Write an exponential function for a graph that
passes through the points (2, 1.4) and (4,5.6)

Yes, the statement "if x is rational and y is irrational, then x + y is irrational" is true.

To understand why, let's break it down step by step:

1. First, let's define what it means for a number to be rational or irrational:
  - A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
  - An irrational number is a number that cannot be expressed as the ratio of two integers.

2. Given that x is rational and y is irrational, we can express x and y as follows:
  - x = a/b, where a and b are integers and b is not zero.
  - y = c, where c is an irrational number.

3. Now, let's consider the sum x + y:
  - x + y = (a/b) + c

4. To prove that x + y is irrational, we'll assume the contrary, that is, x + y is rational. This means we can express x + y as the ratio of two integers:
  - x + y = p/q, where p and q are integers and q is not zero.

5. We can rewrite this equation as follows:
  - (a/b) + c = p/q

6. Rearranging the equation, we get:
  - (a/b) = (p/q) - c

7. Since (p/q) is a rational number and c is an irrational number, the right side of the equation (p/q) - c would be the difference between a rational and an irrational number.

8. However, the difference between a rational number and an irrational number is always irrational. Therefore, the right side of the equation is irrational.

9. This contradicts our assumption that (a/b) is rational, leading us to conclude that x + y must be irrational.

In conclusion, if x is rational and y is irrational, then x + y is always irrational.

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Hi

\(\star\sim\star\sim\star\sim\star\sim\star\sim\)

      bc a negative over a negative gives us a positive , so -72:(-9) is the same as 72:9 which is 8. Then we divide that by 2 and arrive at 4

\(\star\sim\star\sim\star\sim\star\sim\star\sim\)

Answer:

Same

Step-by-step explanation:

Answer:

yes it would be

Answer:

4.8 years

Step-by-step explanation:

10 800 = 8000 e^(i t)        i = decimal interest per year     t = years

10800/8000 = e^(.0625 t)      ln both sides

.300 = .0625 t

t = 4.8 years

Answer:

(0, 0 )

Step-by-step explanation:

y = 4x is the equation of a line passing through the origin.

Then its y- intercept is 0 or (9, 0 )

Answer:

B

Step-by-step explanation:

Depends on what you change. If you change the number of electrons or neutrons, it will still be the same element. It will just become a charged ion or an isotope respectively. If you change the number of protons, it will become a different element.

Hope that helps

Answer:

See explanation.

Step-by-step explanation:

The arc BX, central angle BCX, and inscribed angle BNX are connected through the following relationships:

1. The central angle BCX subtends the arc BX. This means that the central angle is formed by two radii connecting the center of the circle to the endpoints of the arc BX.

2. The inscribed angle BNX subtends the same arc BX. This means that the inscribed angle is formed by two chords connecting a point on the circumference of the circle to the endpoints of the arc BX.

3. The relationship between the central angle BCX and the inscribed angle BNX is given by the Inscribed Angle Theorem, which states that the measure of an inscribed angle is half the measure of the central angle subtending the same arc. In other words, if θ is the measure of the central angle BCX and α is the measure of the inscribed angle BNX, then:

\(\alpha =\frac{1}{2}\) θ

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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This is the standard form of a quadratic function with leading coefficient 1, and  0 and -7.

If the zeros of a quadratic function are 0 and -7, then the function can be written as:

f(x) = a(x - 0)(x - (-7))

Simplifying:

f(x) = a(x)(x + 7)

To find the value of 'a', we can use one of the points on the parabola. Since we know that the x-intercept is 0, we can substitute x = 0 and y = 0 into the equation:

0 = a(0)(0 + 7)

0 = 0

This tells us that a can be any value, as long as it's not 0. Let's choose a = 1 for simplicity. Then the quadratic function with zeros 0 and -7 is:

f(x) = (x)(x + 7)

f(x) = x^2 + 7x

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Step-by-step explanation:

9868866858566586575765578

The product of any two even integers is even.

Odd numbers: An odd number is any natural number that can be written as (2n + 1), where n is any natural number, i.e., a positive integer.

Even numbers: Any natural number that can be written as 2n, where n is any natural number, i.e., a positive integer, is referred to as an even number.

The product of two even numbers is even.

Let us suppose m and n be any integers.

So, 2m and 2k are two even numbers.

Take the product as 2m(2k) = 2(2mk), which is even.

Let the two even integers be x1 and x2.

Let x1 = 2

Let x2 = 6

Therefore, the product of x1 and x2 is

x1 * x2 = 2 * 6 = 12

The product is even since it is divisible by 2.

Hence, the product of any two even integers is even.

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Answer:

3r + 4t = 80

Step-by-step explanation:

Roses cost $3 each, tulips cost $4 each

Sherry used 3/8 of her sugar to make sweet tea, which is the fraction obtained by subtracting 1/2 from 7/8.

The fraction of sugar that Sherry used to make sweet tea, we need to subtract the amount of sugar she used from the total amount of sugar she had.

Sherry had $7/8$ of a cup of sugar in her kitchen, and she used $1/2$ of a cup of sugar to make sweet tea.

To find the remaining amount of sugar, we subtract $1/2$ from $7/8$:

$7/8 - 1/2$

To subtract fractions, we need a common denominator. In this case, the common denominator is 8. We can rewrite $1/2$ as $4/8$:

$7/8 - 4/8$

Now we can subtract the numerators:

$3/8$

Therefore, Sherry used $3/8$ of her sugar to make sweet tea.

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Answer:

Step-by-step explanation:

B - 6 million

b. 6 Million

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Answer:

18. g= -3

19. x= -1

20. n= 3

21. p= -1

22. d= -3

23. a= 5

Step-by-step explanation:

how to solve the variable (using 18 as an example)

step 1: simplify both sides of the equation.

20+g+g=14

(g+g)+(20)=14(combine like terms)

2g+20=14

2g+20=14

step 2: subtract 20 from both sides.

2g+20−20=14−20

2g=−6

step 3: divide both sides by 2.

2g/2 = -6/2

Answer:48%

Step-by-step explanation:

have a good day

Given the function `y = (x-6) / (x^2 + 5x + 6)`, let's identify the vertical asymptotes and holes: Factoring the denominator, we get`(x^2 + 5x + 6) = (x+2)(x+3)`So, `y = (x-6) / (x+2)(x+3)`

The vertical asymptotes of the function are the roots of the denominator. Thus, the vertical asymptotes of the function are `x = -2` and `x = -3`.Now, we'll look for the holes in the function. A hole is a point where the function is undefined but can be simplified by canceling common factors.

In the given function, we notice that the numerator `(x-6)` and the denominator `(x+2)(x+3)` have a common factor of `(x-6)`. Thus, there is a hole at `x = 6`.We can cancel `(x-6)` from both numerator and denominator to obtain the simplified function `y = 1 / (x+3)`.Therefore, the vertical asymptotes are `x = -2` and `x = -3`, and there is a hole at `x = 6`.

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The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).

Given that:

Enrique predicts that he can make additional money from sales of accessories and services for computer products sold by his store.

The store makes x dollars selling computer products, Enrique predicts the store will make 0.05x dollars ($0.05) from selling accessories.

The following steps can be used in order to determine the equation that represents the predicted amount y:

Step 1 - According to the given data, the store makes x dollars selling computer products.

Step 2 - It is also given that, in January and February of this year, the store made $2,500 from sales of accessories and services.

Step 3 - So, the linear equation that represents the given situation is:

y = 0.05x + 2500

Hence the answer is The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).

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      First, we can see that this is a reduction because ΔXYZ is larger than its dilation, ΔX'Y'Z'.

But by how much? We can compare two sides such as XY and X'Y' to see.

      -> I am going to compare sides XY and X'Y' because they are fully vertical lines that we can count without needing to use a distance formula.

             -> XY is 8 units long

             -> X'Y' is 4 units long

      -> 8 / 4 is a scale factor of 2

This is a reduction with a scale factor of 2.

∀The characteristic polynomial of J is λ² - 4λ + 3.The characteristic polynomial of the matrix J is obtained by finding the determinant of the matrix J - λI, where J is the given matrix and I is the identity matrix.

In this case, J is a 2x2 matrix with elements [2 1] and [1 2], and I is the 2x2 identity matrix. The characteristic polynomial can be calculated by subtracting λI from J, resulting in the matrix [2-λ 1] and [1 2-λ]. To find the determinant of this matrix, we use the formula (2-λ)(2-λ) - 1*1, which simplifies to λ²- 4λ + 3.  In this case, J is a 2x2 matrix with elements [2 1] and [1 2], and I is the 2x2 identity matrix [1 0] and [0 1].

Subtracting λI from J gives us the matrix [2-λ 1] and [1 2-λ]. To find the determinant of this matrix, we use the formula (2-λ)(2-λ) - 1*1, which simplifies to λ² - 4λ + 3. Thus, the characteristic polynomial of J is given by the equation λ² - 4λ + 3.The eigenvalues of J are the values of λ that satisfy this polynomial equation. By solving the equation λ²- 4λ + 3 = 0, we can determine the eigenvalues of the matrix J.

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We have verified Chebyshev’s inequality for k = 2 and k = 3 when x ∼ binomial(50, 0.4).

Main answer :Using r’s "pbinom" function, we can verify Chebyshev’s inequality for k = 2 and k = 3 when x ∼ binomial(50, 0.4).The P(X ≤ μ + 2σ) and P(X ≤ μ + 3σ) values were obtained from the "pbinom" function for k = 2 and k = 3, respectively.

Supporting explanation :Chebyshev’s inequality states that for any data set, the proportion of the data within k standard deviations of the mean is at least 1 – 1/k^2, where k is a constant greater than 1. This holds true regardless of the shape of the distribution. To verify Chebyshev’s inequality for k = 2 and k = 3 when x ∼ binomial(50, 0.4), we first calculate the mean and standard deviation using the formula μ = np and σ = sqrt(npq), where n = 50, p = 0.4, and q = 0.6. Thus, μ = 20 and σ = 2.83.Then, we use the "pbinom" function in R to obtain the values of P(X ≤ μ + 2σ) and P(X ≤ μ + 3σ) for k = 2 and k = 3, respectively. For k = 2, P(X ≤ 25.66) = 0.9975, and for k = 3, P(X ≤ 28.49) = 0.9995.These values are greater than or equal to 1 – 1/k^2, where k = 2 and k = 3, respectively.

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Answer:

The other length is 9 feet.

Step-by-step explanation:

Answer:

Assuming that the  purpose of the rest of the paint into to cover the rest ofe the board he would have 2 and 2/3 left

Step-by-step explanation:

Answer:

The average rate of change of the function f(x) = -2x + 15 from x1 = 0 to x2 = 3 is -2.

Step-by-step explanation:

To obtain the average rate of change of a function from x1 to x2, you can use the formula:

Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)

In this case, you are given the function f(x) = -2x + 15, and the values x1 = 0 and x2 = 3.

First, calculate the values of f(x1) and f(x2) by substituting x1 and x2 into the function:

f(x1) = -2(0) + 15 = 15

f(x2) = -2(3) + 15 = 9

Now we can substitute these values into the formula for average rate of change:

Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)

= (9 - 15) / (3 - 0)

= -6 / 3

= -2

Therefore, the average rate of change of the function f(x) = -2x + 15 from x1 = 0 to x2 = 3 is -2.

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The angle measure that corresponds to angle S is angle H.

Given information:

Figure 1 and Figure 3 are congruent figures.

That means, they have the same type of shape but have different sizes.

Therefore, as per the diagram,

PT ≅ GF

TR ≅ FD

RS ≅ DH

SQ ≅ HE

QP ≅ EG.

PTRSQ ≅ GFDHE.

Now, for angle measures,

Angle P is congruent to the angle G.

Angle T is congruent to the angle F.

Angle R is congruent to the angle D.

Angle S is congruent to the angle H.

Angle Q is congruent to the angle E.

As per the congruency of the figures,

∠S ≅ ∠H.

Therefore, ∠S ≅ ∠H.

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Answer:your answer should be 2

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

Since 2 sides of the triangle are congruent then it is isosceles, so

The 2 base angles are congruent, both 29°, thus

11x - 65 = 180 - (29 + 29) = 180 - 58 = 122 ( add 65 to both sides )

11x = 187 ( divide both sides by 11 )

x = 17

As per the given data, the true proportion of nearsighted children is equal to 8%.

When an experiment is employed as the technique of examination, the two variations of the hypothesis the null hypothesis and the alternative hypothesis that is frequently utilised in research are referred to as the experimental hypothesis. The null hypothesis (H0) states that 8% of children are truly nearsighted. The alternative hypothesis (H1) states that the actual percentage of children who are nearsighted is lower than 8%.

The alternative hypothesis contends that the real proportion of nearsighted youngsters is different from 8%, whereas the null hypothesis argues that the 8% estimate is accurate. These hypotheses can be used in a hypothesis test to see if the sample data have enough support for the alternative hypothesis, which states that the 8% number is incorrect, to be accepted instead of the null hypothesis.

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the answer is 10m deep after rising