if a(x) = 3x+1 and b(x) = [tex]square root of x-4[/tex], what is the domain of (boa)(x)

The domain of the function is all real numbers less than 5, and the range is all real numbers greater than or equal to 9.

The given function is f(x) = -log(5-x) + 9.

To determine its domain and range, we need to consider the restrictions on x and the possible values of f(x).

Domain:

The domain refers to the set of all valid inputs or values of x for which the function is defined.

In this case, the function contains a logarithmic term, -log(5-x), which is only defined for positive values inside the logarithm.

Therefore, we must ensure that the expression 5-x is greater than zero:

5 - x > 0

Solving this inequality, we find:

x < 5

Hence, the domain of the function is (-∞, 5).

Range:

The range refers to the set of all possible output values or values of f(x). Since the logarithm term can take any positive value, and we add 9 to it, the range of the function is shifted upward by 9 units.

The range can be defined as all real numbers greater than or equal to 9:

Range: [9, +∞)

To summarize, the domain of the function f(x) = -log(5-x) + 9 is (-∞, 5), and the range is [9, +∞), indicating that f(x) can take any value greater than or equal to 9.

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The other side of the triangle is approximately 4.664 cm.

Let's denote the other side of the triangle as x. We know that the perimeter of the triangle is 22 cm, and one of the sides is 9 cm. The perimeter of a triangle is the sum of the lengths of its three sides. So, we can set up the equation:

9 + x + z = 22

where z represents the remaining side.

Now, we are given that the area of the triangle is 20.976 cm². The area of a triangle can be calculated using the formula:

Area = (1/2) * base * height

Since we know the area and one side (9 cm), we can rearrange the formula to solve for the height (which is the remaining side, z):

z = (2 * Area) / 9

Substituting the given values, we get:

z = (2 * 20.976) / 9

z ≈ 4.664 cm

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Answer:

10: Zero-degree monomial.

8x^4: Quartic monomial.

5x² - 7x + 9: Quadratic trinomial.

2x³ + 3: Cubic binomial.

Step-by-step explanation:

10: This is a constant term, and it can be classified as a zero-degree monomial.

8x^4: This is a monomial with a degree of 4, and it contains one term. It can be classified as a quartic monomial.

5x² - 7x + 9: This is a polynomial with three terms. The highest power of the variable, x, is 2, so it is a quadratic polynomial. Therefore, it can be classified as a quadratic trinomial.

2x³ + 3: This is a polynomial with two terms. The highest power of the variable, x, is 3, so it is a cubic polynomial. Hence, it can be classified as a cubic binomial.

10: Zero-degree monomial.

8x^4: Quartic monomial.

5x² - 7x + 9: Quadratic trinomial.

2x³ + 3: Cubic binomial.

Answer:

The x is an invisible number that is always represented by 1 so you have to solve the equation.

Answer:

it is too blury to read

Step-by-step explanation:

The discriminant of the quadratic equation -2x² + 6x + 13 is 140.

To find the discriminant of the quadratic equation 0 = -2x² + 6x + 13, we can use the formula for the discriminant, which is given by Δ = b² - 4ac. The quadratic equation is in the form ax² + bx + c = 0, with coefficients a = -2, b = 6, and c = 13.

Substituting these values into the discriminant formula, we have:

Δ = (6)² - 4(-2)(13)

Δ = 36 - (-104)

Δ = 36 + 104

Δ = 140

The discriminant provides valuable information about the nature of the solutions of a quadratic equation.

It can take on different values, and each value indicates a different scenario:

If the discriminant (Δ) is greater than zero (Δ > 0), then the quadratic equation has two distinct real solutions.

If the discriminant is equal to zero (Δ = 0), then the quadratic equation has a single real solution (a repeated root).

If the discriminant is less than zero (Δ < 0), then the quadratic equation has no real solutions, but rather two complex solutions.

The discriminant is 140 (Δ = 140), which is greater than zero, the quadratic equation -2x² + 6x + 13 has two distinct real solutions.

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The function g(x) is obtained by stretching the logarithmic function f(x) vertically by 7, reflecting it over the x-axis and y-axis, and shifting it up by 2 units. The equation for g(x) is -7*log₆(-x) + 2.

To find the equation of the function g(x), we can apply a series of transformations step by step. First, we stretch the function vertically by a factor of 7 by multiplying it by 7. This gives us the function g₁(x) = 7*log₆(x).

Next, we reflect the function g₁(x) over the x-axis by multiplying it by -1. This results in the function g₂(x) = -7*log₆(x).

To reflect the function g₂(x) over the y-axis, we replace x with -x, giving us the function g₃(x) = -7*log₆(-x).

Lastly, we shift the function g₃(x) up by 2 units by adding 2 to it. This gives us the final equation for g(x) as g(x) = -7*log₆(-x) + 2.

In summary, the function g(x) is obtained by vertically stretching the logarithmic function f(x) by a factor of 7, reflecting it over the x-axis, reflecting it over the y-axis, and then shifting it up by 2 units.

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The exponential function giving the number of bacteria after x hours is given as follows:

[tex]y = 250(2)^x[/tex]

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 250, b = 2.

Hence the function is given as follows:

[tex]y = 250(2)^x[/tex]

The problem asks for the exponential function giving the number of bacteria after x hours is given as follows:

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The correct answer is C. 2.

To determine the slope of a line, we need to calculate the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, we have the points (0, -5) and (3, 1).

The change in the y-coordinates is 1 - (-5) = 6, and the change in the x-coordinates is 3 - 0 = 3.

Therefore, the slope of the line is the ratio of the change in the y-coordinates to the change in the x-coordinates, which is 6/3 = 2.

Hence, the slope of the line graphed is 2.

Therefore, the correct answer is C. 2.

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The Jack's speed was approximately 85.44 km/h, and Bob's speed was approximately 89.44 km/h.

Let's assume that Jack's speed during the race was "x" km/h. Since Bob was driving 4 km/h faster than Jack, his speed was "x + 4" km/h.

When Bob got a flat tire, he had to stop and repair it, which took 30 minutes. During this time, Jack continued to race. Since both of them finished the race in a tie, it means that Bob caught up to Jack after his tire was repaired.

In 30 minutes, Jack traveled a distance of (x/2) km because the time is half of an hour. During the same time, Bob was stationary due to the tire repair.

Once Bob's tire was fixed, he started racing again and caught up to Jack. At this point, both Bob and Jack had covered the same distance.

So, Bob's time to complete the race was the same as Jack's time plus the 30-minute tire repair time.

We can set up the equation:(1000 km) / (x + 4 km/h) = (1000 km - x/2 km) x km/h

Simplifying the equation, we get:1000x = (1000 - x/2)(x + 4)

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Answer:

undefined

Step-by-step explanation:

To find the slope, we can use the slope formula.

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

    = ( 4-8)/(-5 - -5)

    = (4-8)/(-5+5)

   = -4/0

The slope is undefined.

The equation that represents the total cost of purchasing currency is 1.30x + 1.50y = 3200.00.

The equation that represents the relationship between the number of currency A and number of currency B is x = 5y.

x = 2000 and y = 400

There are 2000 of currency A and 400 of currency B

In order to write a system of linear equations to describe this situation, we would assign variables to the number of currency A and currency B, and then translate the word problem into an algebraic equation as follows:

Since she budgeted $3200.00 for spending money on an upcoming trip and currency A is trading at $1.30 per euro, and currency B is trading at $1.50 per pound, a system of linear equations to describe this situation is given by;

1.30x + 1.50y = 3200.00

x = 5y

1.30(5y) + 1.50y = 3200.00

8y = 3200

y = 3200/8

y = 400

x = 5y

x = 5(400)

x = 2000

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The simplified expression for (2x+7)2 = 4x^2 + 28x + 49.

A simplified expression is an algebraic expression that has been rewritten in a more concise and easier to understand form. This can be done by combining like terms, removing unnecessary parentheses, and using the correct order of operations.

To perform the operation [tex](2x + 7)^{2}[/tex] we need to square the entire expression (2x+7).

(2x+7)2 = (2x+7)(2x+7)

The expression inside the parentheses is multiplied by itself. This is called squaring the expression.

To expand the expression, we can use the distributive property:

(2x+7)(2x+7) = 2x(2x) + 2x(7) + 7(2x) + 7(7)

Simplifying the expression, we get:

(2x+7)2 = 4x^2 + 28x + 49

In words, we can say that the square of 2x + 7 is equal to 4x squared plus 28x plus 49.

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The amount invested in Scheme B is R6,000.

Let's assume that Mr Mangena invested "x" amount in Scheme A and "y" amount in Scheme B.So, as per the problem, the total amount invested by Mr Mangena in Scheme A and Scheme B is equal to R13,890. Hence,x + y = 13,890This is our first equation.

The second equation is that after 3 years, the total interest that Mr Mangena earned was R5,508. Now, we know that the interest earned is simply the product of principal, rate of interest and time. The rate of interest is given as 12% for Scheme A and 10% for Scheme B. Hence, we can write the following equation:0.12x * 3 + 0.10y * 3 = 5,508This is our second equation.

We have two equations and two variables. We can solve these equations simultaneously to get the values of x and y, and hence, we can find the amount invested in Scheme B.x + y = 13,890 ................... Equation 1 0.12x * 3 + 0.10y * 3 = 5,508 .............. Equation 2 Simplifying Equation 1, we get:x = 13,890 - ySubstituting this value of x in Equation 2, we get:0.12(13,890 - y) * 3 + 0.10y * 3 = 5,508Simplifying this equation, we get:y = R6,000.

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The value of x can be found by rearranging the formula S = 6[tex]x^2[/tex] to x = √(S/6).

1. The formula for the surface area of a cube is given as S = 6[tex]x^2[/tex], where S represents the surface area and x represents the side length.

2. To solve for x, we need to isolate it on one side of the equation.

3. Divide both sides of the equation by 6: S/6 = [tex]x^2[/tex].

4. To eliminate the exponent of 2, take the square root of both sides: √(S/6) = x.

5. Therefore, the value of x is given by x = √(S/6).

6. If you have a specific value for S, you can substitute it into the equation to find the corresponding value of x.

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The expanded expression equivalent to log6((2y-3y)/9) using the Quotient Rule of Logarithms is log6(2y) - log6(3y).

The Quotient Rule of Logarithms states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator. Using this rule, we can expand the given expression log6((2y-3y)/9) as follows:

log6((2y-3y)/9) = log6(2y/9) - log6(3y/9)

Now, let's simplify each logarithmic expression separately:

For the first term, log6(2y/9), we can write it as:

log6(2y/9) = log6(2y) - log6(9)

For the second term, log6(3y/9), we can write it as:

log6(3y/9) = log6(3y) - log6(9)

Combining these expressions, we have:

log6((2y-3y)/9) = (log6(2y) - log6(9)) - (log6(3y) - log6(9))

Now, let's simplify further by distributing the negative sign:

log6((2y-3y)/9) = log6(2y) - log6(9) - log6(3y) + log6(9)

Notice that log6(9) appears both as a subtraction and addition term. This cancels out, resulting in:

log6((2y-3y)/9) = log6(2y) - log6(3y)

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Answer:

The given linear equation is -5x-3y=-7. To graph the equation, we need to find three points that satisfy the equation and then plot them on the graph.

Let's find the x and y intercepts first.

At x = 0, we have -3y = -7, which gives us y = 7/3. So the y-intercept is (0, 7/3).

At y = 0, we have -5x = -7, which gives us x = 7/5. So the x-intercept is (7/5, 0).

Now, let's choose another point. We can choose any value for x or y and solve for the other variable. Let's take x = 1.

-5(1) - 3y = -7

-3y = -2

y = 2/3

So the third point is (1, 2/3).

Now we can plot these three points on the graph and draw a line passing through them.

Here's the graph:

|

|

| . (1, 2/3)

|

| .

| (0, 7/3)

|

|_________________________

| |

7/5 -7/15

Step-by-step explanation:

Already explained

The slope of the line represents the speed in miles per hour

The y intercept represents the initial distance

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

The graph

Where, we have

x = time in hours

y = distance in miles

The slope is

slope = change in y/x

So, we can conclude that the slope is the speed

By definition, the y intercept is the initial value of the graph

In this case;

y intercept = initial distance

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Answer:

V = 4(5)(7) + 6(5)(15) = 140 + 450 = 590 cm³

A. The area of the triangle is 108 mm².

B. The area of parallelogram is 286√2 in²

A. Area of a triangle (A) = 1/2 * Base (b) * Height (h)

We have:

b = 18 mm

h = 12 mm

Thus:

A = 1/2 * 18 * 12

A = 108 mm²

B. The area of parallelogram is given by:

A = b * h

where b is the base and h is the height

We have:

b = 26 in

Using trig.:

sin 45 = h/22

h = 22 * sin 45

h = 11√2 in

Thus,

A = 26 * 11√2

A = 286√2 in²

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The simplification of 3 hours : 45 m is 4 minutes : 1 minutes.

Ratio refers to a number representing a comparison between two named quantities.

3 hours : 45 m

Convert hours to minutes:

1 hour = 60 minutes

3 hours = 180 minutes

3 hours : 45 m = 180 minutes : 45 minutes

= 180/45

= 4 / 1

= 4 : 1

Ultimately, 3 hours : 45 m is 4 minutes ratio 1 minutes.

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The three dramatic techniques that make "Look Back in Anger" interesting are social realism, strong language and rhetoric, and character conflict and dynamic relationships.

"Look Back in Anger" by John Osborne is a play known for its compelling portrayal of post-war disillusionment and social critique. Here are three dramatic techniques used in the play that contribute to its enduring interest:

1. Social Realism: Osborne employed social realism, depicting the gritty realities of working-class life, alienation, and societal discontent. This authenticity and portrayal of relatable characters and situations engage the audience emotionally and intellectually.

2. Strong Language and Rhetoric: The play is characterized by sharp, biting dialogue and impassioned monologues. The use of strong language and rhetoric adds intensity, captures the characters' frustrations, and conveys their anger and disillusionment effectively.

3. Character Conflict and Dynamic Relationships: The play revolves around intense conflicts between characters, particularly the central couple, Jimmy and Alison. Their volatile relationship and the clash between Jimmy's anger-fueled rebellion and Alison's desire for a different life create tension and keep the audience engaged.

Overall, these dramatic techniques of social realism, powerful language, and dynamic relationships make "Look Back in Anger" interesting by effectively portraying societal issues, engaging the audience emotionally, and highlighting the complexities of human interactions.

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To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

The expression "dom(s) = {i : i < n} for some n ∈ N" represents the domain of a set or function called 's'.

Let's break down the notation:

- "dom(s)" refers to the domain of the set or function 's'. The domain represents the set of all possible input values or elements for which 's' is defined or applicable.

- "{i : i < n}" is a set comprehension notation. It means that the set contains elements 'i' such that 'i' is less than 'n'. In other words, it represents a set of all natural numbers 'i' that are smaller than a specific value 'n'.

- "for some n ∈ N" denotes that there exists a natural number 'n' (n ∈ N) such that the set 'dom(s)' consists of elements 'i' that are less than 'n'.

In summary, the expression states that the domain of set or function 's' consists of all natural numbers 'i' that are smaller than a specific natural number 'n'. The actual value of 'n' is not specified and can vary depending on the specific context or problem.

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The slope, "m," indicates the rate of change of the line, while the y-intercept, "b," represents the value of y when x equals zero.

I apologize, but as a text-based AI model I'm unable to directly view or analyze any attached images or graphs. However, if you provide me with the equation of the line in the slope-intercept form or describe the relevant details from the graph, I can certainly help you with a response within the given word limit.

The slope-intercept form of a linear equation is given by y = mx + b, where "m" represents the slope of the line and "b" represents the y-intercept, the point where the line intersects the y-axis.

Using this equation, you can determine the slope and y-intercept by comparing the given equation with the slope-intercept form.

Once you provide me with the equation or necessary information, I'll be able to assist you further in understanding the line and its characteristics.

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Triangles (C) and (D) can be solved using the Law of Cosines, while triangles (A) and (B) cannot be solved using this theorem due to missing angle measures.

To determine which triangle should be solved by beginning with the Law of Cosines, let's briefly review the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice their product, multiplied by the cosine of the included angle.

Now, let's analyze each given triangle and determine if the Law of Cosines is applicable:

(A) Triangle mZA with mZA = 115, a = 19, b = 13:

To apply the Law of Cosines, we need to have the measures of two sides and the included angle. In this case, we have the measures of two sides (a = 19 and b = 13), but we don't have the included angle mZA. Therefore, we cannot use the Law of Cosines for this triangle.

(B) Triangle m/B with m/B = 48, a = 22, b = 5:

Similar to the previous triangle, we are missing the measure of the included angle. Therefore, we cannot use the Law of Cosines for this triangle either.

(C) Triangle m/A with m/A = 62, mLB = 15, b = 10:

In this triangle, we have the measure of one side (b = 10) and the measures of the other two sides, including the included angle mLB. Therefore, we can apply the Law of Cosines to solve for m/A.

(D) Triangle m/A with m/A = 50, b = 20, c = 18:

Again, we have the measure of one side (b = 20) and the measures of the other two sides. Therefore, we can use the Law of Cosines to solve for m/A in this triangle as well.

In summary, triangles (C) and (D) can be solved using the Law of Cosines, while triangles (A) and (B) cannot be solved using this theorem due to missing angle measures.

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The line slants downward from left to right, indicating that as x increases, y decreases.

The given linear equation is -x = 2y + 1. To represent this equation graphically, we need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.Rearranging the given equation, we get:2y = -x - 1

Dividing both sides by 2:y = (-1/2)x - 1/2

The slope of the line is -1/2, which means that for every unit increase in x, y decreases by 1/2 unit. The y-intercept is -1/2, indicating that the line intersects the y-axis at (0, -1/2).

Based on this information, the best graph that represents the linear equation y = (-1/2)x - 1/2 is a straight line with a negative slope of -1/2, starting at the point (0, -1/2) and extending infinitely in both directions.

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A. The volume of the hemisphere with a diameter of 48 yards is approximately 1001.1 cubic yards.

B. The volume of the sphere with a circumference of a great circle approximately equal to 26 meters is approximately 359.4 cubic meters.

A. To find the volume of a hemisphere, we first need to calculate the radius. The diameter is given as 48 yards, so the radius is half of that, which is 24 yards.

The formula for the volume of a hemisphere is (2/3)πr^3, where r is the radius. Plugging in the values:

Volume = (2/3) * π * (24^3)

Volume ≈ 1001.1 cubic yards (rounded to the nearest tenth)

Therefore, the volume of the hemisphere is approximately 1001.1 cubic yards.

B. To find the volume of a sphere, we need to know the radius. Since the circumference of a great circle is given as approximately 26 meters, we can use the formula C = 2πr, where C is the circumference and r is the radius.

We can rearrange the formula to solve for the radius: r = C / (2π). Plugging in the circumference:

r = 26 / (2π)

r ≈ 4.134 meters (rounded to the nearest thousandth)

The formula for the volume of a sphere is (4/3)πr^3. Substituting the radius:

Volume = (4/3) * π * (4.134^3)

Volume ≈ 359.4 cubic meters (rounded to the nearest tenth)

Therefore, the volume of the sphere is approximately 359.4 cubic meters.

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