In 2010, the population of Houston, Texas, was 2,099,451. In 2017, Houston's population was estimated to be 2,312,717. What is the estimated annual growth rate of Houston's population?

We conclude that there is no valid domain for the given function g(x, y) = sin^-1(x² + y² - 3). Thus, the concept of circles with radii does not apply in this case.

To determine the domain of the function g(x, y) = sin^-1(x² + y² - 3), we need to examine the range of the arcsine function. The arcsine function, [tex]sin^{(-1)[/tex](z), is defined for values of z between -1 and 1, inclusive. Therefore, for the given function, we have:

-1 ≤ x² + y² - 3 ≤ 1

Rearranging the inequality, we get:

-4 ≤ x² + y² ≤ -2

Now, let's analyze the inequalities separately:

x² + y² ≤ -2:

This inequality is not possible since the sum of squares of two non-negative numbers (x² and y²) cannot be negative. Therefore, there are no points that satisfy this inequality.

x² + y² ≤ -4:

Similarly, this inequality is also not possible since the sum of squares of two non-negative numbers cannot be less than or equal to -4. Therefore, there are no points that satisfy this inequality either.

Based on the analysis, we conclude that there is no valid domain for the given function g(x, y) = sin^-1(x² + y² - 3). Thus, the concept of circles with radii does not apply in this case.

It's important to note that the arcsine function has a restricted range of -π/2 to π/2, and for a valid domain, the input of the arcsine function must be within the range of -1 to 1. In this particular case, the given expression x² + y² - 3 exceeds the range of the arcsine function, resulting in no valid domain.

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Answer:

a. 5π cm

b. 144π in²

c. 6 ft

Step-by-step explanation:

a.

The circumference of a circle is given by:

Circumference pf circle= πd

where d is the diameter.

In this case, d = 5 cm,

Therefore, Circumference of circle = π*5=5π cm

b.

The area of a circle is given by:
Area of circle=πr²,

where r is the radius. In this case, the diameter is d = 24 in,

so, the radius is r = d/2 = 24/2=12in

Therefore, Area of circle=π*12²=144π in²

c.

The area of a circle is given by:

Area of circle=πr²,

where r is the radius. In this case, Area is 36π ft²

Now substituting value

36π=πr²

dividing both side by π, we get

36=r²

[tex]r=\sqrt{36}=6[/tex]

r=6 ft.

Therefore, Radius is 6 ft.

Using the concept of perimeter of polygon, the perimeter of figure C is 27cm shorter than total perimeter of A and B

To solve this problem, we have to know the perimeter of the polygon C.

The perimeter of a polygon is the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The perimeter of the figures are;

Using the concept of perimeter of a rectangle;

a. figure A = 2(4 + 11) = 30cm

b. figure B = 2(8 + 4) = 24cm

c figure C = 11 + 4 + 8 + 4 = 27cm

Now, we can add A and B and then subtract c from it.

30 + 24 - 27 = 27cm

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Answer: 337

Step-by-step explanation: it is 337 because if you subtract it all you get that

Answer:

The recursive formula for an=1/8(2)n-1 is:

a1=1/8 an+1=1/8(2)(n)

This formula defines a sequence where each term is equal to 1/8 of the previous term multiplied by 2.

Step-by-step explanation:

Answer:

  (c)  61°

Step-by-step explanation:

You want the measure of the external angle formed by a tangent and secant that intercept arcs of 73° and 195° of a circle.

The measure of the angle at F is half the difference of intercepted arcs HE and EG.

  (195° -73°)/2 = 122°/2 = 61°

The measure of angle F is 61°.

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The equation of the line of fit is y = 15x + 30.

To determine the equation of the line of fit, we can use the given data points (0,30) and (2,60). We can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.

Using the two data points, we can calculate the slope (m) as the change in y divided by the change in x:

m = (60 - 30) / (2 - 0) = 30 / 2 = 15

Now that we have the slope, we can substitute one of the data points into the equation to solve for the y-intercept (b). Let's use the point (0,30):

30 = 15(0) + b

30 = 0 + b

b = 30

Therefore, the equation of the line of fit is y = 15x + 30. This means that for every additional hour of study time (x), the grade percent (y) increases by 15, and the line intersects the y-axis at 30.

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Answer:

A) No solutions

Step-by-step explanation:

First of all, we know that option B will always be incorrect. You cannot have two solutions. To illustrate this, try drawing two lines. You will find that they will either intersect once (one solution), or they will not intersect, (no solutions, parallel lines), or they are the same line and thus they will always intersect (infinitely many solutions).

With that in mind, let's solve the equation.

4x-4-5x=7-x+5

First, combine all like terms.

-x-4=12-x

Now add 4 to both sides to leave x by itself.

-x=16-x

This statement cannot be true. Therefore, this equation has no solutions (parallel lines. One line starts from 0, or the origin. That line is -x. The other line starts from 16. That line is -x+16.)

Hope this helps!

The percentile of 6.2 in the given data set is 40%.

To determine the percentile of 6.2 in the given data set, we can use the following steps:

Arrange the data set in ascending order:

4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2

Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.

Calculate the percentile using the formula:

Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100

In this case, the percentile of 6.2 can be calculated as:

Percentile = (4 / 10) × 100 = 40%

The percentile of 6.2 in the sample data set is therefore 40%.

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1. The indefinite integral of (v + 1) / (2v - 20)^5 dv is -1 / (8(2v - 20)^4) + C.

2. The indefinite integral of x^2 / (x - 5) dx is (1/2) x^2 + 5x + 25 ln|x - 5| + C.

3. The indefinite integral of x cos(8x^2) dx is (1/16) sin(8x^2) + C.

4. The indefinite integral of 176 / e^(-x) + 1 dx is 176 ln|1 + e^x| + C.

1. To find the indefinite integral of (v + 1) / (2v - 20)^5 dv:

Let u = 2v - 20. Then du = 2 dv.

The integral becomes:

(1/2) ∫ (1/u^5) du

Now we can integrate using the power rule:

(1/2) ∫ u^(-5) du

Applying the power rule, we get:

(1/2) * (u^(-4) / -4) + C

= -1 / (8u^4) + C

Substituting back u = 2v - 20:

= -1 / (8(2v - 20)^4) + C

Therefore, the indefinite integral of (v + 1) / (2v - 20)^5 dv is -1 / (8(2v - 20)^4) + C.

2. To find the indefinite integral of x^2 / (x - 5) dx:

We can use polynomial long division to simplify the integrand:

x^2 / (x - 5) = x + 5 + 25 / (x - 5)

Now we can integrate each term separately:

∫ x dx + ∫ (5 dx) + ∫ (25 / (x - 5) dx)

Using the power rule, we get:

(1/2) x^2 + 5x + 25 ln|x - 5| + C

Therefore, the indefinite integral of x^2 / (x - 5) dx is (1/2) x^2 + 5x + 25 ln|x - 5| + C.

3. To find the indefinite integral of x cos(8x^2) dx:

We can use the substitution method. Let u = 8x^2, then du = 16x dx.

The integral becomes:

(1/16) ∫ cos(u) du

Integrating cos(u), we get:

(1/16) sin(u) + C

Substituting back u = 8x^2:

(1/16) sin(8x^2) + C

Therefore, the indefinite integral of x cos(8x^2) dx is (1/16) sin(8x^2) + C.

4. To find the indefinite integral of 176 / e^(-x) + 1 dx:

We can simplify the integrand by multiplying the numerator and denominator by e^x:

176 / e^(-x) + 1 = 176e^x / 1 + e^x

Now we can integrate:

∫ (176e^x / 1 + e^x) dx

Using u-substitution, let u = 1 + e^x, then du = e^x dx:

∫ (176 du / u)

Integrating 176/u, we get:

176 ln|u| + C

Substituting back u = 1 + e^x:

176 ln|1 + e^x| + C

Therefore, the indefinite integral of 176 / e^(-x) + 1 dx is 176 ln|1 + e^x| + C.

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The fraction that converts to a terminating decimal number is C. 3/8.

To determine which fraction converts to a terminating decimal number, we need to analyze the denominator of each fraction. A fraction will result in a terminating decimal if its denominator has only prime factors of 2 and/or 5.

Let's examine each option:

A. 1/6: The denominator is 6, which can be factored into 2 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.

B. 2/9: The denominator is 9, which can be factored into 3 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.

C. 3/8: The denominator is 8, which can be factored into 2 * 2 * 2. Since all the factors are 2, this fraction does convert to a terminating decimal.

D. 4/7: The denominator is 7, which cannot be factored into 2 or 5. Therefore, this fraction does not convert to a terminating decimal.

Based on our analysis, the fraction that converts to a terminating decimal number is C. 3/8.

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Answer:

80

Step-by-step explanation:

Just average the two numbers to get (70+90)/2 = 160/2 = 80

Answer:

Step-by-step explanation:

To find the midpoint between two numbers, you add them together and divide the sum by 2.

In this case, the midpoint between 70 and 90 would be:

(70 + 90) / 2 = 160 / 2 = 80.

Therefore, the midpoint between 70 and 90 is 80.

Answer:182.12 meters of fencing required.

Step-by-step explanation:

The best answer that matches the calculated values is C. sin θ = -1/3, tan θ = -3/(2√2)

Let's break down the given values and find the values of sine and tangent.

We are given:

cos θ = √(8/9)

csc θ < 0

Using the Pythagorean identity, sin^2θ + cos^2θ = 1, we can find the value of sin θ.

sin^2θ + (√(8/9))^2 = 1

sin^2θ + 8/9 = 1

sin^2θ = 1 - 8/9

sin^2θ = 1/9

Taking the square root of both sides, we get:

sin θ = ±1/3

Since csc θ is negative (csc θ < 0), we can conclude that sin θ is negative. Therefore, sin θ = -1/3.

Next, let's find the value of tan θ.

tan θ = sin θ / cos θ

tan θ = (-1/3) / (√(8/9))

tan θ = -√9/√8

tan θ = -√9/√(4*2)

tan θ = -√9/(2√2)

tan θ = -3/(2√2)

So, the values are:

sin θ = -1/3

tan θ = -3/(2√2)

The best selection from the available options that matches the calculated values is:

C. sin θ = -1/3, tan θ = -3/(2√2)

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The solutions of the system of equations are (2, -1) and (-4, 17)

The given system of equations is:

y = x² - x - 3

y = -3x + 5

To find the solutions, we need to solve these equations simultaneously.

Set the equations equal to each other:

x² - x - 3 = -3x + 5

Simplify and rewrite the equation in standard form:

x² - x + 3x - 3 - 5 = 0

x² + 2x - 8 = 0

Factor the quadratic equation:

(x - 2)(x + 4) = 0

Now we can solve for x by setting each factor equal to zero:

x - 2 = 0 or x + 4 = 0

Solving for x, we get:

x = 2 or x = -4

To find the corresponding y-values, we substitute these x-values into either of the original equations. Let's use equation 1):

For x = 2:

y = (2)² - 2 - 3 = 4 - 2 - 3 = -1

For x = -4:

y = (-4)² - (-4) - 3 = 16 + 4 - 3 = 17

As a result, the system of equations has two solutions: (2, -1) and (-4, 17).

The right responses are therefore (2, -1) and (-4, 17).

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The population at 4:00 P.M., 27 minutes earlier, is[tex]3^3[/tex] times the initial population P.

To determine the population of a bacteria culture 27 minutes earlier, we need to calculate the population growth from 4:00 P.M. to 4:27 P.M. given that the bacteria culture triples every 5 minutes.

Let's break down the time period into intervals of 5 minutes:

From 4:00 P.M. to 4:05 P.M., the population triples once.

From 4:05 P.M. to 4:10 P.M., the population triples again.

From 4:10 P.M. to 4:15 P.M., the population triples for the third time.

From 4:15 P.M. to 4:20 P.M., the population triples for the fourth time.

From 4:20 P.M. to 4:25 P.M., the population triples for the fifth time.

From 4:25 P.M. to 4:27 P.M., the population undergoes partial growth.

Since the population triples every 5 minutes, we can express the population at 4:27 P.M. as 3^5 times the initial population at 4:00 P.M.

Let's denote the initial population at 4:00 P.M. as P. Then, the population at 4:27 P.M. is [tex]3^5[/tex] * P.

To find the population 27 minutes earlier, we need to reverse the growth from 4:27 P.M. to 4:00 P.M. Since the population triples every 5 minutes, we need to divide the population at 4:27 P.M. by [tex]3^{(27/5).[/tex]

Therefore, the population at 4:00 P.M., 27 minutes earlier, can be calculated as:

Population at 4:00 P.M. = (Population at 4:27 P.M.) / [tex]3^{(27/5)[/tex]

[tex]= (3^{5} * P) / 3^{(27/5)\\\\\\\\= 3^{(25/5)} * P\\= 3^5 * P / 3^2\\= 3^3 * P[/tex]

Hence, the population at 4:00 P.M., 27 minutes earlier, is 3^3 times the initial population P.

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Answer:

C) -1/3

Step-by-step explanation:

Slope=rise/run

Slope=-1/3

Hello!

[tex]32 = 25x^2 - 4\\\\32 + 4 = 25x^2\\\\36 = 25x^2\\\\25x^2 - 36 = 0\\\\x = \dfrac{-b \±\sqrt{b^2 - 4ac} }{2a} \\\\\\x = \dfrac{-0 \±\sqrt{0^2 - 4 \times 25 \times (-36) } }{2 \times 25} \\\\\\x = \dfrac{\±60}{50} \\\\\boxed{x = \±\frac{6}{5} }[/tex]

The function rule that describes the given translation is T-9, 1(x, y).

The first value in the function rule represents the horizontal translation, while the second value represents the vertical translation. In this case, the square is translated 1 unit to the right, indicating a positive horizontal translation.

Additionally, the square is translated 9 units down, indicating a negative vertical translation. Therefore, the correct function rule is T-9, 1(x, y).

In the coordinate plane, the x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position. When we apply the function rule T-9, 1 to the coordinates of the square, we subtract 9 from the y-coordinate and add 1 to the x-coordinate.

This results in the square being moved 9 units down and 1 unit to the right from its original position.

The negative sign in front of the 9 indicates a downward movement, and the positive sign in front of the 1 indicates a rightward movement. Hence, the translation is accurately described by the function rule T-9, 1(x, y).

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Answer:

C

Step-by-step explanation:

The row operation on the matrix [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex] is [tex]\left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

From the question, we have the following parameters that can be used in our computation:

[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The row operation is given as

1/2R₁

This means that we divide the entries on the first row by 2

Using the above as a guide, we have the following:

[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

Hence, the row operation on the matrix is [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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Answer:

be more clear of what u mean edit the question so we can tell what u mean and answer correctly

Step-by-step explanation:

no explanation

The equation (-14) + x = 14 is solved by adding 14 to both sides of the equation, resulting in x = 28. This means that 28 is the value of x that satisfies the equation and makes it true.

To solve the equation (-14) + x = 14, we need to isolate the variable x on one side of the equation. Let's go through the steps:

Step 1: Add 14 to both sides of the equation to eliminate the -14 on the left side.

(-14) + x + 14 = 14 + 14

x = 28

The solution to the equation (-14) + x = 14 is x = 28.

In this equation, we start with (-14) on the left side, and we want to determine the value of x that makes the equation true. To do that, we need to isolate x. By adding 14 to both sides of the equation, we cancel out the -14 on the left side, leaving us with just x. On the right side, 14 + 14 simplifies to 28.

Therefore, the solution to the equation is x = 28. This means that if we substitute 28 for x in the original equation, (-14) + 28 will indeed equal 14. Let's verify this:

(-14) + 28 = 14

14 = 14

The left side of the equation simplifies to 14, and the right side is also 14. Since both sides are equal, it confirms that x = 28 is the correct solution to the equation.

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Step-by-step explanation:

The formula to calculate the circumference (C) of a circle is C = 2πr, where r represents the radius of the circle.

In this case, the given circumference is 68 cm. Plugging this value into the formula, we can solve for the radius (r):

68 = 2πr

To find the radius, we can divide both sides of the equation by 2π:

r = 68 / (2π)

Using an approximate value of π ≈ 3.14159, we can calculate the radius:

r ≈ 68 / (2 × 3.14159) ≈ 10.8419 cm

Therefore, the radius of the circle, which has a circumference of 68 cm, is approximately 10.8419 cm.

Therefore, The Radius of the Circle is 10.8 cm.

The surface area and the volume of the rectangular prism are 280 and 300

From the question, we have the following parameters that can be used in our computation:

The rectangular prism

The surface area is caculated as

Surface area = 2 * (10 * 5 + 10 * 6 + 5 * 6)

Evaluate

Surface area = 280

For the volume, we have

Volume = 10 * 5 * 6

Evaluate

Volume = 300

Hence, the surface area and the volume are 280 and 300

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The vertex of h(x) is (-3, 3), and the range is y ≥ 3.

To find the vertex of the quadratic function h(x), we can use the formula x = -b/2a, where the quadratic function is in the form [tex]ax^2 + bx + c[/tex].

From the given table, we can observe that the x-values of the vertex correspond to the minimum points of the function.

The minimum point occurs between -4 and -3, which suggests that the x-coordinate of the vertex is -3. Therefore, x = -3.

To find the corresponding y-coordinate of the vertex, we look at the corresponding h(x) value in the table, which is 3. Hence, the vertex of the function h(x) is (-3, 3).

To determine the range of h(x), we need to consider the y-values attained by the function.

From the table, we see that the lowest y-value is 3 (the y-coordinate of the vertex), and there are no other y-values lower than 3. Therefore, the range of h(x) is all real numbers greater than or equal to 3.

The vertex of h(x) is (-3, 3), and the range is y ≥ 3.

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The vertex of the quadratic function is (-4, 12).

The range of h(x) is [3, ∞).

To find the vertex and range of the quadratic function h(x) based on the given table, we can use the properties of quadratic functions.

The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be determined using the formula:

x = -b / (2a)

The domain of h(x) is all real numbers, we can assume that the quadratic function is of the form h(x) = ax² + bx + c.

Looking at the table, we can see that the x-values are increasing from left to right.

Additionally, the y-values (h(x)) are increasing from -6 to -4, then decreasing from -4 to -1.

This indicates that the vertex of the quadratic function lies between x = -4 and x = -3.

To find the exact x-coordinate of the vertex, we can use the formula mentioned earlier:

x = -b / (2a)

Based on the table, we can choose two points (-4, 4) and (-3, 3).

The difference in x-coordinates is 1, so we can assume that a = 1.

Plugging in the values of (-4, 4) and a = 1 into the formula, we can solve for b:

-4 = -b / (2 × 1)

-4 = -b / 2

-8 = -b

b = 8

The equation of the quadratic function h(x) can be written as h(x) = x² + 8x + c.

Now, let's find the y-coordinate of the vertex.

We can substitute the x-coordinate of the vertex, which we found as -4, into the equation:

h(-4) = (-4)² + 8(-4) + c

12 = 16 - 32 + c

12 = -16 + c

c = 28

The equation of the quadratic function h(x) is h(x) = x² + 8x + 28.

The range of the quadratic function can be determined by observing the y-values in the table.

From the table, we can see that the minimum y-value is 3.

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