5. Simplify the expression,
(-2 - 5i) - (-4+6i)
2 - 11i
-2+i
-6 + 11i
-5i

Answer:

Each order of rings comes with 3 rings. There are 78 order to pack how many rings is there going to be?

Step-by-step explanation:

Answer:

volume = x(x + 2)(x - 1)

soil = 30 ft³

Step-by-step explanation:

volume of a cuboid = width x length x height

Substituting given values into the equation:

⇒ volume = x(x + 2)(x - 1)

If width = 3ft, then x = 3:

⇒ volume = 3(3 + 2)(3 - 1)

                 = 3(5)(2)

                 = 30 ft³

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Let's assume width of rectangle x m and length of rectangle be 3x m. To calculate the dimensions of the rectangle we will use the formula of Perimeter of the rectangle

Perimeter of rectangle = 2(L + B)

Substituting the required values:

→ 168 = 2(3x + x)

→ 168 = 2(4x)

→ 168/2 = 4x

→ 84 = 4x

→ 84/4 = x

→ 21 = x

Hence,

Answer:

⠀

Step-by-step explanation :

⠀

As, it is given that, the perimeter of a rectangle is 168 m and its length is five times its width and we are to find the length and width of the rectangle. So,

⠀

Let us assume the width of the rectangle as w metre and therefore, the length will be 5w metre .

⠀

Now, According to the Question :

⠀

[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{2 (5 w + w )= 168 }}}}[/tex]

⠀

[tex]{\longrightarrow \qquad { {\sf{2 (6 w )= 168 }}}}[/tex]

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[tex]{\longrightarrow \qquad { {\sf{12 w = 168 }}}}[/tex]

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[tex]{\longrightarrow \qquad { {\sf \: w = \dfrac{168}{12} }}}[/tex]

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[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ w = 14 }}}}}} \: \: \bigstar[/tex]

⠀

Therefore,

⠀

Now, we are to find the length of the rectangle :

⠀

[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5w }}}}}} \: \: [/tex]

⠀

[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5 \times 14 }}}}}} \: \: [/tex]

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[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ Length = 70 }}}}}} \: \: \bigstar[/tex]

⠀

Therefore,

Answer:

4200

Step-by-step explanation:

I got that answer because your problem asked for the hundredth. Pretend the first 4 isn't there for a moment and round 184 to the nearest hundredth. Then place the 4 in front of what you got.

Answer:

A= 130

B= 25

Step-by-step explanation:

A is 130 because the amount of degrees that are in a triangle is 180 degrees. From that we can substract 25 from 180 and get 155.

Since B is congruent with 25, B is also 25 degrees. Therefore, A is 130 because 180 - 50 is 130.

Hope this helps.

Answer:

Area of shaded rectangle = 42 cm²

55%

Step-by-step explanation:

The length of the shaded area is equal to the length of the white rectangle.

Therefore, length of shaded rectangle = 7 cm

The width of the shaded rectangle is equal to the length of the white rectangle minus two widths of the white rectangle.

Therefore, width = 7 - (2 x 0.5) = 6 cm

Area of shaded rectangle = width x length

                                          = 6 x 7

                                          = 42 cm²

----------------------------------------------------------------------------------------------

Perimeter of a square = 4 × side length

If the perimeter of the square is 40 cm,
then the side length = 40 ÷ 4 = 10 cm

Area of a square = side length x side length

⇒ area of this square = 10 x 10 = 100 cm²

To determine the shaded area, calculate the areas of the 2 white triangles and subtract these from the area of the square.

Area of a triangle = 1/2 x base x height

⇒ area of left triangle = 1/2 x (10 - 7) x 10 = 15 cm²

⇒ area of right triangle = 1/2 x 10 x (10 - 4) = 30 cm²

Therefore, shaded area = 100 - 15 - 30 = 55 cm²

To calculate the percentage, divide the shaded area by the area of the square and multiply by 100:

(55 ÷ 100) × 100% = 55%

Answer:

Step-by-step explanation:

Answer:

(5,1)

is one of infinitely many possible order pairs.

Step-by-step explanation:

There are an infinite amount of x values that give you an answer to this question. You get to choose. But first let's start off with isolating y.

[tex]-x + 6y = 1\\6y = 1 + x\\y = \frac{1+x}{6}[/tex]

Now the equation is easier to interpret. [tex]y = \frac{1+x}{6}[/tex]

Now here's the part where you actually get to choose. Take any x, value, I'll choose 5.

I'll sub it into the equation and get my y value, [tex]y = \frac{1 + (5)}{6}= 1[/tex]

Okay, we get that y = 1, when x = 5. That's an ordered pair:

(5,1)

Remember you could follow this same procedure for any x value you choose.

We see that Triangle ABC is an isosceles triangle which means:

We see that Angle BCD and Angle BCA are on a straight line, which means that both of the angles' measures are equal to 180 degrees

    --> in equation form:

              Angle BCD + Angle BCA = 180

                118 + Angle BCA = 180

                         Angle BCA = 62 degrees

Since Angle BCA and BAC are equal, then Angle BAC or Angle A in this case is 62 degrees

Hope that helps!

Answer:

$11.25

Step-by-step explanation:

multiply 15 by 25% which is .25

15 * 0.25 = 3.75

minus 3.75 from 15

15 - 3.75 = 11.25

the expression represents a quadratic polynomial with 2 terms.The constant term is 1, the leading tern is x and the leading coefficient is 1

Answer:

19

Step-by-step explanation:

(5x+37)+(3x-9)=180

8x= 152

x=19

Answer:

The required angles are 15, 75 and 90

Step-by-step explanation:

1x + 5x+ 6x = 180
or 12x = 180
180 ÷ 12 = 15
hence,
15, 75, 90.

Answer:

x = 67° (nearest whole degree)

Step-by-step explanation:

Sine Rule

[tex]\sf \dfrac{sin(A)}{a}= \dfrac{sin(B)}{b}= \dfrac{sin(C)}{c}[/tex]

where A, B and C are the angles, and a, b and c are the sides opposite the angles

Given information

From inspection of the triangle:

Finding x:

Substitute given values into the formula and solve for x:

[tex]\sf \implies \dfrac{sin(38)}{12}= \dfrac{sin(x)}{18}[/tex]

[tex]\sf \implies 18\cdot\dfrac{sin(38)}{12}= sin(x)[/tex]

[tex]\sf \implies sin(x)=\dfrac32sin(38)[/tex]

[tex]\sf \implies x=sin^{-1}\left(\dfrac32sin(38)\right)[/tex]

[tex]\sf \implies x=67.44208077...[/tex]

Final Solution

x = 67° (nearest whole degree)

Answer:

∠x = 67°

Step-by-step explanation:

From the Law of Sines,

we know that :

Here we have :

On substituting,

Answer:

(a) To find the missing angle, we would do inverse tan.

[tex]angle =tan^{-1}\frac{opp}{adj}[/tex]

[tex]angle = tan^{-1}\frac{17}{21}[/tex]

angle= 39.0 degrees or 0.7 radians

(b) To find the missing angle, we would do inverse sin.

[tex]angle= sin^{-1}\frac{opp}{hyp}[/tex]

[tex]angle= sin^{-1}\frac{12.7}{22.1}[/tex]

angle= 35.1 degrees or 0.6 radians

Answer:

a) As weekly costs are fixed at $300, we simply need to shift the function up 300 units. (the new function is shown in blue on the attached graph).

b) Reading from the (blue) graph, the total cost of producing 75 books in a week is $600.

fixed cost + variable cost = $300 + $300 = $600

Answer: 48

Step-by-step explanation:

3x16=48

3 gallons=48 cups

There are 48 cups in 3 gallons.

To start your conversion, you need to know how many cups are in one gallon.

There are 2 cups in 1 pint, and 2 pints in 1 cup.

Answer:

the answer is c

Step-by-step explanation:

45% of 1500=675

38% of 1500=570

675+570=1245

1500-1245=255

Answer: Look at the screenshot

Step-by-step explanation:

Ive added a screenshot of what this graph should look like

Answer:

*View attached graph*

Step-by-step explanation:

I graphed 6 points, so you are able to choose the ones you want :)

*View attached graph*

Hope this helps!

Answer:

C

Step-by-step explanation:

Answer:

f(x) = 3^x+3

f(x) = 9.3^x+1

Step-by-step explanation:

Hope it helps you in your learning process.

Answer: $1500

Step-by-step explanation:

Did the quiz on this hope you have a great day.

Answer:

Looking at the first two given ordered pairs (3, 5) and (4, 7), it appears that for every increase of 1 unit of x, there is an increase of 2 units of y.

Let's check by writing the next ordered pairs using this rule:

(5, 9)  (6, 11)  (7, 13)  (8, 15)

As the the ordered pair (8, 15) is in the table, then we can confirm that this is the rule.

Writing the rule as an equation:

y = 2x - 1

Therefore, n = 6

Answer:

y = 2x - 1

n = 6

Step-by-step explanation:

Hello!

This is an arithmetic sequence.

An Arithmetic sequence, also known as an arithmetic progression, is a string of numbers that follow a pattern where the difference between two terms is always the same (constant).

An Arithmetic sequence is modeled by the explicit function:[tex]\bold{t(n) = (CD)n + t(0)}[/tex]

Let's go step by step to solve these equations:

Step 1: Common Difference

The common difference of a sequence is similar to the slope of a line. The slope formula is given as [tex]\bold{\frac{y_2 - y_1}{x_2-x_1}}[/tex].

We can input values of x and y to find the common difference

We have the CD, 2!

Step 2: Starting Value

The starting value can be shown as the y-intercept of the line or the origin point of the sequence.

To find the starting value or t(0), we can input an x and y value for "n" and "t(n)"

We know have the starting value, -1!

Step 3: The Equation

We now have all the values for our equation. let's bring our attention back to the input and output variables. Since we know that "t(n)" is the same as "y" and "n" is the same as "x", we can plug that instead of t(n) and n.

Solve for n:

With our equation, we can plug in 11 as the output and solve for n.

n = 6

_______________________________________________________

Another way to solve this is to find the Recursive Equation

The Recursive Equation is only meant to find the next term, it doesn't do so well in finding the terms in the long run.

The basic form of a recursive equation is t(n + 1) = t(n) + (CD); where t(0) is ____

I'm not going to go in-depth with this, but you can see the values that we solved above can be implemented here.

Our recursive equation is t(n + 1) = t(n) + 2; where t(0) is -1

The port outside of the semi-colon represents where the sequence starts. If only t(n+1) = t(n) + 2 is given, we could start at 5, and go as 5, 7, 9...etc.

We would start by finding t(1) by doing:

We can confirm this using our explicit rule: y = 2x - 1

Break it down gently

f(x) = 1 - sin⁴3x + cos6x/6

let's break ( - sin⁴3x) and (Cos6x/6) and 1 separately

the derivative of ( -sin⁴3x) = 12cos3xsin³3x

the derivative of (cos6x/6) = -sin6x

the derivative of (1) = 0

f'(x) = 0

12cos3xsin³3x - sin6x = 0

Answer:

The first three are not statistical, the last three are.

Using the z-distribution, as we are working with a proportion, it is found that the buyers need a sample of 1505.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.

There is no estimate of the percentage, hence [tex]\pi = 0.5[/tex], and the margin of error is of M = 0.03, hence we solve for n to find the desired sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 2.327(0.5)[/tex]

[tex]\sqrt{n} = \frac{2.327(0.5)}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.327(0.5)}{0.03}\right)^2[/tex]

[tex]n = 1504.2[/tex]

Rounding up, the buyers need a sample of 1505.

More can be learned about the z-distribution at https://brainly.com/question/25890103

The true statement about the equation of the line of best fit (d) For every year a person gets older, their screen time decreases by 3.2 minutes

The equation of the line of best fit is given as:

y = -3.2x + 274.4

Where:

A linear equation is represented as:

y = mx + b

Where:

By comparison, we have:

m = -3.2 and b = 274.4

This means that:

For every year a person gets older, the average screen time decreases by 3.2 minutes

Hence, the true statement is (d)

Read more about line of best fit at:

https://brainly.com/question/17261411

The Horizontal component is 554.889N and the vertical component is

9.8235 Newton

Given Data

Resolving the vertical force

Fy = 555 sin44°

Fy = 555 *0.01770

Fy = 9.8235 Newton

Resolving the horizontal force

Fx = 555 cos 44°

Fx = 555 *0.9998

Fx = 554.889 Newton

Learn more about forces here:

https://brainly.com/question/25997968