The exponential expression 4^-2 is equal to what fraction value

The equation of a line with an x-intercept of 2 and a y-intercept of -8 is y = 4x - 8, which follows from applying the slope-intercept form and calculating the slope based on the intercepts.

To find the equation of a line with an x-intercept of 2 and a y-intercept of -8, we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

We can determine the slope by recognizing that the line crosses the x-axis at (2,0) and the y-axis at (0,-8).

The slope m is the rise over the run, which in this case is (-8 - 0) / (0 - 2) = 4.

Therefore, the equation of the line is y = 4x - 8.

This equation satisfies the given conditions, as plugging in x = 0 gives the y-intercept of -8 and setting y to 0, and solving for x yields the x-intercept of 2.

Answer:

[tex]\sqrt[3]{373248}=\sqrt[3]{18^{3}*64}\\[/tex]

Step-by-step explanation:

A Perfect Cube is an integer number multiple of three that can be expressed as a product of prime factors raised to 3rd power. We have many Perfect Cubes, such as:

15³=3³x5³, and 15 ∈ ={1,3,6,9,12,15,18,..} so 15 is a perfect cube

18³=2³x3³x3³ and 18 ∈ ={1,3,6,9,12,15,18,..} so 18 is a perfect cube.

Finally, for instance, we can rewrite the number 373248 as

cubic root of 18³ times 64. 18 is a perfect cube 64 is not a perfect cube for 64 =[tex]2^{6}[/tex]

Answer:

b

Step-by-step explanation:

Answer:

A. [tex]4x(2x^2+3)[/tex].

Step-by-step explanation:

We have been given an expression [tex]8x^3+12x[/tex]. We are asked to factor our given expression.

We can see that both terms of our given expression share a common factor that is 4x.

Upon factoring out 4x from our given expression, we will get:

[tex]4x(2x^2+3)[/tex]

Therefore, the factored form of our given expression would be [tex]4x(2x^2+3)[/tex] and option A is he correct choice.

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.

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)

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

Answer:

A, C, E   are not polynomials

Step-by-step explanation:

Identify the expressions that are not polynomials

A. x^2-(square root of x)-3

Polynomial cannot have a square root. so it is not polynomial

B. 4 - 3x + 5x^6

C. 5x^1/2 + 4x^2

A polynomial does not have fractional exponent

D. 14x^7

E. x^2-x-12/x+3

Polynomial cannot have x in the denominator

F. 8x^10 + 2x^5

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.

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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]

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.

Melissa sold 5 Volvos. Given that Jane sold eight times as many Volvos as Melissa, Jane sold 40 Volvos.

In order to solve this problem, we can use a simple equation. Let's denote the number of Volvos Melissa sold as 'x'. Since Jane sells 8 times as many Volvos as Melissa, the number of Volvos Jane sold can be denoted as '8x'. We know from the problem that the difference between the number of cars Jane and Melissa sold is 35, so we can write the equation like this: 8x - x = 35.

By simplifying the equation, we get 7x = 35. Therefore, to find the value of 'x', we divide 35 by 7, which gives us 'x' equals to 5.

But 'x' is the number of Volvos Melissa sold. To find out the number of cars Jane sold, we multiply 'x' by 8. Which gives us 5 multiplied by 8 equals to 40 cars.

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Answer: The expected value of the number of gram of the sugar in the cereal is 8 grams.

Step-by-step explanation:

When we multiply each of the possible outcomes by the likelihood each outcome will occur and find out the sum of the all values, we get the expected value of an experiment.

Here, the probability of the different brands 4g, 8g and 16g are 1/4, 5/8 and 1/8 respectively.

Thus, by the above definition,

The expected value of the number of grams of the sugar in the cereal = 4 g × its probability + 8 g × its possibility + 16 gram × Its possibility,

[tex]=4\times \frac{1}{4}+8\times \frac{5}{8}+16\times \frac{1}{8}[/tex]

[tex]=1+5 +2 = 8[/tex]

Thus, The expected value of the number of gram of the sugar in the cereal is 8 grams.

The expected value of the number of grams of sugar in cereal is 8 grams and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the expected value of the number of grams of the sugar in cereal:

Step 1 - The probability concept can be used in order to determine the expected value of the number of grams of sugar in the cereal.

Step 2 - According to the given data, the probability of choosing a cereal with 4 grams of sugar is 1/4, the probability of choosing a cereal with 8 grams of sugar is 5/8, and the probability of choosing a cereal with 16 grams of sugar is 1/8.

Step 3 - So, the expected value of the number of grams of the sugar in cereal is:

[tex]\rm Total \;number \;of\; grams\; of\; sugar=4\times \dfrac{1}{4}+8\times \dfrac{5}{8}+16\times \dfrac{1}{8}[/tex]

Step 4 - Simplify the above expression.

Total number of grams of sugar = 8 grams

Therefore, the correct option is C).

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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.

Answer: -24

Step-by-step explanation:

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

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