Help please.
Simplify: 5i/ 3 + 2i

Answer:

8 problems per day for

12 of the days and

9 problems per day for

24 of the days

Step-by-step explanation:

To determine whether an absolute value inequality is equivalent to a compound inequality joined by the word "and" or "or," you need to examine the absolute value expression and the inequality sign involved.

To determine the equivalence between an absolute value inequality and a compound inequality, consider the structure of the absolute value expression and the inequality sign.

When dealing with an absolute value inequality joined by the word "and," you should check whether the absolute value expression has a less than or equal to inequality sign (≤) and the right side of the compound inequality has a greater than or equal to inequality sign (≥). If both conditions are met, the absolute value inequality is equivalent to the compound inequality with the word "and." This is because the "and" condition means that both inequalities need to be satisfied simultaneously for a solution to exist.

On the other hand, when the absolute value inequality is joined by the word "or," you need to examine whether the absolute value expression has a greater than or equal to inequality sign (≥) and the right side of the compound inequality has a less than or equal to inequality sign (≤). If these conditions are met, the absolute value inequality is equivalent to the compound inequality with the word "or." The "or" condition implies that either one of the inequalities being true is sufficient for a solution to exist.

By carefully analyzing the structure and signs involved in the absolute value inequality and the compound inequalities joined by "and" or "or," you can determine their equivalence and understand the conditions under which the inequalities hold.

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Answer:

40 degrees

Step-by-step explanation:

All the angels of a triangle are equivalent to 180 degrees.

180 - (61 + 79) = 40 degrees

Answer:

x+61+79=180 { being angles of a triangle}

or,x+140=180

or, x= 180-140

hence the value of x=40

-step explanation:

A B

Are you asking for the formula of a line that passes through these points?

Answer:

Step-by-step explanation:

The task is to draw the parabola of the equation \(x^{2} -4x+4\) on the given graph.

The first step we can take to doing this is to use the table on the left hand side to work out our x and corresponding y-values to use as plotting coordinates. To do this you want to substitute the given value for x which will give you a corresponding y-value.

E.g:

x | \(x^{2} -4x+4\)      | y

0 | \((0)^{2} -4(0)-4\) | -4

Here we have gotten the coordinates (0, -4) so this will be a point on the graph.

Repeat with all other values on the table and you should get a bunch of dots which lead upwards in a curved line from a point. Extend the lines to form a parabola shape (A u-shape).

Once you have drawn the graph, label the parts.

Roots: The places where the line crosses the x-axis

Vertex: The lowest point of the parabola

Line of symmetry: The vertical line in which the parabola reflects/ is the same either side (Has equation x=_).

y-intercept: The point where the line crosses the y-axis.

Hope this helped!

Answer:

50%

Step-by-step explanation:

The absolute minimum value of f is -8, which occurs at t = 0, and the absolute maximum value is 12, which occurs at t = π/6.

To find the absolute minimum and absolute maximum values of f(t) = 8cos(t) + 4sin(2t) on the interval [0, 2/π], we need to evaluate the function at the critical points and endpoints.

First, we find the critical points by taking the derivative of f(t) and setting it equal to zero:

f'(t) = -8sin(t) + 8cos(2t) = 0.

Simplifying the equation, we have:

sin(t) = cos(2t).

This equation is satisfied when t = 0 and t = π/6.

Next, we evaluate f(t) at the critical points and endpoints:

f(0) = 8cos(0) + 4sin(0) = 8,

f(π/6) = 8cos(π/6) + 4sin(2(π/6)) = 12,

f(2/π) = 8cos(2/π) + 4sin(2(2/π)).

Finally, we compare the values of f(t) at the critical points and endpoints to determine the absolute minimum and absolute maximum values.

The absolute minimum value of f is -8, which occurs at t = 0, and the absolute maximum value is 12, which occurs at t = π/6.

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No, the equations "a = 3sin 22°/sin 45°" and "a = 3sin(22/45)°" are not the same.

In the equation "a = 3sin 22°/sin 45°," the sine function is being applied individually to the angles of 22° and 45°, and the result is divided. This means that the sine of 22° is divided by the sine of 45°.

On the other hand, in the equation "a = 3sin(22/45)°," the angle 22/45 is being evaluated first, and then the sine function is applied to this value. So, the sine of (22/45)° is calculated.

The key difference between the two expressions is the order of operations. In the first equation, the division is performed after evaluating the sine functions for each angle separately. In the second equation, the division is performed after evaluating the sine of the angle obtained by dividing 22 by 45.

Therefore, these two equations represent different calculations and will yield different results. To ensure accurate calculations, it's important to apply the correct order of operations when using trigonometric functions.

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Answer:

c = 4

See explanation

Step-by-step explanation:

Given:

4c = 3c - 4

Your calculation:

4c = 3c + 4

4c = 4 - 3c

4c = 1c

c = 4/1

c= 4

Correct calculation:

4c = 3c + 4

Collect like terms by subtracting 3c from both sides

4c - 3c = 3c + 4 - 3c

c = 4

Check:

4c = 3c + 4

4(4) = 3(4) + 4

16 = 12 + 4

16 = 16

Therefore,

Your final answer is correct but your method of calculation is not correct

Answer:

The answer that I got was 2123.72

Answer:

5 miles thank me later

Step-by-step explanation:

Answer: The input is 5.

Step-by-step explanation: Since both are functions of f(x), you can set 9x-27 equal to 18 and then solve the equation. 9x-27=18, add 27 to both sides to get 9x=45, divide both sides by 9, x=5.

:)

The second number in terms of n is x = n - 8.

Let the second number be x.

The fact that the first number is eight more than the second number is clear.

n = x + 8.    ...(1)

It is given that the third number is five more than the first number

n + 5 = y     ...(2)

We want to solve for x in terms of n, so we can use the first equation to get x in terms of n:

From equation 1 and 2

n + 5 = y = (x + 8) + 5

n + 5 = x + 13

x = (n + 5) - 13

x = n - 8

Therefore, the second number in terms of n is x = n - 8.

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Answer:

give me a sec and ill do it

Step-by-step explanation:

213.52  feet per minute is linear speed of the wheel in feet per minute of circumference of circle .

What is circumference?

The circumference of the wheel is 2*pi*radius = 2*3.14*26 = 37.7 inches.  

                          d= 28 inches

                          r = 28/2 = 17 inches

  1 rev = 2π radian

 2 rev = 2 * 2π  = 4π

      π = 3.14

angular speed= 4 * 3.14 = 12.56

speed  v = rw

            v = 17 * 12.56

           v = 213.52  feet per minute

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Answer: The options for which the extreme value theorem guarantees the existence of an absolute maximum and minimum are b, c, and d.

Step-by-step explanation:

The extreme value theorem guarantees the existence of an absolute maximum and minimum on a closed and bounded interval. Let's check each function given in the options:a. f(x) = ln(1-x) over [0, 2]

The function f(x) is not defined for x >= 1, which means the interval [0, 2] is not closed. Therefore, the extreme value theorem does not apply to this function on this interval.b. g(x) = ln(1+x) over [0, 2]

The function g(x) is defined on the closed and bounded interval [0, 2]. Also, g(x) is continuous on this interval, which means the extreme value theorem applies. Therefore, there exist an absolute maximum and minimum on this interval.c. h(x) = x-1 over [1, 4]

The function h(x) is defined on the closed and bounded interval [1, 4]. Also, h(x) is continuous on this interval, which means the extreme value theorem applies. Therefore, there exist an absolute maximum and minimum on this interval.d. k(x) = x-1/ x over [1, 4]

The function k(x) is defined and continuous on the closed and bounded interval [1, 4], which means the extreme value theorem applies. Therefore, there exist an absolute maximum and minimum on this interval.

Therefore, the options for which the extreme value theorem guarantees the existence of an absolute maximum and minimum are b, c, and d.

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Answer:

Step-by-step explanation:

What are the Derivatives of the 6 Trig Functions?

Derivation of sin x: (sin x)' = cos x.

Derivative of cos x: (cos x)' = -sin x.

Derivative of tan x: (tan x)' = sec2 x.

Derivative of cot x: (cot x)' = -cosec2 x.

Derivative of sec x: (sec x)' = sec x. tan x.

Derivative of cosec x: (cosec x)' = -cosec x. cot x.

Answer:

14 = c

Step-by-step explanation:

it is just like u said;

a + b = c

6 + 8 = c = 14

(it could also be 8-6 = c = 2)

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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The observation is located to the left of the mean by a distance of 1.2 standard deviations.

The z-score of an observation represents the number of standard deviations the observation is away from the mean.

If the z-score for a particular observation is z = -1.2, this means that the observation is 1.2 standard deviations below the mean.

If the mean is represented by μ and the standard deviation by σ, then we can express this observation as:

observation = μ + (z * σ)

observation = μ + (-1.2 * σ)

This means that the observation is located to the left of the mean by a distance of 1.2 standard deviations.

For example, The z-score represents the number of standard deviations an observation is above or below the mean of the distribution.

In this case, a z-score of -1.2 indicates that the observation is 1.2 standard deviations below the mean height of the group.

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After solving the equation the value of ∠A is 0.64.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: AB = 6

BC = 4

We have to find angle A.

Adjacent is adjacent to the angle,

The opposite is opposite the angle,

and the longest side is the Hypotenuse.

Sinx = Opposite / Hypotenuse

Sinx = 4/6

Sinx = 0.6

Now solve that equation!

sinx = 0.6

x = sin⁻¹(0.6)

x = 0.64

Hence, the value of ∠A is 0.64.

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Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

Answer:

neither, neither, terminating, repeating

Answer:

$9

Step-by-step explanation:

(2 movies returned late)

3 days late

$1.50 per day late fee

equaling $4.50 per movie

TOTALING $9

TOTALING $9.00

Answer:

Step-by-step explanation:

Since its less than 5 days, Susan will have to pay only late charge fee for two movies for 3 days.

The amount to be paid:

Correct choice is B

Step-by-step explanation:

To find - How can you determine the number of solutions of a system

              of linear equations by inspecting its equations?

Proof -

There exists three types of solution for a system of linear equations.

1. No solution.

2. Unique solution.

3. Infinite many solutions.

Now,

Let the 2 linear equations are as follows :

y = ax + b

y = cx + d

1. For no solution -

a = c and b ≠d

For example-

y = -2x + 5

y = -2x  - 1

Subtract first equation from second , we get

y - y = -2x - 1 - ( -2x + 5)

⇒0 = -2x - 1 + 2x - 5

⇒0 = -6

Not possible

So, There exist no solution.

2. For unique solution -

a ≠ c and b , d can be any value

For example -

If b and d are same ,

y = 2x - 4

y = -3x - 4

Subtract equation 1st from 2nd , we get

y - y = -3x - 4 - ( 2x - 4)

⇒0 = -3x - 4 - 2x + 4

⇒0 = -5x

⇒x = 0

⇒y = 2(0) - 4 = -4

∴ we get

x = 0, y = -4

If b and d are different

y = 2x - 4

y = -3x + 5

Subtract equation 1st from second

y - y = -3x + 5 - 2x + 4

⇒0 = -5x + 9

⇒-5x = -9

⇒x = \(\frac{9}{5}\)

⇒y =2(\(\frac{9}{5}\)) - 4 = \(\frac{18}{5} - 4 = \frac{18 - 20}{5} = -\frac{2}{5}\)

∴ we get

x = \(\frac{9}{5}\) , y = \(-\frac{2}{5}\)

3. Infinitely many solution -

a = c and b = d

For example -

y = -4x + 1

y = -4x + 1

Subtract equation first from equation second

y - y = -4x + 1 - ( -4x + 1)

⇒0 = -4x + 1 + 4x - 1

⇒0 = 0

Satisfied

So, Infinite many solution possible.

The number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

To calculate the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels, we can use the concept of stars and bars.

First, we need to ensure that we have at least one of each type of bagel. So, we take one bagel of each type, which leaves us with 14 bagels to buy.

Now, we can use stars and bars to distribute the remaining 14 bagels among the 6 types of bagels. We represent the 14 bagels as stars and the 5 possible locations between the types of bagels as bars.

Using this method, we need to distribute 14 stars among 5 bars, which can be done in

(14+5-1) choose (5-1) = 18 choose 4 = 3060 ways.

Therefore, the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

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Answer:

a. 0.40p

b. 1.4p

c. $78.4

d. $22.4

Step-by-step explanation:

a. 0.40p

b. Retail price = p + 0.4p = 1.4p

c. Retail price = 1.4 (56) = 78.4

d. Mark-up price = 0.4 (56) = 22.4

Answer:

Step-by-step explanation:

The total number of candies in the bag is 4 cherry + 8 orange + 2 lemon + 8 grape + 6 sour raspberry = 28 candies.

The probability of drawing a cherry on the first draw is 4/28, and the probability of drawing a sour raspberry on the second draw given that a cherry was drawn first is 6/27 (since there are 27 candies left in the bag after the first draw).

The probability of drawing a sour raspberry on the first draw is 6/28, and the probability of drawing a cherry on the second draw given that a sour raspberry was drawn first is 4/27.

Therefore, the probability of drawing one cherry and one sour raspberry in either order is:

(4/28) * (6/27) + (6/28) * (4/27) = 24/756 + 24/756 = 48/756

So the probability of drawing one cherry and one sour raspberry in either order is 48/756.

The measure of PR if Q is the midpoint of PR is PQ + QR.

A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line. The midpoint is the point on the middle of the line that is equally distant from the two points if a line is drawn connecting the two points. The midpoint is the point B that lies halfway between any two points, let's say A and C.

For the locations on the coordinate axes, the midpoint formula is specified. Let the endpoints of a line segment be (x), (y), and (x), (y). The midway is determined by taking the total of the x- and y-coordinates of the two points and dividing it in half. The following is the midpoint formula to determine the midpoint of a line segment connecting these points:

\(M = [\frac{(x1 + x2)}{2} , \frac{(y1 + y2)}{2} ]\)

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