The slope m, of a linear equation can be found using the formula m= y2-y1/x2-x1, where the x-and y-values come from 2 ordered pairs, and (x1, y1) and (x2, y2).

As per complex number, the value of [tex]i^{58}[/tex] is (- 1).

"Complex number is the number that is expressed in the form of [tex](a + ib)[/tex]where, 'a', 'b' are real numbers and 'i' is an imaginary number."

Therefore, the simplified value is

[tex]i^{58} \\= (\sqrt{-1})^{58} \\= (-1)^{29} \\= -1[/tex]

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The cost for the internet after an increase is $19.95.

Given that,

Based on the above information, the cost for the internet after an increase is

= $19 + 5% of $19

= $19 + $0.95

= $19.95

Therefore we can conclude that the cost for the internet after an increase is $19.95.

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The excluded values of x for x^2-9x/x^2-7x-18 are -2 and 9

The expression is given as:

x^2-9x/x^2-7x-18

Set the denominator of the expression to 0

x^2-7x-18 = 0

Expand the above expression

x^2 + 2x -9x -18 = 0

Factorize the expression

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

Factor out x + 2

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

Solve for x

x = 9 and x = -2

Hence, the excluded values of x for x^2-9x/x^2-7x-18 are -2 and 9

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Answer:

The growth factor is '2'

Step-by-step explanation:

Here, the given function that represents the population of the rabbits that is increasing exponentially,

[tex]f(x)=5(2)^t----(1)[/tex]

Since, the growth factor is a multiplier that increases the value per period,

Also, in an exponential growth function,

[tex]y=ab^x[/tex]

b is called the growth factor where x is a variable,

Since, in function (1) t is a variable ( time in months )

By comparing, b = 2,

Hence, the growth factor is 2 for the given function.

Answer:

C(0,2) - Not A Right Angle

C(3,-1) - Right Angle

C(0,4) - Right Angle

I took the unit test and after this was the correct and answer. Hope this helps :))

Final answer:

To determine if △ABC is a right triangle, we can use the distance formula to calculate the lengths of the sides of the triangle. By comparing the squares of these lengths, we can determine if △ABC is a right triangle. For the given coordinates of vertex C, △ABC is not a right triangle.

Explanation:

To determine if △ABC is a right triangle, we need to check if the square of the length of the longest side is equal to the sum of the squares of the other two sides. Using the distance formula, we can find the lengths of AB and AC for each set of coordinates for vertex C. We then compare the squares of these lengths to determine if △ABC is a right triangle.

For C(0,2), the distance between A(1,-1) and C is √((0-1)^2 + (2-(-1))^2) = √(1 + 9) = √10. The distance between B(3,2) and C is √((0-3)^2 + (2-2)^2) = √(9 + 0) = 3. The longest side is AB with length √(2^2 + 3^2) = √(4 + 9) = √13. Since √13 is not equal to √10 + 3, △ABC is not a right triangle.

Following the same calculations for C(3,-1) and C(0,4), we find that △ABC is also not a right triangle for both cases. Therefore, the answer for all three sets of coordinates is Not a Right Triangle.

Final answer:

Vehicle A requires 72 gallons and vehicle B requires 28 gallons for a 1,008-mile trip. Therefore, vehicle A needs 44 more gallons of gasoline than vehicle B for the trip.

Explanation:

To calculate the number of gallons of gasoline each vehicle needs for the trip, we would divide the total distance of the trip by the miles per gallon (mpg) that each vehicle gets. Then, to find out how many more gallons of gasoline vehicle A needs than vehicle B, we subtract the gallons of gasoline used by vehicle B from the gallons used by vehicle A.

First, we find the gallons needed for vehicle A:

Next, we calculate the gallons needed for vehicle B:

Finally, we determine how many more gallons vehicle A requires than vehicle B:

Additional gallons needed by vehicle A: 72 gallons - 28 gallons = 44 gallons

Answer:

$130

Step-by-step explanation:

This is a direct proportionality between the amount he makes and the time worked. As the time increases, so does the amount he makes and vice versa.

Let the amount made be A and the time T

A ∝ T,

A = KT where K is the constant of proportionality

where Jon makes $78 in 12 hours of work, A = 78, T = 12

78 = 12K

K = 6.5

A = 6.5T

In 20 hours of work, T =  20

A = 6.5 × 20

A = $130

Answer:

5 is the answer

Step-by-step explanation:

I'm from K12

The answer is c reason I now this is cause I had this on my test

Answer: B) [tex]36\pi \text{cubic inches}[/tex]

Step-by-step explanation:

We know that the volume of a sphere is given by :-

[tex]\text{Volume}=\dfrac{4}{3}\pi r^3[/tex], where r is radius of the sphere.

Given : The radius of the sphere = 3 inches

Then , the volume of the sphere will be :-

[tex]\text{Volume}=\dfrac{4}{3}\pi (3)^3\\\\\Rightarrow\ \text{Volume}=36\pi \text{ cubic inches}[/tex]

Hence, the volume of the sphere = [tex]36\pi \text{ cubic inches}[/tex]

By setting the given equations equal to each other (JX = CJ), we can create a new equation (4y = y +9). This equation simplifies to 3y = 9, giving a solution of y = 3.

The problem you're facing deals with bisecting line segments, which is a topic under Geometry. Remember, if a segment bisects another, that means it divides the second segment into two equal parts. In this case, PQ bisects CX at point J, so JX = CJ.

We're also given that JX = 4y and CJ = y + 9. Because JX = CJ, we can set the two equations equal to each other and solve for y:

4y = y + 9

By subtracting y from both sides, we get

3y = 9

Finally, by dividing both sides by 3, we solve for y, which is 3

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The dimensions √30 inches square and 4 inches high will provide a box with maximum volume.

The Maxima and minima of a function are the extremes within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.

It is given that:

A manufacturer wants to design an open-top box having a square base and a surface area of 120 square inches.

Let's suppose x is the base edge length and h is the box height.

x² + 4xh = 120

h = (120 - x²)/(4x)

h = 30/x - x/4

Volume = x²(30/x - x/4) = 30x - x³/4

dV/dx = 0

30 - x² = 0

x = √30

h = 120/x² = 120/30 = 4 inches

The box is √30 inches square and 4 inches high.

Thus, the dimensions √30 inches square and 4 inches high will provide a box with maximum volume.

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