For the function f(x) = x2 ­ -12, find (f o f­-1)(4)

Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.

Answer:

Spencer and Jeremiah both are correct

Step-by-step explanation:

We have given an equation 6x-2 = -4x+2

In this case spencer and jeremiah both are correct whether we first subtract 6x from both sides or we add 4x to both sides will not lead to any incorrection we will get the same result after simplification from both the methods

If we subtract 6x from both sides we will get 6x-6x-2= -4x-6x+2 after simplification we will get -2 = -10x+2

After further simplification we will get x=4/10=2/5

And if we add 4x on both sides we will get  6x+4x-2= -4x+4x+2 after simplification we will get 10x -2 =2  which eventually gives the result

x=4/10=2/5

Therefore, Both are correct

The probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.

To find the probability that a tile picked at random has a number that is a multiple of 7 or a multiple of 8, we need to count the number of tiles that satisfy this condition and divide it by the total number of tiles.

First, let's find how many numbers from 1 to 50 are multiples of 7 and multiples of 8 separately.

Multiples of 7:

7, 14, 21, 28, 35, 42, 49

There are 7 multiples of 7 between 1 and 50.

Multiples of 8:

8, 16, 24, 32, 40, 48

There are 6 multiples of 8 between 1 and 50.

However, we need to be careful not to count the numbers that are multiples of both 7 and 8 (multiples of 56). There's only one such number in the range (56).

So, the total number of tiles with numbers that are multiples of 7 or multiples of 8 is 7 + 6 - 1 = 12.

The total number of tiles from 1 to 50 is 50.

Now, we can find the probability:

Probability = [tex]\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Probability = [tex]\frac{12}{50}[/tex]

Probability = 0.24

So, the probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.

Answer:

Step-by-step explanation:

P(t)=130t -0.4t^4 +1200

The population will be max when first differential of p(t) =0

So p'(t) =130-1.6t^3=0

1.6t^3=130

t^3 =130/1.6

t^3 =81.25

t = cube root of 81.25

t =4.3 months

P(max) =130(4.3) -0.4(4.3)^4 +1200

= 559-136.75+1200

=1622

Population will disappear when p(t) =0

Final answer:

To solve for g in the equation R = gs/(g+s), you can isolate g by multiplying both sides by (g+s) and rearranging the equation. The final solution is g = -Rs/(R - s).

Explanation:

To solve for g in the equation R = gs/(g+s), we can start by isolating g on one side of the equation. We can do this by multiplying both sides of the equation by (g+s), which cancels out the denominator on the right side:

R(g+s) = gs

Next, distribute the R to both terms on the left side of the equation:

Rg + Rs = gs

Now, we can rearrange the equation to isolate g on one side:

Rg - gs = -Rs

Factor out g on the left side:

g(R - s) = -Rs

Finally, divide both sides of the equation by (R - s) to solve for g:

g = -Rs/(R - s)

The result of 16 times 9/4 is 36.

The original question appears to be asking how to divide 16 by the fraction 4/9, but it also contains an error in stating the mathematical expression. To divide 16 by 4/9, you need to multiply 16 by the reciprocal of 4/9, which is 9/4. Here's the step-by-step calculation:

Find the reciprocal of 4/9, which is 9/4. Reciprocal means exchanging the numerator and denominator.

Multiply 16 by the reciprocal (16 * 9/4).

Come up with the solution: (16 * 9) / 4 = 144 / 4 = 36.

Therefore, 16 divided by 4/9 equals 36.

the answer would be p-28=c

Mark Me Brainliest !

Answer:

P - 28 = C

Step-by-step explanation:

P (Regular Price  )

C ( Cost Savings )

You Noticed These Jeans You Liked.

You Couldn't Afford Them So You Waited Til The Price Dropped.

When Prices Drop Its Either 1 of 2 Reasons

Holiday Seasons Or Price Elasticity

So These Jeans Become $28 On The Market.

Simply You Figure Out How Much You'll Save By Comparing The Original Price To The Discounted Price.

There For Your Answer Will Be The Following :

Regular Price - Discounted Price = Cost Savings

Answer: -24

Step-by-step explanation:

3(-2)^(4-1)=3*-8=-24

we have

[tex]f(x)=4x+8[/tex]

Step 1

Let

[tex]y=f(x)[/tex]

[tex]y=4x+8[/tex]

Step 2

exchanges the variable x for y and the variable y for x

[tex]x=4y+8[/tex]

Step 3

Isolate the variable y

[tex]4y=x-8[/tex]

[tex]y=\frac{1}{4}x-2[/tex]

Step 4

Let

[tex]h^{-1}(x)=y[/tex]

[tex]h^{-1}(x)=\frac{1}{4}x-2[/tex] ------> the inverse function

therefore

the answer is

[tex]h^{-1}(x)=\frac{1}{4}x-2[/tex]

The inverse of the function f(x) = 4x + 8 is h(x) = (x - 8) / 4.

The inverse of the function f(x) = 4x + 8 can be found by switching the x and y variables and solving for y. So, we have:

x = 4y + 8

Now, we rearrange the equation to isolate y:

x - 8 = 4y

y = (x - 8) / 4

Therefore, the inverse function is h(x) = (x - 8) / 4.

The inverse function is [tex]f^{-1}(x) = \frac{x - 3}{2}[/tex].

To find the inverse of the function [tex]f(x) = 2x + 3[/tex], follow these steps:

Replace [tex]f(x)[/tex] with [tex]y[/tex]:
[tex]y = 2x + 3[/tex]

Interchange the variables [tex]x[/tex] and [tex]y[/tex]:
[tex]x = 2y + 3[/tex]

Solve for [tex]y[/tex]:
[tex]x - 3 = 2y[/tex]
[tex]y = \frac{x - 3}{2}[/tex]

Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(x) = \frac{x - 3}{2}[/tex]

Answer:

The value for x will be 5.

Step-by-step explanation:

As the segment AB and BC are tangent to the circle D, it will have the same long. Due to segment longitude is written as function of the variable x, it requires  to solve the following equation:

[tex]long(AB)= 3x+2= long(BC)= x+12[/tex]  

[tex]3x+2=x+12[/tex]  

[tex]3x-x= 12-2[/tex]  

[tex]2x= 10[/tex]  

[tex]x= 5[/tex]

Answer:

The distance traveled is based on the time traveled.

Step-by-step explanation:

I did this question.

The inverse of the given function is t(d) = d/50. The time taken to travel 180 miles is 3.6 hours.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

Here, we have,

It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.

It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).

To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.

Step 1 of 2

The given function is d(t)=50t.

Consider d(t) as d and t as t(d) and rewrite the equation.

The rewritten function is d=50 t(d)

Divide by 50 on both sides of the equation.

d/ 50 =50 t(d)/50

t(d) = d/50

Step 2 of 2

Substitute 180 for $t$ in the simplified expression and interpret the results.

t(d) = 180/50

     = 3.6

The time taken to travel 180 miles is 3.6 hours.

Hence, The inverse of the given function is t(d) = d/50. The time taken to travel 180 miles is 3.6 hours.

To learn more on speed click:

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Answer: 8 L of 100% pure acid and 64 L of 10% acid must be combined

Step-by-step explanation:

According to the dilution law,

[tex]C_1V_1+C_2V_2=C_3V_3[/tex]

where,

[tex]C_1[/tex] = concentration of pure acid solution = 100 %

[tex]V_1[/tex] = volume of pure acid solution = x L

[tex]C_2[/tex] = concentration of another acid solution= 10%

[tex]V_2[/tex] = volume of another acid solution= (72-x) L

[tex]C_3[/tex] = concentration of resulting acid solution = 20 %

[tex]V_1[/tex] = volume of resulting acid solution = 72 L

Putting the values in the equation:

[tex]100\times x+10\times (72-x)=20\times 72[/tex]

[tex]x=8L[/tex]

Therefore, the laboratory technician must take 8 L of 100% pure acid and (72-8) = 64 L of 10% acid to get 72​-liter batch of a 20​% acid solution.

The quadratic function is described by the standard equation [tex]\boxed{ \ f(x) = ax^2 + bx + c \ }.[/tex]

We have the quadratic function [tex]\boxed{ \ f(x) = (x - 1)(x + 4) \ }.[/tex]

Let us configure it to obtain a standard equation.

[tex]\boxed{f(x) = (x - 1)(x + 4)}[/tex]

[tex]\boxed{f(x) = x^2 + 4x - x - 4}[/tex]

Hence, we get [tex]\boxed{\boxed{ \ f(x) = x^2 + 3x - 4 \ }}.[/tex]

Finding the minimum value is as follows:

Notes:

Keywords: which is the graph of f(x) = (x - 1)(x + 4), the x-intercept, quadratic function, a standard equation, the y-intercept, the axis of symmetry, the vertex, parabola, upward, downward

The graph of f(x) = (x-1)(x+4) is an upward-opening parabola with roots at x = 1 and x = -4. It should be plotted carefully, labeling and scaling the axes to show maximum and minimum values, and ensuring it passes through the roots with the proper shape.

The graph of the function f(x) = (x-1)(x+4) can be determined by finding the roots and the shape of the curve. The roots of the function can be found when f(x) = 0, which occurs at x = 1 and x = -4. Therefore, these are the points at which the graph will intersect the x-axis. Since it's a quadratic function, its graph will be a parabola.

Additionally, because the coefficient of x² is positive, the parabola opens upwards. To graph this function accurately, one needs to plot the roots and then sketch the parabola, ensuring that it intersects these points and opens upwards. The vertex of the parabola can also be found by averaging the roots, which gives us the x-value of the vertex as (-4 + 1)/2 = -1.5, with the corresponding y-value obtained by evaluating f(x) at x = -1.5.

The resulting graph would start above the x-axis for x < -4, pass through the x-axis at x = -4, reach a vertex at x = -1.5, pass through the x-axis again at x = 1, and continue upwards for x > 1.

The graph should be accurately scaled and labeled with the function f(x) and the variable x, and include the maximum and minimum values on the axes based on the calculated points and the behavior of the quadratic function.

the probability of a loss is 0.6.

To find the probability of a loss, we first need to understand that in this context, the sum of all possible outcomes (win, draw, and loss) must equal 1.

Given:

- Probability of a win = 0.24

- Probability of a draw = 0.16

Let's denote the probability of a loss as [tex]\( P(\text{loss}) \).[/tex]

We know that:

[tex]\[ P(\text{win}) + P(\text{draw}) + P(\text{loss}) = 1 \][/tex]

So, to find [tex]\( P(\text{loss}) \),[/tex] we rearrange the equation:

[tex]\[ P(\text{loss}) = 1 - (P(\text{win}) + P(\text{draw})) \][/tex]

[tex]\[ P(\text{loss}) = 1 - (0.24 + 0.16) \][/tex]

[tex]\[ P(\text{loss}) = 1 - 0.4 \][/tex]

[tex]\[ P(\text{loss}) = 0.6 \][/tex]

Therefore, the probability of a loss is 0.6.

Answer:

b

Step-by-step explanation: