How would you convince a fellow student that the number 0.57 is a rational number?

[HELP NEEDED]

Answer:

w = 33/4 or  8 1/4

Step-by-step explanation:

-2w + 15= -3/2

Solve for w

Multiply each side by 2

-4w + 30 = -3

Subtract 30 from each side

-4w + 30 -30 = -3-30

-4w = -33

Divide by -4

-4w/-4 = -33/-4

w = 33/4

w = 8 1/4

Answer:

Step-by-step explanation:

The gradient or slope of the line is given by the equation m = -3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P = P ( -1 , 0 )

Let the second point be represented as Q = Q ( 0 , -3 )

Now , the slope of the line passing through the points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -3 - 0 ) / ( 0 - ( -1 ) )

On simplifying the equation , we get

Slope m = -3/1

Slope m = -3

Hence , the slope of the line is m = -3

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The y-intercept of the function is -3. The function of f(-x) is not equal to f(x) hence, it is not symmetric.

According to the Intermediate Value Theorem, there must be at least one value c in the interval (a, b) such that f(c) = k if f(x) is a continuous function on the closed interval [a, b] and if k is any number between f(a) and f(b).

The Intermediate Value Theorem in calculus is frequently employed to demonstrate the reality of a function's roots or zeros. The Intermediate Value Theorem may be used to determine that there is at least one value c in the interval (a, b) such that f(c) = 0 if we know that a function is continuous on the interval [a, b] and that f(a) and f(b) have opposite signs.

The given function is: ​f(x) = x³ + 3x²- x - 3.

Using synthetic division we have:

-1 | 1 3 -1 -3

| -1 -2 3

|___________

1 2 -3 0

The polynomial can be factored as:

f(x) = (x + 1)(x² + 2x - 3)

The quadratic equation can be factored as:

x² + 2x - 3

x² + 3x - x - 3

(x + 3)(x - 1)

Now, set x = 0:

f(0) = 0³ + 3(0)² - 0 - 3 = -3

Therefore, the y-intercept is (0, -3).

For symmetry we have:

Substituting -x for x:

f(-x) = (-x)³ + 3(-x)² - (-x) - 3x = -x³ + 3x² + x - 3x

This is not equal to f(x), so the function is not symmetric about the y-axis.

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To find the standard matrix of a linear transformation, we need to apply the transformation to the standard basis vectors of the domain and express the results in terms of the standard basis vectors of the codomain.

In this case, the linear transformation is the projection onto the line y=6x, which means that any vector in ℝ2 will be projected onto the closest point on the line.

The standard basis vectors of ℝ2 are (1,0) and (0,1), so let's apply the transformation to each of these vectors:

- (1,0) will be projected onto the point (x, 6x) that lies on the line y=6x. The closest point on the line to (1,0) is when x=0, so the projection of (1,0) onto the line is (0,0). Therefore, the first column of the standard matrix will be (0,0).
- (0,1) will be projected onto the point (x, 6x) that lies on the line y=6x. The closest point on the line to (0,1) is when x=1/6, so the projection of (0,1) onto the line is (1/6,1). Therefore, the second column of the standard matrix will be (1/6,1).

Putting these columns together, we get the standard matrix of the projection onto the line y=6x:

[0  1/6]
[0   1 ]

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Answer:

Answer:

5z– 2 = 43

5z=43+2

z=45/5=9

9 makes the equation below true

(a) \(\frac{x}{x^2 + x + 3}\) will be a continuous function in interval (- ∞ ,  ∞), (b)   \(\frac{x + 7}{\sqrt{x} }\) will be a continuous function in interval (0,  ∞), and (c) \(x\sqrt{x + 6}\) will be a continuous function in interval [-6,  ∞).

(a)  \(\frac{x}{x^2 + x + 3}\)

x² + x + 3 will never be zero.

so it will be a continuous function all the time or in the interval (- ∞ ,  ∞).

(b)  \(\frac{x + 7}{\sqrt{x} }\)

in this function x cannot be negative or zero.

so the function will be a continuous function for x >0

or in the interval (0,  ∞)

(c)  \(x\sqrt{x + 6}\)

for this function, the value of  (x + 6) cannot be a negative value.

or x + 6 >=0 or x >= -6

so the function will be continuous in the interval [-6,  ∞)

Therefore, (a) \(\frac{x}{x^2 + x + 3}\) will be a continuous function in interval (- ∞ ,  ∞), (b)   \(\frac{x + 7}{\sqrt{x} }\) will be a continuous function in interval (0,  ∞), and (c) \(x\sqrt{x + 6}\) will be a continuous function in interval [-6,  ∞).

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The complete question is:

describe the interval(s) on which the function is continuous. (enter your answer using interval notation.)

(a)  \(\frac{x}{x^2 + x + 3}\)

(b)  \(\frac{x + 7}{\sqrt{x} }\)

(c)  \(x\sqrt{x + 6}\)

To maximize its profit, a monopolist would choose option d: q = 30 and p = 60.

To maximize profit, a monopolist would choose the outcome that corresponds to the highest profit level.

Profit is calculated as total revenue minus total cost.

Let's analyze each option:

a. q = 45 and p = 45:

In this case, the monopolist produces a quantity of 45 units and sets the price at $45.

To determine if this is the optimal choice, we need to compare the revenue and cost associated with this outcome with the other options.

b. q = 60 and p = 30:

Here, the monopolist produces a higher quantity of 60 units but sets a lower price of $30.

c. q = 30 and p = 30:

This option represents a lower quantity of 30 units and a price of $30.

d. q = 30 and p = 60:

In this scenario, the monopolist produces a lower quantity of 30 units but sets a higher price of $60.

To determine the optimal outcome, we need to consider the monopolist's cost structure.

Without information about costs, we cannot definitively identify the optimal choice.

The monopolist would consider both revenue and cost implications to maximize profit.

However, we can make some general observations:

Option a (q = 45 and p = 45) and option c (q = 30 and p = 30) result in the same price and may have similar revenue implications.

The choice between these options would depend on the cost structure and profit margins.

Option b (q = 60 and p = 30) could result in higher revenue due to the higher quantity sold, but the lower price may affect profit margins.

Option d (q = 30 and p = 60) may result in higher prices and potentially higher profit margins, but the lower quantity sold may affect revenue.

Ultimately, the monopolist would need to assess the revenue, cost, and profit implications of each option to determine the optimal outcome for maximizing profit.

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Step-by-step explanation:

Using a calculator, if you typed in 7 divided by 8, you'd get 0.875. You could also express 7/8 as a mixed fraction: 0 7/8. If you look at the mixed fraction 0 7/8, you'll see that the numerator is the same as the remainder (7), the denominator is our original divisor (8), and the whole number is our final answer (0).

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Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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Answer:

\(5^{2}\)(7) = 175

Step-by-step explanation:

hope this helps! just follow the order of operations. :)

Answer:

f=x-9

Step-by-step explanation:

Answer:

f(x) = 10

Step-by-step explanation:

f(x)=9-x   f(-1)

Put in the -1 for x

f(x) = 9 - (-1)

f(x) = 9 + 1

f(x) = 10

Hope this helps :)

The given expression is

First, we solve the powers and the root

We solve the products on each side of the fraction

Now, we divide whole numbers each other and powers each other

Answer: 5280 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is 4

The length of fence that Mr johnson had is 24.6m.

A rectangle's perimeter would be the total length and distance of all its boundaries on all sides. A perimeter of rectangle would be a linear measurement that is expressed in meters, feet, inch, or yards.

A rectangle's perimeter is the whole length of its outside boundary. It is equal to twice the sum of its length and breadth and is computed to use the formula:

Perimeter = 2(length + width).

Now according to the question;

Let 'L' be the length of the rectangle garden = 7m.

Let 'B' be the breadth of the rectangle garden = 7m.

Using the formula;

Perimeter = 2(length + width).

Substitute the values;

Perimeter = 2(7 + 7).

Perimeter = 28m

Mr johnson needed an extra of 3.4 m of fence.

The original length of the fence is

= 28m - 3.4m

=  24.6m.

Therefore, The length of fence that Mr johnson had is 24.6m.

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The two triangles n = (75 + 3) / 5 = 18. The measure of angle q is 18 degrees.

1. First, find the value of n by using the equation 5(n - 3) = 75 + 3

2. Next, add 75 and 3 together and divide by 5. This gives us a value of 18 for n.

3. Finally, use the equation 5(n - 3) to determine the measure of angle q in triangle qrs. This equals 5(18 - 3) = 5(15) = 75 degrees.

The two triangles qrs and xyz are similar, meaning they have the same angle measures. In order to find the measure of angle q in triangle qrs, we must first find the value of n. The measure of angle x in triangle xyz is 75 degrees and the measure of angle q in triangle qrs is equal to 5(n - 3) degrees. We can use this equation to solve for the value of n. To do this, we add 75 and 3, then divide by 5. This gives us a value of 18 for n. Therefore, the measure of angle q in triangle qrs is 18 degrees.

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4 units

Number lines are linear representations of length or some other unit.

Number Lines

Number lines are always straight lines that only have one dimension. This means that there is only one axis or line that has values. As seen in the picture, number lines are usually drawn horizontally and marked with numbers to visually represent data.

Line of QR

The question asks for the units of QR. This notation represents the line between the 2 points Q and R. So, to find the length of the line we can simply count the distance between the two points. Between the values of -3 and 1, there are 4 units. So, the line has a length of 4 units.

We can also find the length by subtracting the two numbers.

The unit rate is $60.20 ÷ 5.  Solve that (that's what goes in the 1 hour box) and then multiply it by each number of hours. If you want to comment with your answer I can tell you if it's right. :)

Answer:

2

Step-by-step explanation:

slope= change of y/change of x

slope=6/3=2

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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Answer:

D is correct.

Step-by-step explanation:

\(3 |x + 1| < 6\)

\( |x + 1| < 2\)

\( - 2 < x + 1 < 2\)

\( - 3 < x < 1\)

x > 3 and x < 1, so D is correct.

Answer:

6 whole pieces.

Step-by-step explanation:

0.54/0.08 = 6.75

You can divide the 0.54m string into 6 whole pieces.

The value of x from the given diagram is -6

Line is defined as the distance between two points. Given the line RP with the following measures

RP = 17

RQ = x + 14

QP = x + 15

Using the expression

RP = RQ + QP

Substitute

17 = x + 14 + x + 15

17 = 2x + 29

Determine the value of x

2x = 17 - 29
2x= -12

x = -6

Hence the value of x from the given diagram is -6

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Answer:  The shadow of the tree is 280 feet long.

Step-by-step explanation:

We can use a ratio to solve this:

Use the Height to shadow for each. This works because the fractions must reduce to the same equivalent.

5/10 = 140/x

We can see that 5/10 is 1/2, so we need another fraction using 140 as the numerator that is equal to 1/2.  That's easy here: Multiply 140 × 2 to get the new denominator, 280 that replaces x. That is the length of the shadow.

If you have a less obvious ratio, you can use Cross Multiplication to solve the unknown value in the ratio:

5/10 = 140/x  Cross multiply the numerator of the left side times the denominator on the right side, and the denominator on the left side by the numerator on the right side:

5 × x = 10 × 140

5x = 1400  Divide both sides by 5 (the 5s "cancel" on the left)

5x/5 = 1400/5

x = 280

I hope this helps, especially when you see more questions like this in the future.

Answer 3 hours

Step-by-step explanation:

\( \frac{6a - {b}^{2} }{2} + \binom{b}{a} ^{2} \)

a=2 b=4

\( \frac{6(2) - {4}^{2} }{2} + \binom{4}{2}^{2} \)

\( \frac{12 - 16}{2} + \frac{16}{4} \)

\( \frac{ - 4}{2} + 4 \)

\( - 2 + 4 = 2\)

answer is option a 2

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Answer:

54 marbles

Step-by-step explanation:

The question is a word problem leading to a simultaneous equation

Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,

If Mary gives Sam 5 marbles, we have;

x + 5 = 2 × (y - 5)...(1)

If Sam gives Mary 4 marbles, we get;

x - 4 = y + 4...(2)

From equation (1), we get;

x + 5 = 2 × (y - 5) = 2·y - 10

x = 2·y - 10 - 5 = 2·y - 15

x = 2·y - 15...(3)

From equation (2), we have;

x - 4 = y + 4

∴ x = y + 4 + 4 = y + 8

x = y + 8...(4)

Equating the two values of 'x' in equation (3), and equation (4), we get;

2·y - 15 = y + 8

2·y - y = 8 + 15 = 23

∴ y = 23

From equation (4), we get;

x = y + 8 = 23 + 8 = 31

x = 31

The total number of marbles they have altogether = x + y

However, x + y = 23 + 31 = 54

Therefore;

The total number of marbles they have altogether = 54 marbles.

Given the topological spaces X = {D, O, R, K} with the topology Tx and Y = {M, A, T, H} with the topology Jy, we are asked to determine whether the set E = {0, K} is open in X and open in Y.

To determine whether the set E = {0, K} is open in the topological spaces X and Y, we need to check if E belongs to the respective topologies, Tx and Ty.

In X, the topology Tx is given by: Tx = {Ø, {0}, {D, O}, {O, R}, {D, O, R}, X}. We can see that E = {0, K} is not explicitly listed in Tx. Therefore, E is not open in X since it does not belong to the topology.

In Y, the topology Ty is given by: Jy = {0, {M}, {M, A}, {M, A, T}, Y}. Again, E = {0, K} is not explicitly listed in Ty. Hence, E is not open in Y as it does not belong to the topology.

In both cases, the set E = {0, K} is not open in the respective topological spaces X and Y because it is not a member of the defined topologies.

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If $\operatorname{gcd}(a d-b c, n)=1$, then the matrix \($\begin{pmatrix}a & b\\ \ d & e\end{pmatrix}$\) is invertible modulo n, and its inverse is given by:

\($\begin{pmatrix}a & b\\ \ d & e\end{pmatrix}^{-1}=\frac{1}{ad-bc}\begin{pmatrix}e & -b \\\ -d & a\end{pmatrix}$\)

The system of linear congruences is given by:

a + b ≡ c (mod n)

d + e ≡ f (mod n)

We can rewrite this system in matrix form as:

\($\begin{pmatrix}a & b \\\ d & e\end{pmatrix}\begin{pmatrix}x \ y\end{pmatrix}=\begin{pmatrix}c \ f\end{pmatrix}$\)

If the matrix \($\begin{pmatrix}a & b\\ \ d & e\end{pmatrix}$\) is invertible modulo n, then the system has a unique solution modulo n. This is because we can multiply both sides of the matrix equation by the inverse of the matrix to obtain:

\($\begin{pmatrix}x \ y\end{pmatrix}=\begin{pmatrix}a & b\\ \ d & e\end{pmatrix}^{-1}\begin{pmatrix}c \ f\end{pmatrix}$\)

To express the solutions for x and y in terms of the constants and the inverse, we need to find the inverse of the matrix\($\begin{pmatrix}a & b\\ \ d & e\end{pmatrix}$\) modulo n.

The inverse of a matrix \($\begin{pmatrix}a & b\\ \ c & d\end{pmatrix}$\) is given by:

\($\begin{pmatrix}a & b\\ \ c & d\end{pmatrix}^{-1}=\frac{1}{ad-bc}\begin{pmatrix}d & -b\\ \ -c & a\end{pmatrix}$\)

Therefore, if $\operatorname{gcd}(a d-b c, n)=1$, then the matrix \($\begin{pmatrix}a & b\\ \ d & e\end{pmatrix}$\) is invertible modulo n, and its inverse is given by:

\($\begin{pmatrix}a & b\\ \ d & e\end{pmatrix}^{-1}=\frac{1}{ad-bc}\begin{pmatrix}e & -b \\\ -d & a\end{pmatrix}$\)

To obtain the solutions for x and y, we can substitute the constants and the inverse into the formula:

\($\begin{pmatrix}x \ y\end{pmatrix}=\begin{pmatrix}a & b\\ \ d & e\end{pmatrix}^{-1}\begin{pmatrix}c \ f\end{pmatrix}$\)

which yields:

\($\begin{pmatrix}x \ y\end{pmatrix}=\frac{1}{ad-bc}\begin{pmatrix}e & -b\\ \ -d & a\end{pmatrix}\begin{pmatrix}c \ f\end{pmatrix}$\)

This gives us the solutions for x and y in terms of the constants and the inverse.

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