Does the term investment mean the interest of something or the principle?

[tex] \text{Given a,b,c and d are in GP}[/tex]

[tex] \therefore \frac{b}{a} = \frac{ c}{b} = \frac{d}{c} = r \\ \\ \implies b = ar ,c = br,d = cr \implies \: b = ar,c = (ar)r,d = (br)r \\ \\ \implies b = ar,c = a {r}^{2} ,d = {br}^{2} \implies b = ar,c = {ar}^{2} ,d = (ar)r {}^{2} = a {r}^{3} ...(i)[/tex]

[tex] \text{Now, Consider}[/tex]

[tex]( {a}^{2} + {b}^{2} + {c}^{2} )( {b}^{2} + {c}^{2} + {d}^{2} ) = ( {a}^{2} + {a}^{2} {r}^{2} + ( {a}^{2} {r}^{4} )( {a}^{2} {r}^{2} + {a}^{2} r {}^{2} + {a}^{2} {r}^{4} + {a}^{2} {r}^{6} )[/tex]

[tex] = {a}^{2} (1 + {r}^{2} + {r}^{4} ) {a}^{2} {r}^{2} (1 + {r}^{2} + {r}^{4} ) = a {}^{4} {r}^{2} (1 + {r}^{2} + {r}^{4} ) {}^{2} = [a {}^{2}r(1 + {r}^{2} + {r}^{4}) ] {}^{2} [/tex]

[tex] = ( {a}^{2} r + {a}^{2} {r}^{3} + {a}^{2} r {}^{5} ) {}^{2} = (a. \: ar + ar. \: a {r}^{2} + a {r}^{2} .a {r}^{3} ) {}^{2} [/tex]

[tex] = (ab + bc + cd) {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \text{[From Equation (i)]}[/tex]

Hope This Helps!!! :)

The given polynomial can be rewritten as factors of the common ratio of

the geometric progression.

Response:

If a, b, c, d are in GP, (a² + b² + c²) × (b² + c² + d²) = [tex]\underline{(a\cdot b + b \cdot c + c\cdot d)^2}[/tex]

The assumed parameters are;

a, b, c, and d for a geometric sequence

Therefore;

[tex]\mathbf{\dfrac{b}{a}} = \dfrac{c}{b} = \dfrac{d}{c} = r[/tex]

Which gives;

b = a·r

c = b·r

d = c·r

Therefore;

c = b·r = a·r²

d = c·r = a·r³

(a² + b² + c²) × (b² + c² + d²) = (a² + (a·r)² + (a·r²)²) × ((a·r)² + (a·r²)² + (a·r³)²)

(a² + a²·r² + a²·r⁴) × ((a²·r²) + (a²·r⁴) + a²·r⁶) = a⁴·r²·(r⁸ + 2·r⁶ + 3·r⁴ + 2·r² + 1)

Which gives;

a⁴·r²·(r⁸ + 2·r⁶ + 3·r⁴ + 2·r² + 1) = a²·r·(r⁴ + r² + 1) × a²·r·(r⁴ + r² + 1)

a²·r·(r⁴ + r² + 1) × a²·r·(r⁴ + r² + 1) = (a²·r·(r⁴ + r² + 1))²

a²·r·(r⁴ + r² + 1) = a²·r⁵ + a²·r³ + a²·r

a²·r = a·b

a²·r³ = b·c

a²·r⁵ = c·d

Therefore;

a²·r⁵ + a²·r³ + a²·r = a·b + b·c + c·d

(a² + b² + c²) × (b² + c² + d²) = (a²·r·(r⁴ + r² + 1))² = [tex]\underline{(a\cdot b + b \cdot c + c\cdot d)^2}[/tex]

Learn more about geometric progression (GP.) here:

https://brainly.com/question/140530

Product of polynomials can be done by distribution of multiplication over addition. The product of  [tex](2x - 3)(2x^2 + 7x - 1)[/tex] is [tex]4x^3 + 8x^2 -23x + 3[/tex]

Suppose a, b and c are three numbers. Then we have:

[tex]a(b + c) = a\times b + a\times c[/tex]

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

The product result of the given expression is

[tex](2x - 3)(2x^2 + 7x - 1) = 2x(2x^2 + 7x - 1) -3(2x^2 + 7x - 1) \\(2x - 3)(2x^2 + 7x - 1) = 4x^{1+2} + 14x^2 -2x - 6x^2 - 21x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + (14 -6)x^2 + (-2 -21)x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + 8x^2 -23x + 3[/tex]

It is because when bases are same and there is multiplication, then powers add up, so we have: [tex]a^b \times a^c = a^{b+c}[/tex]

Also, we've

[tex](-ve \times (+ve) = -ve\\(-ve) \times (-ve) = +ve\\(+ve) \times (+ve) = +ve\\(+ve) \times (-ve) = -ve[/tex]

where -ve, +ve are sign of operands and result.

That's why [tex]2 \times -1 = -2[/tex]

Thus,

The product of   [tex](2x - 3)(2x^2 + 7x - 1)[/tex]  is [tex]4x^3 + 8x^2 -23x + 3[/tex]

Learn more about product of polynomials here:

https://brainly.com/question/9106484

Answer: B

Step-by-step explanation:

Answer:

B) 9/3 * 2/3

Step-by-step explanation:

B is correct since 9/3 * 2/3 = 18/9 = 2

If you check the other answer choices, they will not be between 2 and 3

Answer:

y= 2 x - 7/3

Step-by-step explanation:

Answer:

S4, E17 (Judgement)

Step-by-step explanation:

Hope that helps!

Answer:

  15

Step-by-step explanation:

Let 'a' represent Artaud's age. He notices the relationship ...

  -a +39 = 24

If we add a-24 to both sides, we get ...

  15 = a

Artaud is 15 years old.

Answer: 15 years old

Step-by-step explanation:

Let x be Artaud's age. Let the opposite of his age be -x

-x + 39 = 24

-x = 24-39

-x = -15 (multiply both sides by -1)

x = 15 years old

Answer:

it is 5 I belive

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

You move the decimal point twice to the right because 100 has two zeros. But if it was 7.20÷100 it would be 0.072 because you move the point to the left.

Answer:

  9

Step-by-step explanation:

Ron can deliver 300t pounds of mulch in t trips. The number of trips needed to deliver at least 2700 pounds is ...

  300t ≥ 2700

  t ≥ 9 . . . . . . . . divide by 300

Ron needs to make at least 9 trips to deliver at least 2700 pounds of mulch.

The amount left by Diana is percent part of total food cost. The 15% tip of $44 total cost given by Diana is : Option D: $6.60

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Since the total food cost was $44 and the tip was 15% of the total cost, thus,

[tex]\text{Tip amount} = \dfrac{44}{100} \times 15 = 6.6 \text{\:dollars}[/tex]

Thus,

The 15% tip of $44 total cost given by Diana is : Option D: $6.60

Learn more about percentage here:

https://brainly.com/question/11549320

Answer:

So for number 1 and 2

Step-by-step explanation:

Perimeter is = 2(L+W)

L=2w as it said on the problem above.

60=2 (2w+w)

60= 2 (3w)

60 = 6w

w= 10 , L=20 P=60

Area of rectangle = L x W

20 x 10 = 200

2)You would have twice as many hot dogs and 24 is two times 12 and if you add them you get 36.

Answer:

2^18

Step-by-step explanation:

Every true or false question can be either answered true / false (2 options)
So, there are 2.2.2.2.2... (2^18) ways to answer if a student answers every question.

Answer:

35v

Step-by-step explanation:

5(6v)+5v

[tex]5 \times 6v + 5v \\ 30v + 5 \\ combine \: the \: terms \\ = 35v[/tex]

Answer:

35v

Step-by-step explanation:

5 times 6v = 30v, then you add 5v which gives you 35v. Hope that helps :)

Answer:

I believe the answer is B. 15/5 = n/12

Step-by-step explanation:

Once again same method as I've explained before. However, this one tricked me a little bit and still is because of the appearance of the smaller triangle. However, If I don't focus on that I believe this answer is correct. This is because in order to find the missing side we need to find the factor of which the triangle was expanded. So we must divide a given side of the bigger triangle by the same similar side of the little triangle, like 15/5. Then we must divide n by its similar side which the appearance made me think 13 which is not an option so I believe it is 12 and it was just trying to throw me off. So n/12. Therefore that is why I believe B is correct.

Answer:

24°

Step-by-step explanation:

Let x = one complementary angle

Let y = the other complementary angle

As the sum of two complementary angles is 90°:

x + y = 90

If one angle is 18° more than two times the other angle:

y = 18 + 2x

Rewrite x + y = 90 to make x the subject:

x = 90 - y

Now substitute x = 90 - y into y = 18 + 2x and solve for y:

y = 18 + 2(90 - y)

⇒ y = 18 + 180 - 2y

⇒ 3y = 198

⇒ y = 198 ÷ 3 = 66

Now substitute found value of y = 66 into x + y = 90 and solve for x:

x + 66 = 90

⇒ x = 90 - 66 = 24

Therefore, the larger angle = 66° and the smaller angle = 24°

Answer: 20

Step-by-step explanation:

log 5x^3 - log x^2 = 2

log 5x = 2

5x = 100

x = 20

Answer:

x=20

Step-by-step explanation:

keep smiling

Rhombus can have harmonious diagonals provided that this is true we talk about the square unique instance of rhombus which additionally has four equivalent length sides and its diagonals are opposite and divide each other with respect to a square shape rhombus doesn't constantly need to be a square shape since it doesn't must have 4 right points

Answer:

-30.44

Step-by-step explanation:

50.54 - 20.10 = 30.44

well, we know the directrix is at y = 4 and the focus point is down below it at (-6 , -3), meaning is a downward opening vertical parabola, like the one you see in the picture below.

keeping in mind that the vertex is equidistant from the directrix and focus point by a distance "P", that puts this vertex at ( -6 , 1/2 ), and since the parabola is opening downwards, P is negative.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex][tex]\begin{cases} h=-6\\ k=\frac{1}{2}\\[1em] P=-\frac{7}{2} \end{cases}\implies 4\left( -\cfrac{7}{2} \right)\left(y-\cfrac{1}{2} \right)=[x-(-6)]^2 \\\\\\ -14\left(y-\cfrac{1}{2} \right)=(x+6)^2\implies y-\cfrac{1}{2}=-\cfrac{1}{14}(x+6)^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{14}(x+6)^2+\cfrac{1}{2}~\hfill[/tex]

Answer:

steps below

Step-by-step explanation:

volume of rock : 16 * 12 * 12 = 2304

height will take when it was threw into tank: 2304 / (32*24) = 3

Original water height + rock height: 12 + 3 = 15 cm

Answer:

2n³ - 3n² - 7n + 3

Step-by-step explanation:

Hi there! Don't worry, polynomials seem hard but you will get them with practice.

I am going to show you 2 methods of multiplying polynomials. These methods are universal, or they work with any polynomial multiplication problem:

This is perhaps the most common method. You distribute 1 value to another or multiply each and every single term.

Let's solve it!

Now, we add up like terms. Like terms should have the same coefficient and should be raised to the same power.

There you have it! This is how you solve with The distributive Property Method.

This is the next universal method, Area modeling.

Area models can be set up by the number of terms we have. In the first polynomial we have three terms:

Just for this method, keeping the positive signs helps.

For the binomial, we have two terms (hence, binomial)

We set up our are model like this, with the terms laid out as side lengths of a rectangle.  (Attachment "A")

Next, we find the area of each individual tile.  (Attachment "B")

Now, we add like terms. Something nice about area models is that most of the time, the like terms are matched up in a diagonal.  (Attachment "C")

We end up with the same answer as before.

-Chetan K

Answer:

36, 44, 52

Step-by-step explanation:

Answer:

$752.69 + 12.5%=$753+$50=$803+ 3.35%=803.0335=

answer: c. $818.

Step-by-step explanation:

Answer:

⬇️ i got 100% on the test

Answer:

(-4, 4)

(6, 2)

(0, -2)

(-∞, -4), (0, 6)

(-4, 0), (6, ∞)

Step-by-step explanation:

(-4, 4)

(6, 2)

(0, -2)

(-∞, -4), (0, 6)

(-4, 0), (6, ∞)

Answer:

There are a few ways to solve systems of equations.

If you are looking at a multiple choice question use the ordered pair to plug into the answer choices and whichever one balances out will be your answer. To assist you further I would need more information from the problem.

Step-by-step explanation:

hope it will help you have a great day bye and Mark brainlist if the answer is correct

[tex]kai6417[/tex]

#carry on learning

Answer:

2091.9

Step-by-step explanation:

multiply 4580 by 243 and then divide your answer by 532.

10k^3 , 6k^3

k^3 ( 10, 6 )

2k^3 (5, 3)

so 2k^3 is the greatest common factor of both the numbers .

Answer:

greatest common factor: 2k³

Step-by-step explanation:

given 10k³ and 6k³

for gcf just simply break them down:

10k³ = 2 * 5 * k * k * k

6k³ =  2 * 3 * k * k * k

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

Analyse both of them and find similarities:

the similarities are: 2 * k * k * k

so the greatest common factor is 2k³