Which set includes ONLY rational numbers that are also integers?

Answer:

x=-7 y=-2x²-4x-5

Step-by-step explanation:

Answer:

49°

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

let x be the other exterior angle then sum and equate to 360

37 + 84 + 49 + 38 + 35 + 68 + x = 360

311 + x = 360 ( subtract 311 from both sides )

x = 49

The other exterior angle = 49°

Answer:

\( \frac{2}{x - 3} - \frac{12}{ {x}^{2} - 9} \\ = \frac{2}{x - 3} - \frac{12}{(x - 3)(x + 3)} \\ = \frac{2(x + 3) - 12}{( {x}^{2} - 9)} \\ = \frac{2x - 6}{( {x}^{2} - 9)} \\ = \frac{2(x - 3)}{(x - 3)(x + 3)} \\ = \frac{2}{x + 3} \)

Answer:

The answer is 74

Step-by-step explanation:

Since 25 increased to 50, it was multiplied by 2. Youd do the same to 37 so it would be 37×2:)

The solution is: the solution for the system of linear equations 3x+2y=-6 and y=1/2x+4 is , x = -3.5 and, y = 2.25.

Here we have,

to determine the solution to the system:

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

3x + 2y = -6 ....1

and,  y=1/2x+4

=> 2y = x + 8

=> x - 2y = -8.....2

Add the equations

So, we have

4x = -14

Divide both sides by 4

x  = - 7/ 2

Substitute x  = - 7/ 2  in x - 2y = -8

we get,

-7/2 - 2y = -8

Evaluate

y = 2.25

Hence, the solution for the system of linear equations 3x+2y=-6 and y=1/2x+4 is , x = -3.5 and, y = 2.25

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The limit from the left and the right are not equal, limx→−1f(x) does not exist.

The given piecewise function is:

f(x) =

2x^2 − 3x − 2, if x ≤ -1

−x^2 + 2x + 1, if -1 < x < 2

−2x^2 − x − 1, if x ≥ 2

To evaluate limx→−1f(x), we need to find the limit of the function as x approaches -1 from both the left and the right sides.

From the definition of the piecewise function, we can see that the middle piece of the function is undefined at x = -1, so we cannot use that piece to evaluate the limit at this point.

However, we can evaluate the limits of the other two pieces. For x ≤ -1, the limit is:

limx→-1- f(x) = limx→-1- (2x^2 − 3x − 2) = 3

For x ≥ 2, the limit is:

limx→-1+ f(x) = limx→-1+ (−2x^2 − x − 1) = -2

Since the limit from the left and the right are not equal, limx→−1f(x) does not exist.

In calculus, finding the limit of a function is an important concept. The limit of a function is the value that the function approaches as its input approaches a particular value or point. In this problem, we are asked to evaluate the limit of a piecewise function at a specific point.

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To prove that the function f: R - {0} → R defined by f(x) = 4x^(-1) is one-to-one, we need to show that for any two distinct values a and b in the domain of f, their corresponding function values f(a) and f(b) are also distinct.

Let's assume that a and b are two distinct values in the domain of f, meaning a, b ∈ R - {0}, and a ≠ b.

Now, we will evaluate f(a) and f(b) separately:

\(f(a) = 4a^(-1) = 4/a\)

\(f(b) = 4b^(-1) = 4/b\)

Since a and b are distinct values and a ≠ b, it follows that 1/a ≠ 1/b.

Hence, f(a) = 4/a and f(b) = 4/b are also distinct.

Therefore, for any two distinct values a and b in the domain of f, their corresponding function values f(a) and f(b) are distinct. This proves that the function f: R - {0} → R defined by f(x) = \(4x^(-1)\)is one-to-one.

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Answer:

yes they will be equal in 1.3 years

Step-by-step explanation:

The value of x for the expression is 168 = 18x + 12.2x.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

168 = 18x + 12.2x

Add like terms.

168 = 30.2x

Divide both sides by 30.2

168/30.2 = x

x = 5.56

Thus,

The value of x is 5.56.

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Based on the information the amount that Agnes paid as state income tax is $2,040.

Federal Income Tax is the tax system in the United States, levied and governed by Internal Revenue Services (IRS) which helps determine the tax that is charged on the income earned by individuals, corporates, and various other legal entities.

The first step is to calculate Agnes' federal taxable income.

Federal taxable income=$15449.60/0.284

Federal taxable income= $54,400

The second step is to calculate Agnes' state income tax.

State income tax=0.0375 ×$54,400

State income tax=$2,040

Hence, the amount that Agnes paid as state income tax is $2,040.

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Answer:

its d

Step-by-step explanation:

Answer:

x=75

Step-by-step explanation:

2/5x=26+4

2/5x=30

2x=30*5

2x=150

x=150/2

x=75

Answer: x=75

Step-by-step explanation:

Answer:

42cm²

Step-by-step explanation:

*internal screaming* okay, let's go:

So, at this point, I don't even know what I'm doing, so I'm not going to guarantee that this is right, I'm sorry, but let's do some random math:

So we know that the length (the top and bottom) of the rectangle is 7 cm, we just have to figure out the width (the sides), and we're gonna do that by:

0.5 x 2 = 1

7 - 1 = 6

So now we just do the basic rectangle area calculation:

7 x 6 = 42

So, I hope that the area of the shaded area is 42cm²

if this is wrong, let me know so I can fix it

hope this helps:/

The equation square root of (x + 3) + 6 = 9 has two potential solutions, x = 0 and x = 6. However, upon analysis, it is determined that x = 0 is an extraneous solution while x = 6 is not extraneous.

To find the result of the given equation, we'll break it step by step and also determine if any results are extraneous.

 The given equation is

 √( x + 3) 6 = 9

 Let's break it

Step 1 Subtract 6 from both sides of the equation

√( x +3) = 9- 6

√( x +3) = 3

 Step 2 Square both sides of the equation to exclude the square root

( x + 3) = \(3^{2}\)

( x + 3) = 9

 Step 3 Subtract 3 from both sides of the equation

x = 9- 3

x = 6

 The result to the equation is x = 6.

Now, let's determine if this result is extraneous or not.

 To check if the result is extraneous, we need to substitute it back into the original equation and see if it holds true.

Original equation √( x + 3) + 6 = 9

 Substituting x = 6

√( 6 +3) + 6 = 9

√ 9 +6 = 9

3 +6 = 9

9 = 9

Since the equation holds true when x = 6, the result x = 6 is NOT an extraneous result.

thus, the correct statements are

 x = 0; not extraneous

x = 6; not extraneous

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Answer:

it is A.

Step-by-step explanation:

The answer is not an equation, because for it to be an equation, an equal sign is required. Therefore it is an expression.

It is algebraic because there are variables involved. If there were only numbers, it would be numerical.

hope this helps!

Answer:

A. an algebraic expression

Step-by-step explanation:

It is algebraic because there is a variable involved, s. It is also an expression because there is no equal sign before or after the terms.

Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

The number of bills received by brady family are 781.

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable with the form an x + b = 0 are solved utilizing basic algebraic operations.

Let x equal the number of letters obtained,

(x - 3) equal the number of bills obtained,

(x + 5) equal the number of advertisements received, and also

the number of magazines did receive is also given (x - 3).

The following equation can be derived:

x + (x - 3) + (x + 5) + (x - 3) = 3131

4x - 1 = 3131

4x = 3132

x = 784

Thus, number of bills received are-

(x - 3) = 784 - 3

number of bills received = 781.

Therefore, the number of bills obtained by brady family are 781.

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Answer:

the second one

Step-by-step explanation:

edge 2020

Answer:

b .

Step-by-step explanation:

The series converges for all values of k greater than or equal to 2.

We can use the ratio test to determine the convergence of the series:

r = lim(n→∞) |[(n+1)! / k(n+1)]!| / |[n! / k n]!|

r = lim(n→∞)\((n+1)^k / k^(n+1)\)

Using the ratio test, we need to find the values of k for which the limit of r is less than 1.

If k = 1, then r = 1, and the series does not converge.

If k > 1, then as n approaches infinity, the numerator \((n+1)^k\) grows faster than the denominator\(k^(n+1)\), and the limit of r is infinity. Therefore, the series does not converge for k > 1.

If k = 2, then r = 1/2, and the series converges by the ratio test.

If k > 2, then the limit of r is less than 1, and the series converges by the ratio test.

Therefore, the series converges for all values of k greater than or equal to 2.

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Answer:

b = 9 cm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

here h = 2b , then

\(\frac{1}{2}\) × b × 2b = 81

\(\frac{1}{2}\) × 2b² = 81

b² = 81 ( take square root of both sides )

b = \(\sqrt{81}\) = 9 cm

The surface area of just the base of the cone is approximately 314.16 cm^2.

The base of a cone is a circle, and the surface area of a circle can be calculated using the formula:

Surface Area of a Circle = π * radius^2

In this case, the radius of the base of the cone is given as 10 cm.

So, the surface area of just the base of the cone can be calculated as:

Surface Area of Base = π * (10 cm)²

Surface Area of Base = π * 100 cm²

∴ Surface Area of Base ≈ 314.16 cm²

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The number of days Bilquis can afford to rent while staying within her budget is 2 days.

The question has the following data

amount charged =  $48

Rent per mile = $0.08

The mile to drive = 175 miles.

Amount to spend = 110 dollars

The inequality would be written as

48x + 0.08(175) ≤ 110

we are to solve for the value of x

this would be

48x + 14 ≤ 110

48x ≤ 110 - 14

48x ≤ 96

We have to divide through by 48

x ≤ 96 / 48

x ≤ 2

Hence we can say that the number of days Bilquis can afford to rent while staying within her budget is 2 days.

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Answer:

answer is 12

....

.

.

...

.

. :-)))

The probability of choosing all five white balls correctly from a bowl of 69 white balls and the probability of choosing the correct red ball from a bowl of 29 red balls is \({}^{69}C_5/29\) .

The probability of choosing all five white balls correctly can be calculated using the formula for combinations, where the order does not matter and the balls are chosen without replacement. The probability is given by:

P(Choosing all 5 white balls correctly) = (Number of ways to choose 5 white balls correctly) / (Total number of possible combinations)

The number of ways to choose 5 white balls correctly is 1, as there is only one correct combination.

The total number of possible combinations can be calculated using the formula for combinations, where we choose 5 balls out of 69. It is given by:

Total number of combinations = \({}^{69}C_5\)

Next, we need to calculate the probability of choosing the correct red ball from a bowl of 29 red balls. Since there is only one correct red ball, the probability is 1/29.

Finally, to find the likelihood of being the winner of the Powerball lottery, we multiply the probability of choosing all five white balls correctly by the probability of choosing the correct red ball:

Likelihood = P(Choosing all 5 white balls correctly) * P(Choosing correct red ball)

=\({}^{69}C_5 \times 1/29\\\)

This gives us the probability of being the winner of the Powerball lottery.

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Answer:

her distance would be 0 after 8 hours since 8*3 = 24 and just add a zeor behind the 24 from the 30

Step-by-step explanation:

To find the volume of all pairs of vertices (s, t) in a directed graph G using an efficient Dijkstra-like algorithm, we can adapt the Dijkstra's algorithm with some modifications.

Here is the algorithm:

Initialize all vertices' volumes as negative infinity, except for the starting vertex s, which has a volume of 0.

vol(v) = -∞ for all v in G.V

vol(s) = 0

Create a priority queue Q to store vertices based on their volumes (minimum volume first). Initially, insert vertex s into Q.

While Q is not empty, do the following:

a. Extract the vertex u with the minimum volume from Q.

b. For each neighbor v of u:

Calculate the capacity of the path from s to v via u: cap(s, v) = min(cap(s, u), w(u, v)), where w(u, v) is the weight of the arc from u to v.

If cap(s, v) > vol(v), update vol(v) with cap(s, v) and insert v into Q if it's not already present.

After the algorithm finishes, the volumes vol(s, t) will represent the maximum capacity of paths from s to t for all vertices t in G.V{s}.

This modified Dijkstra-like algorithm finds the maximum capacity (volume) from s to all other vertices by considering all possible paths and updating the volume as we encounter smaller capacities along the way. By using a priority queue to extract the minimum volume vertex efficiently, the algorithm can run in O((|V| + |E|) log |V|) time complexity, where |V| is the number of vertices and |E| is the number of edges in the graph.

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Answer:

13a:   Measure of angle 1 is 120 degrees

13b:   Angle 2 is 60 degrees

Step-by-step explanation:

Angle 1 is alternate exterior (so in a parallel pair they are equal) to the angle on line m given as 120 deg.

Angle 2 is 180 minus 120= 60   Sum of the two angles must equal 180.

The addition of the discrete-time signals gives x₃(n) = (0, 1, 4, 4), and the multiplication of discrete-time signals gives x₄(n) = (-4, -2, 3, 4).

To perform the addition of discrete-time signals, we simply add the corresponding samples at each time index.

Given:

x₁(n) = (2, 2, 1, 2)

x₂(n) = (-2, -1, 3, 2)

Adding the corresponding samples:

x₃(n) = x₁(n) + x₂(n) = (2 + (-2), 2 + (-1), 1 + 3, 2 + 2)

      = (0, 1, 4, 4)

Therefore, x₃(n) = (0, 1, 4, 4)

To perform the multiplication of discrete-time signals, we multiply the corresponding samples at each time index.

Given:

x₁(n) = (2, 2, 1, 2)

x₂(n) = (-2, -1, 3, 2)
Multiplying the corresponding samples:

x₄(n) = x₁(n) * x₂(n) = (2 * (-2), 2 * (-1), 1 * 3, 2 * 2)

      = (-4, -2, 3, 4)

Therefore, x₄(n) = (-4, -2, 3, 4)

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Answer:

32, 45

Step-by-step explanation: