Find the inverse of the following function pairs

The time Amy has left for the question C is 13.9 minutes.

The mixed fraction can be converted into a fraction by interchanging the numerator with the sum of the  product of denominator and the whole number and the numerator of the mixed fraction. It can be shown as 2(¹/₂) = (2 × 2 + 1)/2 = 5/2.

Given that,

The total time for quiz is 30 minutes.

The time taken to do problem A is 10(⁷/₁₀) and for B is 4(²/₅).

Thus, the remaining time left can be calculated by the as follows,

30 - (10(⁷/₁₀) + 4(²/₅))

Change the mixed fraction into the fraction to obtain,

30 - (107/10 + 22/5) = 13.9

Hence, the time left for question C is given as 13.9 minutes.

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Answer: 3/20

Step-by-step explanation:

     With our fraction, we will have officer members over total number of members. Three is a prime number, so this fraction cannot be simplified any more. This gives us the fraction;

             3/20

Answer:

We can use the point-slope formula to find the equation of the tangent line. The point-slope formula is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line. To find the equation of the tangent line, we need to find the slope of the line and a point on the line.

To find the slope of the line, we can use the definition of derivative. The derivative of a function f(x) at a point x0 is defined as:

f'(x0) = lim(h->0) (f(x0 + h) - f(x0))/h

In our case, the function f(x) is given by f(x) = x^2 - 5, and the point x0 is -2, so we have:

f'(-2) = lim(h->0) (f(-2 + h) - f(-2))/h

Substituting the value of the function f(x) = x^2 - 5, we get:

f'(-2) = lim(h->0) (((-2 + h)^2 - 5) - ((-2)^2 - 5))/h

Simplifying the expression, we get:

f'(-2) = lim(h->0) (h^2 - 4h)/h

Since the limit is defined as h approaches 0, we can drop the h from the denominator since it will become insignificant in the limit:

f'(-2) = lim(h->0) (h^2 - 4h)

Now we can evaluate the limit as h approaches 0:

f'(-2) = lim(h->0) h^2 - 4h

In the limit, h^2 becomes 0, so we are left with:

f'(-2) = lim(h->0) - 4h

Since the limit is defined as h approaches 0, the value of the limit is simply -4 times 0, which is 0. Therefore, the slope of the tangent line is 0.

Now that we know the slope of the tangent line, we need to find a point on the line. We are told that the line passes through the point (-2, f(-2)) on the function f(x) = x^2 - 5. Substituting the value of the function, we get:

(-2, f(-2)) = (-2, (-2)^2 - 5) = (-2, -9)

So the point on the line is (-2, -9).

We now have the slope and a point on the line, so we can use the point-slope formula to find the equation of the line. Substituting the values into the point-slope formula, we get:

y - (-9) = 0(x - (-2))

Simplifying, we get:

y = -9

Therefore, the equation of the tangent line that passes through the point (-2, -9) with a slope of 0 is given by y = -9.

The solution to the equation is x = -28/9.To solve the equation 2 1/7 + 3/7(3x - 5) = -4, let's break it down step by step.

Step 1: Convert the mixed number 2 1/7 to an improper fraction. Multiply the whole number (2) by the denominator (7), then add the numerator (1). This gives us (2 * 7 + 1) / 7 = 15/7.

Step 2: Distribute the 3/7 to the terms inside the parentheses. Multiply 3/7 by each term, which gives us (3/7) * 3x = 9x/7 and (3/7) * (-5) = -15/7.

Step 3: Substitute the converted mixed number and the distributed terms back into the equation. The equation becomes 15/7 + 9x/7 - 15/7 = -4.

Step 4: Combine like terms. Add the fractions with the same denominator: (15/7 - 15/7) + 9x/7 = -4. The fractions cancel each other out, leaving us with 9x/7 = -4.

Step 5: Isolate the variable. Multiply both sides of the equation by the reciprocal of 9/7, which is 7/9. This gives us (7/9)(9x/7) = (7/9)(-4). The 7/9 on the left side cancels out, leaving x = (-28/9).

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The image of y which is g(x) is 3x² + 60x + 82.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, y = 3x² - 24x + 2.

Now, g(x) is an image of y after a translation left 5 units and up 5 units.

∴ g(x) =  3(x + 5)² + 2 + 5.

g(x) = 3(x² + 20x + 25) + 7.

g(x) = 3x² + 60x + 75 + 7.

g(x) = 3x² + 60x + 82.

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Answer: B

Step-by-step explanation:

3(x-4)+5=2(x-3)+4

3x-12+5=2x-6+4

3x-7=2x-2

x-7=-2

x=5

Here is the two column proof:

     Statement                                        Reason                                              

Answer: number 3

Step-by-step explanation:

Answer: 30%

Step-by-step explanation:

Answer: hi

Step-by-step explanation:

The Number of kids in the fair is x + 12

A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

According to the given information

Let x be the variable

Let the number of adults in the fair = x

Number of kids in the fair is 12 more than the adults

So

Number of kids in the fair = 12 + Number of adults in the fair

                                           = 12+x

Hence

The Number of kids in the fair is x + 12

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The vertex and range of y = |x + 1| + 3 will be (−1, 3); 3 ≤ y < ∞ respectively.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

You may get the vertex of y = |x + 1| + 3 as follows.

Where the absolute values are zeros are the vertex points of the absolute value function.

|x + 1| = 0

x + 1 = 0

x = -1

Substitute the value into an original function,

y = |-1 + 1| + 3

y= 0 + 3

y = 3

As a result, the vertex is at (-1, 3)

Remember that the domain is specified in the range of (-∞, ∞) while determining the range.

Given that |x + 1| ≥ 0 , (absolute value is always 0 or positive)

The result of adding 3 to the inequality's two sides is

|x + 1| + 3 ≥ 3

But since |x+1| + 3 is identical to f(x) = y, we have y = f(x) 3, which means that the range is specified for all values larger than 3.

So the range is 3 ≤ y < ∞

Thus,the vertex and range of y = |x + 1| + 3 will be (−1, 3); 3 ≤ y < ∞ respectively.

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Answer:

The slope is a value that describes the steepness and direction of a line

Step-by-step explanation:

I think ts either 2 or nagtive 2

Answer:

gradient (slope) = 2

Step-by-step explanation:

gradient (slope) = difference of y-coordinates / difference of x-coordinates = (y₂-y₁)/(x₂-x₁)

Pick two points, ex: (0,1) and (-2,0)

= (0-1)/((-2)-0)

= -1/-2

= 1/2

Answer:

It has a mode of 11

Step-by-step explanation:

A mode is a # in a data set that occurs more then any other one

The tangent line to the graph of f(x) = 2e²ˣ-5 at the point (2, 1/e) is given by y=2e⁴+1-2e⁵/e

Two or more expressions with an Equal sign is called as Equation.

The equation of the tangent line to the graph of f(x) = e²ˣ-5

To find the Equation of a tangent to any curve you must first find the derivative of the function.

y = e²ˣ-5

y'=2e²ˣ

sub x=2 into derivative function

y'(2)=2e⁴

so we have found that the tangent line is y=2e⁴+c

now we have to sub in the point and solve for c:

1/e=2e⁴+c

c=1/e-2e⁴

c=1-2e⁵/e

c=0 when x is 2.

The equation of tangent to the line is y=2e⁴+(1-2e⁵)/e

Hence,  the equation of the tangent line to the graph of f(x) = 2e²ˣ-5 at the point (2, 1/e) is given by y=2e⁴+1-2e⁵/e

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Answer:

$54.06

Step-by-step explanation:

$60x0.85=51

51x1.06=$54.06

The time the Road Runner been running is 7.3 minutes

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

Roadrunner speed = 72mph

Time for repair = 15 minutes

Speed = 220mph

Represent the time the Road Runner been running with x

The speed is calculated using

Speed = Distance/Time

So, we have the following representations

Roadrunner speed = Distance/Time

Wile Coyote speed = Distance/Time

This gives

72 = Distance/(15 + x) -- for the roadrunner

220 = Distance/x for the Wile Coyote

So, we have

Distance = 72(15 + x)

Distance = 220x

Substitute the known values in the above equation, so, we have the following representation

220x = 72(15 + x)

Open the brackets

220x = 1080 + 72x

Evaluate the like terms

148x = 1080

So, we have

x = 7.3

Hence, the minutes is 7.3 minutes

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Answer:

The zeros of the function are x = -3, x = 1, x = 3. The multiplicity of the zero x = 3 is 3.

Step-by-step explanation:

Answer:

0, 1, -1

Step-by-step explanation:

7x³ - 7x = 0

=> x(7x² - 7) = 0

=> 7x(x² - 1) = 0

=> x(x² - 1) = 0

=> x(x+1)(x-1) =0

=> x = 0 or x = -1 or x = 1

The value of the fraction 3/4 of 56 is 42.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

The value of the fraction will be:

= 3/4 × 56

= 3 × 14

= 42

The value is 42.

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Answer:4x-12

Step-by-step explanation:

Answer:

= 4x - 4

Step-by-step explanation:

4(x-2) + 4

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

= (4x - 8) +4

= 4x + 4 - 8

= 4x - 4

Answer:

Step-by-step explanation:

Find the asymptotes.

Vertical Asymptotes:

x

=

0

Horizontal Asymptotes:

y

=

0

No Oblique Asymptotes

Based on the definition of complementary angles, the value of d is: 10.

Complementary angles can be described as two angles that have a sum of 90 degrees when added together.

Given that the two angles, 24° and (7d - 4)°, are complementary angles, it implies that their sum will give a measure of 90°. Therefore, to find the value of d, the following equation would be created based on the definition of complementary angles:

24 + (7d - 4) = 90

Open the parentheses:

24 + 7d - 4 = 90

Combine like terms:

7d + 20 = 90

Subtract 20 from both sides

7d + 20 - 20 = 90 - 20

7d = 70

Divide both sides by 7

7d/7 = 70/7

d = 10

The value of d is: 10.

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Answer:

x = 56

y = 124

z = 56

Step-by-step explanation:

The 124° angle and y° are vertical angles. vertical angles are congruent. they have equal measures.

y = 124

Angles 124° and x° form a linear pair. Angles in a linear pair are supplementary. Their measures add to 180°.

124 + x = 180

x = 180 - 24

x = 56

Angles x° and z° are vertical angles.

z = x = 56

Answer:

x = 56

y = 124

z = 56

Inequality: x>12

Interval Notation: ( 12, ∞ )

Answer: I believe it would be 55 but It would help if it says what kind of triangle it is.

Step-by-step explanation:

Answer:

The answer is 91°

Step-by-step explanation:

In any triangle, the sum of all angles is equal to 180°

So,

35° + 54° + x = 180°

x = 180 - 89

x = 91°

Thus, The third angle is 91°

Domain of the function is (1,4) and the domain is discrete.

What is linear function?

A linear function may be a operate that forms a line during a graph. it's usually a polynomial operate whose degree is utmost one or zero. though the linear functions also are delineate in terms of calculus also as algebra.

Main body:

According to the question :

y=15.95 x

where y = cost ,

x = number of tickets

Each customer can buy a maximum of four tickets.

Plot the ordered pairs. Because you cannot buy part of a ticket,

the graph consists of individual points.

domain of the function is (1,4).

Hence , the domain is discrete.

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Answer:

each girl scored 1 point and each boy scored 20 points.

Step-by-step explanation:

Let $g$ be the number of points scored by each girl and $b$ be the number of points scored by each boy. We can set up the following system of equations:

$$3g + 2b = 43$$

$$3g - 2b = 11$$

We can solve this system of equations using substitution. From the first equation, we have that $3g = 43 - 2b$. Substituting this expression for $3g$ into the second equation gives:

$$3(43 - 2b) - 2b = 11$$

Solving for $b$, we get:

$$129 - 6b = 11$$

$$6b = 118$$

$$b = 19.5$$

Since $b$ must be a positive integer, the only possible value for $b$ is $20$. Substituting this value into the first equation, we get:

$$3g + 2(20) = 43$$

Solving for $g$, we get:

$$3g = 3$$

$$g = 1$$

Therefore, each girl scored $1$ point and each boy scored $20$ points.

Answer:

4th answer option

Step-by-step explanation:

both side angles are 45°, that makes the triangle an isoceles triangle (both legs are equally long).

therefore, v = 7.

Pythagoras gives us

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.

in our case

u² = 7² + 7² = 49 × 2

u = sqrt(49 × 2) = 7 × sqrt(2)