Proof by contradiction: (a) Let a and b be integers. Show that if a²b a is even, then a is even or b is odd. (b) Let G be a simple graph on n ≥ 4 vertices. Prove that if the shortest cycle in G has length 4, then G contains at most one vertex of degree n - 1. (c) Let x be a rational number and let y be an irrational number. Show that if x(y − 1) is rational, then x = 0.

The value of the expression after evaluating it according to the values of c and d is 42.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Since, no expression is given, let us assume that the expression is

c + d / 4

Now we have to evaluate the value of the expression according to the values of c and d,

For that, we will simply put the given values in the expression and solved it accordingly,

Put c = 36 and d = 24 in the expression we assumed,

c + d / 4 = 36 + 24/4

= 36 + 6 = 42

Hence, the value of the expression after evaluating it according to the values of c and d is 42.

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Hey there! :)

Answer:

These two figures are similar because 5/3 equals 15/9.

Step-by-step explanation:

These figures are similar to each other, which means the side-lengths are proportional. Therefore:

\(\frac{5}{9} = \frac{15}{9}\)

Side-lengths 15 and 9 are proportional to 5 and 3 because the two fractions are equivalent; the larger rectangle is just 3 times larger.

The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer: 240ft

Step-by-step explanation:

Width:

10(15) + 10

= 150 + 10

= 160

Length:

4(15) + 20

= 60 + 20

= 80

L x W

= 160 + 80

= 240

The equation y=1 represents a line Perpendicular to x=0.

The equation x=0 represents a vertical line passing through the point (0,0) on the x-axis. A line perpendicular to this line will be a horizontal line passing through the point (0, c) where c is a constant.

So, the equation of the line perpendicular to x=0 is y = c, where c is any constant.

Among the given options, the equation that represents a horizontal line is:

� = 1 y=1

Therefore, the equation y=1 represents a line perpendicular to x=0.

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Answer:

The mean absolute value is 7.7, when rounded to the nearest tenth.

Step-by-step explanation:

1.) To get the mean absolute deviation you have to find the mean first:

2.) Then, you have to find the difference of each element in your data set that is away from the mean. Then, you have to find the absolute values of the answers:

3.) Then, you have to find the mean of the absolute values:

Answer:

its 7.7

Step-by-step explanation:

i got it right in edg

Answer:

(6x+16) = 16+6x

Step-by-step explanation:

= 23x

again

23-x

= 23

Answer:

Step-by-step explanation:

Rate of decrease = 3% = 0.03

Number of decreased employees = Current number of employees * rate of decrease * number of years

= 810 * 0.03 * 16

= 388.8

= 389

Number of employees = 810 - 389 = 421

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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Answer:

negative 2 over 3 is located to the right of -1

Step-by-step explanation:

-1 is further to the left than negative 2/3.  Negative 2/3 is closer to 0.

Negative 2/3 is between -1 and 0.

These statements eliminate the other possible answers.

Total electrons

Answer:

Given:

To calculate how many electrons have the same mass as one dust particle, divide the mass of a dust particle by the mass of an electron:

\(\begin{aligned}\implies \dfrac{\textsf{Mass of a dust particle}}{\textsf{Mass of an electron}} & = \sf \dfrac{7.5 \times 10^{-10}}{9.1 \times 10^{-31}}\\\\& = \sf \dfrac{7.5}{9.1} \times \dfrac{10^{-10}}{10^{-31}}\\\\& = \sf 0.8241... \times 10^{(-10-(-31))}\\\\& = \sf 0.8241... \times 10^{21}\\\\& = \sf 8.2 \times 10^{20}\end{aligned}\)

Therefore, approximately \(\sf 8.2 \times 10^{20}\) electrons have the same mass as one dust particle.

The resulting expressions for \((f\,\circ\,g)(x)\) and \((g\,\circ\,f)(x)\) are \(5- 2\cdot x^{2}\) and \(-4\cdot x^{2} + 12\cdot x -5\), respectively.

A composition is a operation two functions in which the independent variable of the first function is substituted by the entire second function. In other words, we have the following expressions:

\((f\,\circ\,g) (x) = f(g(x))\) (1)

\((g\,\circ \,f)(x) = g(f(x))\) (2)

If we know that \(f(x) = 2\cdot x - 3\) and \(g(x) = 4 - x^{2}\), then we have the following compositions:

\((f\,\circ\, g) (x) = 2(4-x^{2})-3\)

\((f\,\circ\,g)(x) = 5-2\cdot x^{2}\)

\((g \circ f) (x) = 4 - (2\cdot x-3)^{2}\)

\((g\,\circ f) (x) = -4\cdot x^{2} +12\cdot x -5\)

The resulting expressions for \((f\,\circ\,g)(x)\) and \((g\,\circ\,f)(x)\) are \(5- 2\cdot x^{2}\) and \(-4\cdot x^{2} + 12\cdot x -5\), respectively.

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Therefore, the solutions to the given system of equations are: (2√2, -5) and (-2√2, -5).

Hence, option D (3, 0) and (−4, 7) are not solutions of the system of equations.

The given system of equations is: xy = 3.............(1)y = x² - 9..........(2) We have to solve the system of equations.

The value of y is given in the first equation. Therefore, we will substitute the value of y from equation (1) into equation (2).xy = 3x(x² - 9) = 3x³ - 27x  Now, we will substitute the value of x³ as a variable t.x³ = t

Therefore, t - 27x = 3t-24x=0t = 8x Substitute t = 8x into x³ = t.

We get:x³ = 8x => x² = 8 => x = ± √8 = ± 2√2. Substitute the value of x in y = x² - 9 to get the value of y corresponding to each value of x.y = (2√2)² - 9 = -5y = (-2√2)² - 9 = -5

A system of equations refers to a set of two or more equations that are to be solved simultaneously. The solution to a system of equations is a set of values for the variables that satisfies all the equations in the system.

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The exact value of tan θ in simplest radical form is 9/4.

To find the exact value of tan θ, we need to determine the ratio of the y-coordinate to the x-coordinate of the point (-4, -9) on the terminal side of the angle θ in standard position.

First, let's determine the length of the hypotenuse using the Pythagorean theorem. The hypotenuse can be calculated as follows:

hypotenuse = √((-4)^2 + (-9)^2) = √(16 + 81) = √97

Now, we can determine the value of tan θ by dividing the y-coordinate (-9) by the x-coordinate (-4):

tan θ = (-9) / (-4) = 9/4

Therefore, the exact value of tan θ in simplest radical form is 9/4.

Explanation: By applying the concept of trigonometry in a right triangle formed by the coordinates (-4, -9), we can determine the ratio of the opposite side (y-coordinate) to the adjacent side (x-coordinate), which gives us the value of tangent (tan) of the angle θ.

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Answer:

A.   52°

Step-by-step explanation:

The measure of an inscribed angle is 1/2 the measure of the intercepted arc.

m∠B = 1/2 (m of arc AC)

26 = 1/2 (m of arc AC)

52 = (m of arc AC)

Answer:

No solution occurs only for k = 1. (2) Infinitely many solutions occurs for no value of k. (3) A unique solution occurs for k = 1.

Step-by-step explanation:

Answer: sale price of the ski set ​$328 Find the original selling price thats the answer

Step-by-step explanation:

Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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The relationship between two variables in which one variable doubles when the other variable doubles is called a direct proportion or direct relationship.

This means that the two variables are directly related, and their values increase or decrease in the same proportion.

In mathematical terms, this is represented by a linear equation in the form of y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.

Therefore, when x doubles, y doubles as well, and when x triples, y triples as well.

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Answer:

Multiply to remove the fraction, then set equal to 0 and solve.

Exact Form: y = − 1/10

Decimal Form: y = − 0.1

Step-by-step explanation:

Answer:

y = -1/10 or -0.1

Step-by-step explanation:

Multiply both sides of the equation by 100.

To find the opposite of 5y−17, find the opposite of each term.

The opposite of −17 is 17.

Combine 155y and −5y to get 150y.

Subtract 17 from both sides.

Subtract 17 from 2 to get −15.

Divide both sides by 150.

​Reduce the fraction  

​ to lowest terms by extracting and canceling out 15.

A scatter diagram is the chart called when the paired data (the dependent and independent variables) are plotted.

Explain the meaning of a scatter diagram.

In a scatter diagram, pairs of numerical data are graphed with one variable on each axis in an effort to find a correlation between them.

                A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the better the association.

What three types of scatter diagrams are there?

The slope, or trend, of the data points can be used to classify the scatter plot, as was previously mentioned: With Strong Positive Correlation Scatter Diagram Spreadsheet with Weak Positive Correlation. Strongly Correlated Negative Scatter Diagram.

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Answer:

P(A or B) = 1 - P(neither A nor B)

= 1 - 5/55 = 1 - 1/11 = 10/11

= about .91 = about 90.91%

Answer:

Step-by-step explanation:

Answer:

x<−7

Step-by-step explanation:

5x−4<−39

Add 4 to both sides.

5x<−39+4

Add −39 and 4 to get −35.

5x<−35

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

x< -35/5

Divide −35 by 5 to get −7.

x<−7

Answer:

  x < -7

Step-by-step explanation:

You want to solve the inequality 5x -4 < -39.

Identify the term containing the variable, and the constant on that side of the equation. Add the opposite of that constant to both sides of the equation. (Variable term: 5x; constant there: -4.)

  5x -4 +4 < -39 +4

  5x < -35

Note that the coefficient of x is positive. Divide both sides of the equation by that number. (x coefficient: 5)

  (5x)/5 < (-35)/5

  x < -7

Because the number we divided by is positive, we do not need to adjust the direction of the inequality symbol. (If we multiply or divide by a negative number, the direction must be reversed.)

The solution is x < -7.

__

Additional comment

Multiplication or division by a negative number changes the ordering:

  1 < 2

  -1 > -2 . . . . . both numbers multiplied (or divided) by -1

There are other operations you can do that change the ordering, too. This is the one most commonly encountered.

Answer:

If I am not mistaking it should be -7.5

Step-by-step explanation:

Answer:

  b = -15/2

  y = -3x -15/2

Step-by-step explanation:

The value of the y-intercept can be found from a point and the slope of the line by solving the slope-intercept equation for the intercept.

__

  y = mx + b . . . . . . . equation of a line with slope m and y-intercept b

  y -mx = b . . . . . . . . subtract mx from both sides

For the point (x, y) = (-2, -3/2) and slope m = -3, the value of b is ...

  b = -3/2 -(-3)(-2) = -3/2 -6

  b = -15/2 . . . . . the value of b for this line

__

Then the equation for the line is ...

  y = mx +b

  y = -3x -15/2

Answer:

Did you mean 7.81 'cause if so-

the rounded answer would be 8.0

Step-by-step explanation: