If i² = -1, then (i)(1 + 2)(2-3i)² = ?

Max can draw Rectangles of side lengths which are the integral divisors of 24 that can be (2,12) or (3,8) or (4,6) etc.

You can calculate a rectangle's area if you know its length and width. However, because these two amounts are distinct, you can't do a reverse computation to find both of them if you only know the area. You can find both of them in the specific case where they are equal, which gives the shape of a square, and you can compute one if you know the other. If you are aware of the rectangle's perimeter as well, you can utilize that knowledge to determine two potential length and width numbers.

Area of a Rectangle = Length × Breadth

Area= 24 square centimeters

So, Side Lengths or Breadth of the Rectangle can be the divisors of 24.

Lengths and Breadths can be (2,12) or (3,8) or (4,6) etc.

Max can draw Rectangles of side lengths which are the integral divisors of 24 that can be (2,12) or (3,8) or (4,6) etc.

To refer more about Rectangles, visit:

https://brainly.com/question/25292087

#SPJ1

The expression representing the situation is (r+6).

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given that, Conrad has 6 more marbles than Rory and r represents the number of marbles that Rory has,

We see, Conrad has more marble than Rory and Rory has r marbles,

Mathematical can be represented as,

c = r+6

Hence, The expression representing the situation is (r+6).

For more references on the expressions, click;

https://brainly.com/question/14083225

#SPJ1

Answer: c = 7

Step-by-step explanation:

180 = 86 + 31 + 9c
180 = 117 + 9c
63 = 9c
7 = c

Answer:

  c = 7°

Step-by-step explanation:

You want the value of c given that angles in a triangle are marked 86°, 31°, and 9c.

The angle sum theorem tells you the sum of angles in a triangle is 180°. Using given angle values, this means ...

  86° +31° +9c = 180°

  117° +9c = 180° . . . . collect terms

  9c = 63° . . . . . . . subtract 117°

  c = 7° . . . . . . . . divide by 9

The value of c is 7°.

the probability that the first song played is a folk song is 9.1%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Carter has 153 songs on a playlist. He's categorized them in the following manner:

20 country, 31 blues, 8 Latin American, 17 jazz, 26 rap, 14 folk, and 37 hip hop.

The number of folk songs is 14

P(folk) = number of folk songs/ total

= 14/ 153

=0.091

Hence the probability that the first song played is a folk song is 9.1%.

Learn more about probability, by the following link.

brainly.com/question/24756209

#SPJ1

Here is the two column proof:

    Statement                                        Reason                                              

===================================================

    Statement                                        Reason                                              

Answer:

3 hr

Step-by-step explanation:

750 ml  /  (250 ml/hr) = 3 hr

Answer:

100000000000000000000000000000000000000000000000000

Step-by-step explanation:

Answer:13 is a prime number

Step-by-step explanation:

Answer:

b) 13

Step-by-step explanation:

Now we have to,

→ find prime number from the options.

Generally we know that,

→ 2 is the only even prime number.

→ Other all prime numbers are odd.

Then the prime number is,

→ 13

(Because, it is the only odd number given)

Hence, the option (b) is correct.

Answer:

No, there is not sufficient evidence that the scores improved.

Step-by-step explanation:

Just because these people were given a six-page review handout doesn't mean that:

a. They actually did any of it

b. They learned anything

c. Since the kids have other experiences in class, the scores might not have necessarily improved that much, if at all

d. They had enough time to study

e. They cared enough in the first place

Generally, there is no rock-solid evidence at all pointing to the fact that their test scores improved. While you could make the assumption assuming every kid did what they were supposed to do, there isn't enough evidence to say that the scores improved.

Answer:

part A: The appropriate design for the study includes;Treatment used; Chamomile oil treatment

Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves

Treatment assignment; Treatment should be assigned to patients with pinched nerves

Variables that should be measured; Reduction or relief of pain as reported by the patients

Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female

Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.

Step-by-step explanation:

a) The total number of books in Tim's collection is; 300 books

b) If Tim adds 20 more nonfiction books to his collection, the new percentage of nonfiction books is; 17.5%

We are given;

Number of Non fiction books Tim has = 36

Percentage of non-fiction books = 12%

a) Let the total number of books in his collection be x. Thus;

(12/100) * x = 36

x = 3600/12

x = 300 books

b) He adds 20 more non fiction books to his collection. Thus;

New total non fiction books = 36 + 20 = 56

New total number of all books = 300 + 20 = 320

Thus;

New percentage of non fiction books = 56/320 * 100%

New percentage of non fiction books = 17.5%

Read more about Algebraic word problems at; https://brainly.com/question/21405634

#SPJ1

According to the Pythagorean theorem, The Answer is Yes the third side is greater than 1 foot.

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

p=1 foot

b=1 foot

[tex]h^{2} = p ^{2} + b ^{2}[/tex]

[tex]h=\sqrt {1^{2}+1^{2}}\\=\sqrt 2\\=1.41\\[/tex]

To learn more about right angle triangle visit:

https://brainly.com/question/2773823

#SPJ4

Answer:

1/6

Step-by-step explanation:

A (6,1)

B (12,2)

slope = (2-1)/(12-6)

1/6

We follow the inclusive rule, The answer to the question is (A) that is

if y>=10 and y <=50

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.

The intervals used are:

(a , b) , All the numbers between a & b without including them.

[a, b] , All the numbers between a & b including them.

y lies in [10,50].

And since it means that it includes 10 and 50 and all the numbers between them.

The final answer is (A) that is if y>1=10 and y <=50.

To learn more about number intervals visit:

https://brainly.com/question/13708942

#SPJ4

Both the coordinate points are plotted on the graph. The cartesian graph is attached with the answer.

Given are the two coordinates to be plotted on a Cartesian plan -

(5, 4) , (3, 4).

The two given coordinate points are (5, 4) , (3, 4).

Refer to the graph attached. It shows both the points plotted.

Therefore, both the coordinate points are plotted on the cartesian graph.

To solve more questions on coordinates plotting and graphs, visit the link below -

https://brainly.com/question/24952385

#SPJ1

Triangle ΔPMO and  ΔNMO are congruent, therefore  ΔPMO ≅ ΔNMO.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

MO bisects ∠PMN and OM bisects ∠PON.

1.

MO bisects ∠PMN,

Reason : It is given condition.

2.

∠PMO ≅ ∠NMO

Reason : The image is symmetrical, therefore ∠PMO ≅ ∠NMO.

3.

MO = MO

Reason : In triangle, PMO and NMO the side MO is common,

Therefore, MO = MO

4.

OM bisects ∠PON.

Reason : It is given condition.

5.

∠POM =  ∠NOM

Reason : The image is symmetrical, therefore  ∠POM =  ∠NOM.

6.

ΔPMO ≅ ΔNMO

Reason : The figure is symmetric, and triangle ΔPMO and  ΔNMO are congurent.

Therefore, ΔPMO ≅ ΔNMO.

To know more about Triangle on:

https://brainly.com/question/2773823

#SPJ1

Answer:

[0, 799.95]

Step-by-step explanation:

First, we need to isolate the variable by subtracting 9 from both sides of the inequality:

20t + 9 - 9 ≤ 16,000 - 9

This gives us:

20t ≤ 16,000 - 9

Next, we can divide both sides of the inequality by 20 to isolate the variable:

20t / 20 ≤ (16,000 - 9) / 20

This simplifies to:

t ≤ 799.95

Finally, we need to express the solution in interval notation. Since the value of t cannot be negative, the solution is:

[0, 799.95]

Therefore, the solution to the inequality in interval notation is [0, 799.95].

The area of the figure is 84.139 square ft

From the question, we have the following parameters that can be used in our computation:

Shapes = Rectangle and Semicircle

For the rectangle, we have

Length = 5 ft and Width = 14 feet

For the circle, we have

Diameter = 14 ft - 4 ft - 4 ft

Evaluate

Diameter = 6 feet

Start by calculating the radius of the semicircle

So, we have the following representation

radius = Diameter/2

This gives

radius = 6/2

Evaluate

radius = 3

The area of the shape is then calculated as

Area = Length * WIdth + πr²/2

So, we have

Area = 5 * 14 + 3.142 * 3²/2

Evaluate

Area = 84.139

Hence, the area is 84.139 square ft

Read more about area at

brainly.com/question/25292087

#SPJ1

Answer:

angle b

Step-by-step explanation:

let's assume the triangle is a right angle triangle . either angle a or c can be equal to 60 degree

The simplification of the expressions in the question using the rules of indices are as follows;

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2. (3⁻⁴ + 5⁻³)⁻¹ = [tex]49\frac{31}{206}[/tex]

3. (3⁻⁴ + 5⁻³)⁻² = [tex]2415\frac{32685}{42436}[/tex]

4.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}[/tex] = [tex]\dfrac{c^5\cdot e^8}{2\cdot d^5}[/tex]

5.)  [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}[/tex]

An index or indices is the power by which a number or variable or expression raised.

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰

6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1

6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2

Therefore;

6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2.) (3⁻⁴ + 5⁻³)⁻¹

(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))

1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))

1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209

10125/206 = 49 + 31/206

(3⁻⁴ + 5⁻³)⁻¹ = [tex]49 \frac{31}{206}[/tex]

3.) (3⁻⁴ + 5⁻³)⁻²

(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)

1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)

1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)

1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)

1/((206/10125)²) = (10125)²/(206)² = 102515625/42436

102515625/42436 = 2415 32685/42436

(3⁻⁴ + 5⁻³)⁻² = [tex]2415\frac{32685}{42436}[/tex]

4.)  [tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}[/tex]

[tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }[/tex]

[tex]\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }[/tex]

[tex]\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }[/tex]

[tex]\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}[/tex]

[tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}[/tex]

5.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}[/tex]

[tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }[/tex]

[tex]\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }[/tex]

[tex]\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }[/tex]

[tex]\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }[/tex]

[tex]\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}[/tex]

[tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}[/tex]

6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = [tex]3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)[/tex]

[tex]3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2[/tex]

3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴

Therefore;

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴

Learn more about the rules of indices here:

https://brainly.com/question/27150968

#SPJ1

Answer:

y = 10.5x - 8.25

Step-by-step explanation:

m = (44.25 - 12.75)/(5 - 2) = 10.5

y = mx + b

y = 10.5x + b

12.75 = 10.5 × 2 + b

b = -8.25

y = 10.5x - 8.25

To solve this problem, we need to use the formula for the area of a rectangle, which is length times width. We can set up the formula as follows:

Area = length * width

Since we know that the width is 7 greater than ⅔ the length, we can represent the width as follows:

width = ⅔ * length + 7

We can substitute this expression for the width in the area formula to get the following:

Area = length * (⅔ * length + 7)

We are given that the area of the rectangle must be 172, so we can set up the following equation:

172 = length * (⅔ * length + 7)

To solve for the length of the rectangle, we can first distribute the length on the right-hand side of the equation, like this:

172 = length * ⅔ * length + 7 * length

We can then combine like terms on the right-hand side of the equation to get the following:

172 = ⅔ * length^2 + 7 * length

To solve for the length, we can use the quadratic formula, which is as follows:

length = (-b +/- sqrt(b^2 - 4ac)) / 2a

In this case, a = ⅔, b = 7, and c = -172. Plugging these values into the quadratic formula, we get the following:

length = (-7 +/- sqrt(49 - 4 * ⅔ * -172)) / 2 * ⅔

Simplifying this expression, we get the following:

length = (-7 +/- sqrt(49 + 576)) / ⅓

We can further simplify this expression by calculating the value of the square root, like this:

length = (-7 +/- sqrt(625)) / ⅓

Simplifying again, we get the following:

length = (-7 +/- 25) / ⅓

To find the final value of the length, we need to calculate the two possible values of the square root, which are 25 and -25. Plugging these values into the equation for the length, we get the following:

length = (-7 + 25) / ⅓ = 18 / ⅓ = 6

length = (-7 - 25) / ⅓ = -32 / ⅓ = -10

Since the length of a rectangle must be positive, we can discard the negative value and only consider the value of 6. This means that the length of the rectangle is 6, and the width is ⅔ * 6 + 7 = 11. Therefore, the dimensions of the rectangle are 6 by 11.

Answer:

19.048%

Step-by-step explanation:

The formula for the increase in cost will be :

[(New cost - Original Cost)÷Original Cost] × 100

So let's substitute values in from the question :

[(50-42)÷42] × 100

[8÷42] × 100

0.19048 × 100

19.048%

Hope this helped and have a good day

Answer: 1.06

Message: If this was helpful, let me know by giving me a thanks! :)

Answer:

To solve this inequality, we need to isolate the x-variable on one side of the equation. To do this, we can add 38 to both sides of the equation to get the following:

-200 - 12x - 38 = 38

-200 - 12x = 76

Next, we can divide both sides of the equation by -12 to get the following:

-200 - 12x = 76

x = -17

Finally, we can use the value of x to determine how long it will take the explorer to reach an elevation deeper than -200 feet. Since the explorer moves at a rate of -12 feet per minute, it will take her 17 minutes to reach this depth.

we are allowed to change the vertical axis on a line chart.

suppose we have a large range of value needed to plot along the vertical and horizontal axis, but the current line chart cannot meet this demand. in such cases, we can customize the scales to provide more vertical and horizontal spaces.

dramatic slopes are the steep slopes of a straight line calculated by vertical and horizontal coordinate of two points laying on it. By changing the vertical axis as well as the horizontal axis we can plot a graph of a straight line more properly and finally more dramatic slope is visible there.

hence, we can change the scale values on a line chart to meet the requirement of the plot.

to learn more about line chart visit the link:

https://brainly.com/question/29833410

Answer:

[tex]\boxed{\bf{\underline{ y\le -\cfrac{3}{2}x-2}}}[/tex]

Step-by-step explanation:

From the given graph,

[tex]\bf y-intercept :\boxed{\tt -2}[/tex]

[tex]\bf Slope:\tt \cfrac{\Delta y}{\Delta x} =\cfrac{-3}{2} =\boxed{-\cfrac{3}{2} }[/tex]

Notice that graph is shaded below (not above), so y is less than the other side of the inequality. the graph elso has a solid line (not dashed), so we are dealing with an "or equal to" inequality.

Therefore, we should use the less than or equal to symbol.

[tex]\boxed{\bf{ y\le -\cfrac{3}{2}x-2}}[/tex]

_____________________

Hope this helps!

Have a great day!

Answer:

no

Step-by-step explanation:

If the triangles are similar, then the ratios of the lengths of corresponding sides must be equal.

3/4 must equal 5/6 which must equal 6/7

3/4 = 0.75

5/6 = 0.8333...

6/7 = 0.857142...

None of the ratios are equal, so the triangles are not similar.

The value of the given equation 3 2/3x = 2 2/5 is 36/55.

A mixed number is one that combines a whole number and a legal fraction. A number that contains both an integer (whole number) and a correct fraction is known as a mixed number or mixed fraction.

Pretzels, peanuts, Cheerios, and of course, rice and corn Chex are all included in this mix, which is why it is called a mix. Mixed numbers are those that contain both an integer and a fraction.

A mixed fraction is a fraction that is represented by both its quotient and remainder. For instance, 2 1/3 is a mixed fraction, where 2 is the quotient and 1 is the remainder. Therefore, a mixed fraction is a combination of a whole number and a proper fraction.

3 2/3x= 2 2/5

11/3 x=12/5

55x=36

x=36/55

Therefore, the value of the given equation 3 2/3x = 2 2/5 is 36/55.

To know more about mixed number, visit:

https://brainly.com/question/24137171

#SPJ1

Answer:

The anwser is 1.769

Step-by-step explanation:

I did this on a calculator