in the rectangle below, what is x?

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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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.

To integrate 1 / sqrt(25 - 16x^2) dx, we use trigonometric substitution with x = (5/4)sinθ. After substitution, integration, and back-substitution, the result is arcsin(4x/5) + C, where C is the constant of integration.

The integral to solve is ∑ (1 / sqrt(25 - 16x^2)) dx, which resembles the inverse trigonometric function, specifically the arcsine function. To solve this integral, we can use a trigonometric substitution. Since the integral involves a square root of a difference of squares, we can substitute x with (5/4)sinθ, which simplifies the integral considerably.

After substitution, we can then use the derivative of sinθ, which is cosθ, in order to find the full differential dx to replace in our integral. The resulting integral in terms of θ can be integrated using standard techniques, yielding an arcsine function as the antiderivative. After integrating, we must then convert back from θ to x to express the solution to the original integral in the original variable.

The answer to the integral ∑ (1 / sqrt(25 - 16x^2)) dx is arcsin(4x/5) + C, where C is the constant of integration. The substitution step is crucial in solving this type of problem and is a commonly used method in calculus.

Answer:

$77.72

Step-by-step explanation:

This is the total cost of the book with tax.

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.

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.

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:

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:

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

Answer:

It's A. translation

Step-by-step explanation:

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.

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).

The person's body temperature will approach 98.6ºF as time lapses. Option A is correct.

A horizontal asymptote for a function is an imaginary line that is not part of the graph and lies along the x-axis of the graph either to the left or right.

The horizontal asymptote of the given function can be described as the nature of the function T(f) as t approaches infinity.

This is the point where the line y=0 which means that the person's body temperature will approach 0ºF above 98.6ºF as t goes to infinity.

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Answer:

The domain is all real integers 0 through 9.

I've done the test, hope this helps

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

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.