x) = 5 · 1.02ˣ

The exponential model for the sample of a bacteria is equal to m(x) = 5 · 1.02ˣ.

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Answer:

Yes this is a resendable prediction

Step-by-step explanation:

The slope of a line that is perpendicular to a line whose equation is; 3y = -4x + 2 is; 3 / 4.

As evident in the task content is; the given equation is; 3y = -4x + 2.

To determine the slope of the given line; the equation can be expressed in slope-intercept form by dividing through by; 3.

y = -4/3x + 2/3

On this note, by comparison with the slope-intercept form of a linear equation; the slope, m is; -4/3.

Therefore, since the product of the slopes of perpendicular lines equal; -1;

The slope of the required line which is perpendicular to the given line can be determined as follows;

Slope of perpendicular; m = -1 ÷ (-4/3)

= -1 × 3 / -4

= -3 / -4

= 3/4.

On this note, the slope of the line perpendicular to the given line is; 3 / 4.

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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]

The perimeter of triangle XYZ is 48 units

What is the perimeter of a triangle?

The total of a triangle's sides equals the triangle's perimeter. The space encircled by a triangle's three sides is known as its area.

Here, we have

In The triangle XYZ

A is the midpoint of XY

B is the midpoint of YZ

AB = 1/2 XZ

AB = 5 units

Substitute the value of XZ in AB

5 = 1/2 × XZ

XZ = 10 units

B is the midpoint of YZ

C is the midpoint of XZ

BC =  1/2 XY

XY = 24 units

BC = 1/2 × 24 = 12 units

A is the midpoint of XY

C is the midpoint of XZ

AC = 1/2 YZ

AC = 7

7 = 1/2 YZ

YZ = 14

The perimeter of a triangle = the sum of the lengths of its sides

Perimeter ΔXYZ = XY + YZ + ZX

Perimeter ΔXYZ = 24 + 14 + 10

Hence, the perimeter of triangle XYZ is 48 units

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Answer: The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of -0.993 indicates a very strong negative relationship, which means that as one variable increases, the other variable decreases. This suggests that you can be quite confident that your predicted value will be reasonably close to the actual value.

there you go i think

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.

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The statement "Return on equity will not change if the firm increases its use of debt" is false.

Return on equity (ROE) is a financial ratio that shows how well a company is managing the capital that shareholders have invested in it. To calculate ROE, one would divide net income by shareholder equity.

Given is a statement, "Return on equity will not change if the firm increases its use of debt".

As we know that, The equity equals the assets minus total debt, a company decreases its equity by increasing the debt, or we can say, when debt increases, the equity decreases and since equity is ROE's denominator, ROE in turns gets a boost.

Hence, the statement "Return on equity will not change if the firm increases its use of debt" is false.

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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

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)

Answer:

Factored form is (x - 5) (x² + 5x + 25)

Step-by-step explanation:

You can get the factors directly by using the formula for a³ - b³.

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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