Convert the measurement.
56.8 grams= ounces

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90°\\b) cos^(-1)(1/2) = 60°\\c) tan^(-1)(√3) = 60°\)

a) \(sin^(-1)(1) = 90°\)

The inverse sine function, \(sin^(-1)(x)\)gives the angle whose sine is equal to x. In this case, we are looking for the angle whose sine is equal to 1. The angle that satisfies this condition is 90 degrees, so\(sin^(-1)(1) = 90°\).

b) \(cos^(-1)(1/2) = 60°\)

The inverse cosine function, cos^(-1)(x), gives the angle whose cosine is equal to x. Here, we are looking for the angle whose cosine is equal to 1/2. The angle that satisfies this condition is 60 degrees, so \(cos^(-1)(1/2)\)= 60°.

c) \(tan^(-1)(√3) = 60°\)

The inverse tangent function, tan^(-1)(x), gives the angle whose tangent is equal to x. In this case, we are looking for the angle whose tangent is equal to √3. The angle that satisfies this condition is 60 degrees, so tan^(-1)(√3) = 60°.

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90° b) cos^(-1)(1/2) = 60°c) tan^(-1)(√3) = 60°\)

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a) The completed equalities are:

sin-¹(x) = 30°, sin-¹(x) = 45°, sin-¹(x) = 60°

b) The completed equalities are:

cos-¹(x) = 30°, cos-¹(x) = 45°, cos-¹(x) = 60°

c) The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. C.

a) sin-¹(x) = 30°, 45°, 60°

The inverse sine function, sin-¹(x), gives the angle whose sine is equal to x.

Let's find the angles for each option given:

sin-¹(x) = 30°:

If sin-¹(x) = 30°, it means that sin(30°) = x.

The sine of 30° is 0.5, so x = 0.5.

sin-¹(x) = 45°:

If sin-¹(x) = 45°, it means that sin(45°) = x.
The sine of 45° is √2/2, so x = √2/2.

sin-¹(x) = 60°:

If sin-¹(x) = 60°, it means that sin(60°) = x.

The sine of 60° is √3/2, so x = √3/2.

The completed equalities are:

b) cos-¹(x) = 30°, 45°, 60°

The inverse cosine function, cos-¹(x), gives the angle whose cosine is equal to x.

Let's find the angles for each option given:

cos-¹(x) = 30°:

If cos-¹(x) = 30°, it means that cos(30°) = x.

The cosine of 30° is √3/2, so x = √3/2.

cos-¹(x) = 45°:

If cos-¹(x) = 45°, it means that cos(45°) = x.
The cosine of 45° is √2/2, so x = √2/2.

cos-¹(x) = 60°:

If cos-¹(x) = 60°, it means that cos(60°) = x.

The cosine of 60° is 0.5, so x = 0.5.

Therefore, the completed equalities are:

c) tan-¹(x) = 30°, 45°, 60°

The inverse tangent function, tan-¹(x), gives the angle whose tangent is equal to x.

Let's find the angles for each option given:

tan-¹(x) = 30°:

If tan-¹(x) = 30°, it means that tan(30°) = x.

The tangent of 30° is 1/√3, so x = 1/√3.

tan-¹(x) = 45°:

If tan-¹(x) = 45°, it means that tan(45°) = x.

The tangent of 45° is 1, so x = 1.

tan-¹(x) = 60°:

If tan-¹(x) = 60°, it means that tan(60°) = x.

The tangent of 60° is √3, so x = √3.

The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. c)

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Answer:

d = 5

| | = absolue value

do any steps necessary inside of them and then turn it positive

Answer:

5

Step-by-step explanation:

you bring down -3d but make it positive because of absolute value then divide both sides of the equation by 3

Answer:

the original price times the % discount will give u the scale price

Answer: Z'(-7;8)

suppose the coordinates of Z' is Z'(x,y)

we have:

\(\left \{ {{x=8.cos90-7.sin90=-7} \atop {y=8.sin90+7.cos90=8}} \right.\)

=> Z'(-7;8)

Step-by-step explanation:

Answer:

x = 3.5

Step-by-step explanation:

\( \triangle DEF \sim \triangle XYZ\\\\

\therefore \frac{DE}{XY} =\frac{DF}{XZ} \\\\

\therefore \frac{5}{7.5} =\frac{7}{3x} \\\\

\therefore 3x = \frac{7.5\times 7}{5} \\\\

\therefore x = \frac{7.5\times 7}{3\times 5} \\\\

\therefore x = \frac{52.5\times 7}{15} \\\\

\therefore x = 3.5\)

Step-by-step explanation:

If \(\triangle\)DEF~\(\triangle\)XYZ

\(\tt{\dfrac{DE}{XY}=\dfrac{EF}{ZY}=\dfrac{DF}{XZ} }\)

According to the question

\(\tt{\dfrac{5}{7.5}=\dfrac{3}{4.5}=\dfrac{7}{3x} }\)

\(\tt{\dfrac{3}{4.5}=\dfrac{7}{3x} }\)

\(\tt{ 9x=4.5×7}\)

\(\tt{ 9x=31.5 }\)

\(\tt{ x=\dfrac{22.5}{9} }\)

\(\tt{x=3.5 }\)

Hello!

In order to solve this equation,we must first find out what distance is being traveled in 4 hours. If we travel 4 hours, at a constant speed of 60 miles,we must multiple those two numbers to find the distance travelled.

60x4 is 240.

This means we must divide 240 by 3 hours to find our constant rate of speed.

240 divided by 3 is 80.

This means, we would need to travel 80 mph to arrive to the same location in three hours.

x=80.

Hope this helps & good luck.

Answer:

The equation that can be used to find its speed (x) to cover the same distance is f(x) = x + 60

Step-by-step explanation:

First off, let's gather what we know. The car will take 4 hours to cover a distance if it is going 60 mph. We need the car to be a speed where it can cover the same distance within 3 hours.

THe first step to solving this problem is dividing 60 by 4 to see how much the speed of the car should increase in order to travel the same distance within 3 hours.

60/4 = x

We need to add x to the original speed of 60 mph.

Therefore, the equation that can be used to find its speed (x) to cover the same distance is f(x) = x + 60

Therefore, the equation that can be used to find its speed (x) to cover the same distance is f(x) = x + 60

Hope this helps! :)

To write a linear function f(x) with the values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation:

f(x) - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

Using the two given points, we have:

f(3) = -4 and f(5) = -4

This means that (3, -4) and (5, -4) are two points on the line.

To find the slope, we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (-4 - (-4)) / (5 - 3)

m = 0 / 2

m = 0

Therefore, the slope of the line is 0.

Using the point-slope form with the point (3, -4) and the slope m = 0, we get:

f(x) - (-4) = 0(x - 3)

f(x) + 4 = 0

f(x) = -4

So, the linear function f(x) that passes through the points (3, -4) and (5, -4) is f(x) = -4.

The relative frequency distribution of the values of the mean of these 15,504 different samples would specify the sampling distribution of the mean.

The sampling distribution of the mean refers to the distribution of sample means obtained from repeated sampling from the same population.

In this case, we have 15,504 different samples of size 5 drawn from a population of 20 hospitals.

Each sample has its own sample mean. The relative frequency distribution of these sample means would specify the sampling distribution of the mean.

The sampling distribution of the mean is important in statistics because it allows us to make inferences about the population mean based on the distribution of sample means.

It helps us understand the variability of sample means and provides a basis for constructing confidence intervals and conducting hypothesis tests.

Therefore, the relative frequency distribution of the mean values from the different samples would describe the characteristics of the sampling distribution of the mean..

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1, 2, 3, 6, 8, 12, 16, 24, 48.

The number of bags she can make are shown in the table:

Number of CC cookies in each bag 1 2 3 4 6 8 12 16 24 48

Number of bags 48 24 16 12 8 6 4 3 2 1

Since the number of cookies that goes in a bag is a factor of the total number of cookies, all the factors of 48 are listed in the first row of the table. Each column corresponds to a situation where the 48 cookies are divided equally among some bags, and the product of the numbers in each column is 48. The number of bags is also a factor of the total number of cookies.

The height of the column is 60 feet. This means that the rock column reaches a height of 60 feet based on the given volume and the area of its hexagonal base.

To find the height of the column, we can use the formula for the volume of a hexagonal prism:

V = Bh

Where:

V is the volume of the prism,

B is the area of the base,

and h is the height of the prism.

In this case, we know that the volume of the column is 180 cubic feet and the area of the hexagonal base is 3 square feet. Substituting these values into the formula, we get:

180 = 3h

To solve for h, we divide both sides of the equation by 3:

h = 180 / 3

h = 60 feet.

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Answer:

5:1, 10:2, and 15:3

Step-by-step explanation:

9514 1404 393

Answer:

  in Step 2, the student added 4 on the right and subtracted 4 on the left

Step-by-step explanation:

In Step 2, the student subtracted 4 on the left side of the equation, but incorrectly added 4 on the right. (The same operation needs to be performed on both sides of the equation.) The correct step 2 would be ...

  -8x = -32 . . . . correct step 2

  x = 4 . . . . . correct step 3

The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

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Answer:

0.9

Step-by-step explanation:

6.3/7 7*9=63

Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)

Answer:

x=-1

Step-by-step explanation:

0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )

- Distribute 0.5 by 5 and -7x

2.5 - 3.5x = 8 - ( 4x + 6 )

Second- Distribute the invisible one into 4x and 6

2.5 - 3.5x = 8 - 4x - 6

- Combine like terms: Subtract 6 from 8

2.5-3.5x= - 4x + 2

-Add 4x from both sides of the equation

2.5 + 0.5x = 2

-Subtract 2.5 from both sides of the equation

0.5x = 2- 2.5

0.5x = -0.5

-Then divide each side by 0.5x

0.5x  = -0.5

0.5      0.5

-Cancel the common factor of 0.5

x = - 0.5

      0.5

-Divide -0.5 by 0.5

X = -1

a. The statement is true.

b. The statement is false.

c. The statement is false.

  a. When the null hypothesis of equal means for four groups is rejected using ANOVA at a significance level of 0.05, it implies that there is sufficient evidence to suggest differences between the group means. ANOVA compares the variability between groups to the variability within groups. If the null hypothesis is rejected, it means that the standardized variability between the groups is higher than the standardized variability within the groups.

b. The appropriate significance level for pairwise comparisons of group means, also known as post hoc tests, is not simply divided by the number of groups. Dividing the significance level by the number of groups, as stated in option b, is not a valid approach. To appropriately account for multiple comparisons, adjustments like the Bonferroni correction, Tukey's HSD, or the Sidak correction are commonly used. These methods ensure that the overall Type I error rate is controlled.

c. Rejecting the null hypothesis using ANOVA only indicates that there are differences between at least two group means. It does not provide information about which specific group means differ from each other. To identify which group means are significantly different, additional post hoc tests or pairwise comparisons are required. These tests allow for a more detailed analysis of specific group differences and provide insights into which pairs of group means are statistically significant.

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We have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

To solve the given equations for the equilibrium values of C, NX, CF, r, and ε, let's go step by step.

First, we'll substitute equations (2), (3), (4), (5), (6), (7), (8), and (9) into equation (2) to eliminate the variables C, I, G, NX, CF, and T.

Equation (2) becomes:
Y = (1/2)(Y - T) + (2,000 - 100r) + 1,500 + (500 - 500ε)

Next, let's simplify the equation:

Y = (1/2)(Y - 1,000) + 2,000 - 100r + 1,500 + 500 - 500ε

Distribute (1/2) to the terms inside the parentheses:

Y = (1/2)Y - 500 + 2,000 - 100r + 1,500 + 500 - 500ε

Combine like terms:

Y = (1/2)Y + 3,500 - 100r - 500ε

Now, let's isolate Y by subtracting (1/2)Y from both sides:

(1/2)Y = 3,500 - 100r - 500ε

Multiply both sides by 2 to get rid of the fraction:

Y = 7,000 - 200r - 1,000ε

We now have one equation (10) in terms of Y, r, and ε.

Next, let's substitute equation (1) into equation (10) to solve for Y:

5,000 = 7,000 - 200r - 1,000ε

Subtract 7,000 from both sides:

-2,000 = -200r - 1,000ε

Divide both sides by -200:

10 = r + 5ε

This gives us equation (11) in terms of r and ε.

Now, let's substitute equation (11) into equation (5) to solve for NX:

NX = 500 - 500ε

Substitute r + 5ε for ε:

NX = 500 - 500(r + 5ε)

Simplify:

NX = 500 - 500r - 2,500ε

This gives us equation (12) in terms of NX, r, and ε.

Finally, let's substitute equation (12) into equation (6) to solve for CF:

CF = -100r

Substitute 500 - 500r - 2,500ε for NX:

CF = -100(500 - 500r - 2,500ε)

Simplify:

CF = -50,000 + 50,000r + 250,000ε

This gives us equation (13) in terms of CF, r, and ε.

To summarize, we have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

These equations represent the equilibrium values of Y, r, ε, NX, and CF in the given open economy.

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To use the quadratic formula, we need to identify the values of a, b, and c.

1. In this case, the equation is 4x² - 3x - 8 = 0, so a = 4, b = -3, and c = -8.

2. x = (-b ±√(b² - 4ac))/2a.

3.  x = (3 ±√137)/8.

The Quadratic Formula is a mathematical equation used to solve second-degree equations.

To use the quadratic formula, we need to identify the values of a, b, and c in the equation ax² + bx + c = 0.

In this case, the equation is

4x² - 3x - 8 = 0,

so a = 4, b = -3, and c = -8.

Once the values of a, b, and c are known, we can substitute them into the Quadratic Formula:

x = (-b ±√(b² - 4ac))/2a.

In this equation, a = 4, b = -3, and c = -8, so the equation becomes

x = (-(-3) ±√((-3)² - 4(4)(-8)))/2(4).

Simplifying, we get x = (3 ±√(9 + 128))/8.

Finally, solving for x yields x = (3 ±√137)/8.

Therefore, the solution to the equation is

x = (3 ±√137)/8.

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Answer:

Step-by-step explanation:

Defining CB

CB is not the hypotenuse of triangle ABC. The hypotenuse is the longest side of any right triangle. CB is the other side other than the hypotenuse that makes up <C. It is the adjacent side because AC and CB make up angle C.

Defining Cos(C)

All of this makes up what you need to know to define the Cos(C)

Cos (C) = adjacent side / hypotenuse.

adjacent side = 6

Hypotenuse = 10

Cos(C) = 6/10

Answer: B

Answer:

\(x = 8\)

Step-by-step solution:

2D dimensions give us this equation when it comes to parallelograms like these:

\( \frac{area}{height} = side\)

In this case, x is side. So now you do 104/13=x, so x=8.

Answer:

2

Step-by-step explanation:

slope : ( The amount y increases , when x is increased by 1 )

slope : { y2 - y1 / x2 - x1 }

slope : y2 = 2

           y1 = -4

           x2 = 5

           x1 = 2

You must minus the values in the formula to find the slope line that passes through the points:

slope : { y2 - y1 / x2 - x1 }

slope : (2) - (-4) / (5) - (2)

=> 2 + 3 / 3

=> 6/3

=> 2

Text explanation:

Difference between both y-coordinates. = 6

Difference between both x-coordinates. = 3

Divide the difference between y and x. =

y/x =2

Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.

Hope this helps! Sorry it took so long! ⸜(｡˃ ᵕ ˂ )⸝ xx

The slope of the line that passes through the points (2, -4) and (5, 2) is 2.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,

Slope = (y₂-y₁)/(x₂-x₁) =  [2 - (-4)] / (5 - 2)= 6/3 = 2

Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.

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The respοnse tο the given questiοn wοuld be that As a result, it will take equatiοn arοund 9.7 days frοm the day Sandy placed her sandwich in her lοcker fοr 500 bacteria tο cοmpletely cοver it.

When twο statements are cοnnected by a mathematical equatiοn, the equals sign (=) implies equality. An equatiοn in algebra is a mathematical statement that prοves the equivalence οf twο mathematical expressiοns. Fοr instance, the equal sign separates the numbers in the equatiοn 3x + 5 = 14. It is pοssible tο determine the relatiοnship between the twο sentences οn either side οf a letter using a mathematical fοrmula. The lοgο fοr the particular piece οf sοftware is frequently the same. as 2x - 4 = 2, fοr dinstance.

This issue's expοnential equatiοn is as fοllοws:

N(t) = N0  × \(e^{(kt)\) ×  (kt)

We can utilise the abοve infοrmatiοn tο determine the values οf N0 and k:

N(4) = 71 × N(7) = 185

When we enter these numbers intο the equatiοn, we οbtain:

71 = N0  × \(e^{(4k)\)  × (4k)

185 = N0  × \(e^{(7k)\)   × (7k)

185/71 =  \(e^{(3k)\)  × (3k)

As a result, the equatiοn fοr this issue is:

N(t) = 23.77  × \(e^{(0.3056t)}\)  × (0.3056t)

We may set N(t) equal tο 500 and sοlve fοr t tο see hοw many days it will take fοr 500 germs tο grοw:

500 = 23.77  × \(e^{(0.3056t)}\) × (0.3056t)

9.7 days based οn t = ln(500/23.77) / 0.3056.

As a result, it will take arοund 9.7 days frοm the day Sandy placed her sandwich in her lοcker fοr 500 bacteria tο cοmpletely cοver it.

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Answer:

D.) 5 x 25 = 125

Step-by-step explanation:

The two numbers are 25 and 5. If you take 1/5 of 25, or simply divide by 5, you will get 5.

Answer:

A) X + Y = 30

B) X = .2Y OR X - .2Y = 0

We subtract B) from A)

1.2Y = 30

Y = 25  X = 5

X * Y = 125

Answer is d.) 125

Step-by-step explanation:

Answer:

It should be around 10.536

Step-by-step explanation:

For this one, I'm pretty sure you divide the speed value by 5

The Inverse Laplace transform of F(s)=(1+e^(?2s))^2 / (s+2) can be found by partial fraction decomposition and using the inverse Laplace transform of each term. After partial fraction decomposition, we obtain:

F(s) = (1+e^(?2s))^2 / (s+2) = (1/4) [1/(s+2)] + (1/2) [e^(?2s)/(s+2)] + (1/4) [e^(?4s)/(s+2)]

Using the inverse Laplace transform of each term, we have:

f(t) = L^(-1){F(s)} = (1/4) [L^(-1){1/(s+2)}] + (1/2) [L^(-1){e^(?2s)/(s+2)}] + (1/4) [L^(-1){e^(?4s)/(s+2)}]

The inverse Laplace transform of 1/(s+2) is simply e^(-2t) * h(t), where h(t) is the Heaviside function. The inverse Laplace transform of e^(-2s)/(s+2) can be found using the shifting property of the Laplace transform:

L{e^(-2s)f(s)} = F(s+a), where F(s) is the Laplace transform of f(t)

Letting f(s) = 1/(s+2), a = 2, and F(s) = (1+e^(?2s))^2 / (s+2), we obtain:

L{e^(-2s)/(s+2)} = F(s+2) = (1+e^(?2(s+2)))^2 / (s+4)

Taking the inverse Laplace transform, we get:

L^(-1){e^(?2s)/(s+2)} = e^(-2t) * (t+1) * h(t+2)

Similarly, the inverse Laplace transform of e^(-4s)/(s+2) can be found using the shifting property:

L^(-1){e^(?4s)/(s+2)} = e^(-4t) * (t+1) * h(t+4)

Substituting the values we found, we get:

f(t) = (1/4) [e^(-2t) * h(t)] + (1/2) [e^(-2t) * (t+1) * h(t+2)] + (1/4) [e^(-4t) * (t+1) * h(t+4)]

Therefore, the inverse Laplace transform of F(s) is given by f(t) = (1/4) * e^(-2t) + (1/2) * e^(-2t) * (t+1) * h(t+2) + (1/4) * e^(-4t) * (t+1) * h(t+4).

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The inverse Laplace transform of F(s) is given by f(t) = (4 + t) * e^(-2t) * h(t), where h(t) represents the Heaviside function.

The inverse Laplace transform of the function F(s) = (1 + e^(-2s))^2 / (s + 2) can be found using partial fraction decomposition and properties of Laplace transforms. The inverse Laplace transform of F(s) can be denoted as f(t) = L^(-1){F(s)}.

By applying partial fraction decomposition to F(s), we can write it as F(s) = (4 / (s + 2)) + (e^(-2s) / (s + 2))^2. Using the Laplace transform table, we know that L^(-1){1 / (s + a)} = e^(-at) and L^(-1){e^(-as) / (s + a)^2} = t * e^(-at).

Therefore, we can express f(t) as f(t) = 4 * L^(-1){1 / (s + 2)} + L^(-1){e^(-2s) / (s + 2)^2}. Applying the Laplace transform table, we find that L^(-1){1 / (s + 2)} = e^(-2t) and L^(-1){e^(-2s) / (s + 2)^2} = t * e^(-2t).

Substituting these results into the expression for f(t), we get f(t) = 4 * e^(-2t) + t * e^(-2t).

Therefore, the inverse Laplace transform of F(s) is f(t) = 4 * e^(-2t) + t * e^(-2t), which can be written using the Heaviside function as f(t) = (4 + t) * e^(-2t) * h(t).

In conclusion, the inverse Laplace transform of F(s) is given by f(t) = (4 + t) * e^(-2t) * h(t), where h(t) represents the Heaviside function.

Learn more about inverse Laplace transform here:

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Answer:

(- 3, 0 ), (4, 0 )

Step-by-step explanation:

To find the x- intercepts let f(x) = 0

\(\frac{x^2-x-12}{5x^2+ 4x}\) = 0

The denominator cannot equal zero as this would make f(x) undefined.

Equate the numerator to zero and solve for x

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

x- intercepts are (- 3, 0 ) and (4, 0 )