Simplify each expression. Select the correct answer from the drop-down menu.

−6(3i)(−2i) =

2(3 − i)(−2 + 4i) =

"4√7" means four times the square root of 7, approximately equal to 10.582, an irrational number with decimal expansion.

The expression "4√7" represents the square root of 7, multiplied by 4. Let's break it down step by step:

1. Square Root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Similarly, the square root of 25 is 5 because 5 × 5 = 25.

2. √7: This symbol (√), called the radical symbol, represents the square root. So, √7 represents the square root of 7, which is an irrational number, meaning it cannot be expressed as a simple fraction and has decimal places that go on indefinitely without repeating.

3. 4√7: This means you're taking the square root of 7 and then multiplying it by 4. So, if you calculate it, it's like doing 4 times the square root of 7.

To give a numerical example, if we want to find the value of 4√7:

  4 × √7 ≈ 4 × 2.6457513110645905905016157536393... (approximately)

Thus, 4√7 is approximately equal to 10.582, depending on how many decimal places you round to.

In summary, "4√7" represents four times the square root of 7, which is an irrational number, approximately equal to 10.582.

[tex]\text{Consider the sum of the finite arithmatic series}\\ \\ 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)\\ \\ \text{We know that the sum of the finite arithmatic series }\\ \\ a_1,a_2, a_3, ..., a_n \text{ is given by the formula}\\ \\ S_n=\frac{n}{2}\left ( a_1+a_n \right )\\ \\ \text{here in the given series, we can see that }a_1=7.6, \ a_n=-1.5 \text{ and}\\ \text{the number of terms is, }n=8. \text{ so using above formula, we get}[/tex]

[tex]S_8=\frac{8}{2}\left ( 7.6+(-1.5) \right )\\ \\ =4\left ( 7.6-1.5 \right )\\ \\ =4\left ( 6.1 \right )\\ \\ =24.4[/tex]

Hence the sum of the finite Arithmetic series is: 24.4

The round off to nearest half is 1/2.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

The fraction = 5/9.

Now, rounded to the nearest half is 1/2

we know 9 halved value is 4.5 which is much closer to 5.

So, we can write it as 5/10 = 1/2.

Learn more about Round off here:

https://brainly.com/question/13391706

#SPJ2

The statement that justifies how the area of a sector of a circle is derived is:

This refers to the quantity that expresses the extent of a region on the plane such as on a curved surface.

Furthermore, the area of sector of a circle is talking about the amount of space enclosed within the boundary of the sector.

Generally, it is explained in step that we first calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply ​the area of the circle​ by this fraction.

Therefore, the Option B is correct.

Read more about sector of a circle

brainly.com/question/22258287

#SPJ6

Answer:

9 or (5,4)

Step-by-step explanation:

Just subtract it on each side :)

area of triangle is = 1/2 * base * altitude

1- each side is made 8 times

so the net change in area is 64 times

The area of A'B'C' is 64 times the area of ABC

2- each side is made 4 times

so the net change in area is 16 times

The area of D'E'F' is 16 times the area of DEF

3- each side is made 3 times

so the net change in area is 9 times

The area of A'B'C' is 9 times the area of ABC

Answer:

  a. The cost of 10 tickets

Step-by-step explanation:

We don't know what the expression is supposed represent, but the answer choices suggest that ...

  c = 5t +3

represents the cost of t tickets. Then, when t=10, c = 53 will represent the cost of 10 tickets.

Answer:

Triangle with interior angles measuring 36° and 32°

Triangle with interior angles measuring 32° and 112°

Step-by-step explanation:

we know that

If two triangles are similar, then its corresponding angles are congruent

If two triangles have two equal internal angles, then the triangles are similar by AA Similarity Postulate

step 1

Calculate the measure of the third internal angle

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

Let

x------> the measure of the third internal angle

[tex]x\°+36\°+112\°=180\°\\ \\x=180\°-148\°\\ \\x=32\°[/tex]

step 2

Verify each triangle

case A) Triangle with interior angles measuring 36° and 32°

Is true -----> by AA Similarity Postulate

case B) Triangle with interior angles measuring 36° and 148°

Is false -----> Is not a triangle because the sum of its internal angles is greater than 180 degrees

case C) Triangle with interior angles measuring 32° and 112°

Is true -----> by AA Similarity Postulate

case D) Triangle with interior angles measuring 112° and 148°

Is false -----> Is not a triangle because the sum of its internal angles is greater than 180 degrees

Answer:

agree

Step-by-step explanation:

Answer:

Steve has 19 pencils

Step-by-step explanation:

4 times of 19 is 76

So, Martha has 76 and Steve has 19

76+19=95

hope this helps!

Answer:

C. (11 unit cubes and 2 smaller cubes of volume 1/8 cubic inch each.)

Step-by-step explanation:

90 cubes * 1/8 inch = 11 1/8 inch.

Final answer:

Solomon has 2/3 of the book left to read. To finish it over 5 nights, he needs to read 2/15 of the book each night.

Explanation:

Solomon has read 1/3 of his book already. To finish the remaining 2/3 of the book in 5 nights, we need to calculate the fraction of the book he should read each night. Since he has to evenly distribute the remaining portion over 5 nights, we will divide 2/3 by 5.

Here's the calculation step-by-step:

First, represent the remaining part of the book as a fraction, which is 2/3.

To divide this fraction by 5, we multiply the denominator by 5. This gives us (2/3) × (1/5).

Multiplying these fractions, we get (2 × 1) / (3 × 5), which simplifies to 2/15.

Thus, Solomon reads 2/15 of the book each night for the next 5 nights.

let x = amount invested at 3%

so, (2600 - x) is invested at 7%

.07 *(2600 - x) + .03 *(x) = 138

182 - .07x + .03x = 138

-.07x + .03x = 138 - 182

-.04x = -44

-.04x / -.04 = -44 / -.04

x = 1,100

so amount invested at 7% is (2600 - 1100) or 1500

consequently amount invested at 3% is 1100

$1,100 invested at 3%

$1,500 invested at 7%

The money invested in both of the funds are $800 and $1800 respectively.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Suppose the money invested in one of the funds be x.

Then, in the other fund the investment is (2600 - x).

Now, the equation for the total profit from both investments can be obtained as,

7% × x + 3% × (2600 - x) = 150

⇒ 7/100 × x + 3/100 × (2600 - x) = 150

⇒ 4x/100 = 150 - 78

⇒ x = 1800

Thus, the investment in the other fund is 2600 - 800 = $800.

Hence, the investment for both the funds are $800 and $1800 respectively.

To know more about percentage click on,

brainly.com/question/29306119

#SPJ2

Answer:

Step-by-step explanation: so the problem is asking for the missing dimensions of the rectangle. The smaller rectangle has a length of 12 inches, a width of 8 inches, and an area of 96 inches. To clarify, 8x12 is 96 so when looking at the bigger rectangle, it says that it was scaled by a factor of 4.

The Answer-

Length:48

Width:32

Area:1,536