How would you explain the relationship between an exponential function and a logarithmic function to an English major you are tutoring in math? Can you give me a real life example of it?

Answer:

1. a, -3,-1,1,3

2. a, 3+i/2, 3-i/2, -4

3. d, 6- sqrt 6

4. a, x3-8x2-11x+148=0

5. d, there are either 2 or 0 positive roots and one negative

Step-by-step explanation:

I did the quick check.

Final answer:

The roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0 are complex.

Explanation:

To find the roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0, we can use the factoring method or the quadratic formula. Let's use the quadratic formula. The formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 2, and c = 20. Plugging the values into the quadratic formula, we get:

x = (-2 ± √(2² - 4(2)(20))) / (2(2))

x = (-2 ± √(4 - 160)) / 4

x = (-2 ± √(-156)) / 4

Since we cannot take the square root of a negative number in the real number system, the roots of the given equation are complex, which means there are no real solutions.

Answer with explanation:

Cost of a Pencil = $ 0.25

Cost of a Eraser = $ 0.50

⇒Total Amount Spent on Pencil and Eraser < 3.

⇒Cost of x Pencil +Cost of y Eraser < 3

⇒ 0.25 x + 0.50 y < 3

[tex]\Rightarrow \frac{25 x}{100}+\frac{50y}{100}< 3\\\\\Rightarrow 2 5 x +50 y < 300\\\\\Rightarrow x +2 y < 12\\\\\Rightarrow \frac{x}{12}+\frac{2y}{12}<1\\\\\Rightarrow \frac{x}{12}+\frac{y}{6}<1[/tex]

⇒Put, x=0 and y=0,to know which side of the graph you have to shade.

0+0< 12⇒0< 12

Shade that part under line,  which contains origin.

Final answer:

Absolute extrema refer to the highest or lowest points on the entire domain of a function, while relative extrema are high or low points within a specific region. Calculus techniques such as finding derivatives are used to identify these points.

Explanation:

The concepts of absolute extrema and relative extrema are important in the context of mathematics, specifically in calculus and the study of functions. An absolute extrema (or global extrema) refers to the highest or lowest point over the entire domain of a function. Relative extrema (or local extrema), on the other hand, are points where the function takes on a maximum or minimum value within a particular region or interval, but not necessarily the highest or lowest over the entire function. More formally, an absolute maximum is the largest function value and an absolute minimum is the smallest function value in the entire domain; relative maximums and minimums may not be the absolute highest or lowest, but are higher or lower than points immediately around them. To find extrema, calculus students typically use techniques involving derivatives to identify where function values change from increasing to decreasing or vice versa.

For example, let's consider the function f(x) = x^2 on the interval [-1,1]. The absolute extrema of this function would be the global maximum and minimum values, which occur at x = -1 and x = 1, respectively. The relative extrema of this function would be the local maximum and minimum values, which occur at x = 0.

Answer:

C. [tex]3x+6=36[/tex]

Step-by-step explanation:

Let x represent the first integer, [tex]x+2[/tex] represent the second integer, and [tex]x+4[/tex] represent the third integer.

The sum of these integers would be [tex]x+x+2+x+4[/tex].

We have been given that the sum of three consecutive even integers is 36. We can represent this information in an equation as:

[tex]x+x+2+x+4=36[/tex]

Combine like terms:

[tex]3x+6=36[/tex]

Therefore, the equation [tex]3x+6=36[/tex] can be used find the first integer.

Answer:

There are infinitely many solution.

Step-by-step explanation:

Given  : 16(x + 2) - 8 = 16x + 24.

To find : How many solutions are there to the equation below.

Solution : We have given

16(x + 2) - 8 = 16x + 24.

On distributing 16 over ( x +2) .

16 x + 32 - 8 = 16x + 24 .

16 x + 24 = 16x + 24.

We can see left hand side is equal to right hand sides .

Therefore, There are infinitely many solution.

Answer:

The product of two mixed fraction lies between 9 and 12.        

Step-by-step explanation:

We are given the following information in the question:

Two mixed fractions between 3 and 4.

[tex]3\displaystyle\frac{1}{6} = \frac{19}{6} = 3.17\\\\3\displaystyle\frac{1}{2} = \frac{7}{2} = 3.5\\\\[/tex]

Product of the mixed fraction:

[tex]3\displaystyle\frac{1}{6}\times 3\frac{1}{2} = \frac{19}{6}\times \frac{7}{2}\\\\= \frac{133}{12} = 11\frac{1}{12} = 11.084[/tex]

Hence, the value of the product of two mixed fraction lies between 9 and 12.

Answer:

3 1/6

Step-by-step explanation: it is because you would have to divide the  1 and the 6 well not really divide more of the multiplying then after that you switch 1 and 2 and the 2 is and the top and 1 at the bottom and you to butterfly some  of you should know then you get 3 1/6

Final answer:

The system of equations given has no solution because substitution leads to a contradiction, indicating that the lines are parallel and do not intersect.

Explanation:

To solve the given system using the substitution method, we start with the two equations:

From the second equation, we can express y in terms of x by dividing by 2:

y = 2x

Now, we substitute this expression for y into the first equation:

2x − 2x = 816

This simplifies to:

0 = 816

This is a contradiction since 0 cannot equal 816. Therefore, there is no solution to the system of equations. This means that the two lines represented by these equations are parallel and never intersect.

Answer:

The correct option is C. 0.213

Step-by-step explanation:

Percentage of students at high school who takes chemistry = 40%

So, probability of students who take chemistry = 0.4

So, probability of students who do not take chemistry = 1 - 0.4

                                                                                          = 0.6

Total number of students taken for survey = 12

Now, we need to find the probability that exactly 4 students have taken chemistry among the 12 surveyed students.

By using binomial distribution :

n = 12 , p = 0.4 , q = 0.6 , k = 4

[tex]\text{Required Probability = }_{k}^{n}\textrm{C}\cdot(p)^k\cdot(q)^{n-k}\\\\\implies\text{Required Probability = }_{4}^{12}\textrm{C} \cdot(0.4)^4 \cdot(0.6)^8 \\\\\implies \text{Required Probability = }0.2128\approx 0.213[/tex]

Therefore, The correct option is C. 0.213

To determine the price of each cupcake, subtract the price of the pie from the total bill and then divide the result by the number of cupcakes. Each cupcake costs $1.62.

To determine the price of each cupcake, Rich can subtract the price of the pie from the total bill and then divide the result by the number of cupcakes:

Therefore, each cupcake costs $1.62.

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Answer:

It's A. translation

Step-by-step explanation:

Answer:

The domain is all real integers 0 through 9.

I've done the test, hope this helps

To find the inverse of a function, switch x and y and solve for y. The inverse of f(x) = (x-1)/5 is f^-1(x) = 5x + 1. Verify that f(f^-1(x)) = x and f^-1(f(x)) = x.

To find the inverse of a function, we need to switch the roles of x and y and solve for y. In other words, we need to solve the equation y = (x-1)/5 for x. Let's do that:

Step 1: Replace y with x and x with y: x = (y-1)/5.

Step 2: Solve for y: Multiply both sides by 5: 5x = y - 1. Add 1 to both sides: 5x + 1 = y.

So, the inverse of f(x) = (x-1)/5 is f-1(x) = 5x + 1.

To verify that f(f-1(x)) = x, substitute f-1(x) into f(x) and simplify:

f(f-1(x)) = f(5x + 1) = ((5x + 1) - 1)/5 = 5x/5 = x.

Similarly, to verify that f-1(f(x)) = x, substitute f(x) into f-1(x) and simplify:

f-1(f(x)) = f-1((x-1)/5) = 5((x-1)/5) + 1 = x-1+1 = x.

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For the given function f(x) = 10x + 20, substituting 0 for x yields f(0) = 20. Graphically, this corresponds to the point (0, 20) on the function's line, illustrating that the output is 20 when the input is 0.

Find the value of f(0) for the function f(x) = 10x + 20:

1: Understand the function:

We are given that f(x) is defined as 10x + 20. This means that for any input value (x), the function outputs the result of multiplying x by 10 and adding 20.

2: Substitute x with 0:

We are asked to find the value of f(0). This means we need to plug in 0 for x in the function equation.

f(0) = 10 * 0 + 20

3: Simplify the expression:

Multiplying 10 by 0 gives us 0. Therefore, the equation becomes:

f(0) = 0 + 20

4: Evaluate the expression:

Adding 0 and 20 gives us:

f(0) = 20

Therefore, the value of f(0) is 20.

This means that when you input 0 into the function f(x) = 10x + 20, the function outputs 20.

To visualize this geometrically, you can imagine the function as a straight line on a coordinate plane. The point (0, 20) would lie on this line, indicating that the function output is 20 when the input is 0.

Complete question:

What is the value of f(0)?

If f(x) = 10x + 20

The value of ( f(0) ) is 5. To calculate it, we substitute ( x = 0 ) into the expression [tex]\( 3x^{2x} + 5 \)[/tex]ero number raised to the power of 0 is 1, the simplified result is [tex]\( f(0) = 3 \cdot 1 + 5 = 8 \).[/tex]

The expression for ( f(x) ) is given as [tex]\( 3x^{2x} + 5 \)[/tex] , we substitute ( x = 0 ) into the expression:

[tex]\[ f(0) = 3 \cdot 0^{2 \cdot 0} + 5 \][/tex]

Since any non-zero number raised to the power of 0 is 1, the term [tex]\( 0^{2 \cdot 0} \)[/tex]re,

[tex]\[ f(0) = 3 \cdot 1 + 5 \][/tex]

Simplifying further,

f(0) = 3 + 5

Combining like terms,

f(0) = 8

So, the final answer is ( f(0) = 8 ).

In summary, when evaluating ( f(0) ), we substitute 0 for ( x ) in the given expression. The calculation involves raising 0 to the power of 0, which results in 1. The remaining terms are simplified to arrive at the final answer of 8. This process follows the principles of algebraic substitution and simplification, providing a clear understanding of how the value of ( f(0) ) is determined.

Complete Question:

Consider the function f(x) with the following expression: ( f(x) = [tex]3x^2[/tex]x + 5 ). Calculate the value of f(0).

To multiply numbers in scientific notation, multiply the coefficients and add the exponents.

To multiply numbers in scientific notation, we multiply the coefficients and add the exponents.

In this case, we have (9.16 × 10-3) multiplied by (5.5 × 1016).

The product of the coefficients is 9.16 × 5.5 = 50.38.

The sum of the exponents is -3 + 16 = 13.

Therefore, the product in scientific notation is 5.038 × 1013.