Which is the standard form of the equation 8n + 4 = -2n + 9 ? *

The sum of three consecutive terms in an arithmetic sequence is 27, and their product is 585. find the three terms.

sammy [17]

$\text{the three consecutive terms in an arithmetic sequence}\\a;\ a+d;\ a+2d\\\\\text{system of equals}\\\\ \left\{\begin{array}{ccc}a+a+d+a+2d=27\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}3a+3d=27&|:3\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}a+d=9&\to d=9-a\\a(a+d)(a+2d)=585\end{array}\right\\$
$\text{substitute to the second equation}\\\\a(a+9-a)(a+2(9-a))=585\\\\a(9)(a+18-2a)=585\\9a(18-a)=585\ \ \ |:9\\a(18-a)=65\\18a-a^2=65\ \ \ |\text{change the signs}\\a^2-18a=-65\\a^2-2a\cdot9=-65\ \ \ |+9^2\\\underbrace{a^2-2a\cdot9+9^2}_{(a-b)^2=a^2-2ab+b^2}=-65+9^2\\(a-9)^2=16\to a-9\pm\sqrt{16}\\a-9=-4\ \vee\ a-9=4\ \ \ |+9\\a=5\ \vee\ a=13\\\\d=9-5=4\ \vee\ d=9-13=-4$
$Answer:\ a=5;\ a+d=9; a+2d=13\ vee\ a=13;\ a+d=9;\ a+2d=5$

5 0

3 years ago

Three pizzas are shared equally among 12 people.what fraction of pizza will each person get

8_murik_8 [283]

Answer:

1/4

Step-by-step explanation:

3/12 =0.25

0.25 = 1/4

8 0

2 years ago

Read 2 more answers

What is the exact volume of the sphere?

sasho [114]

We know, Volume of a Sphere = 4/3 πr³
V = 4/3 * π * (12.3)³
V = 4/3 * π * 1860.71
V = <span>2481.156π cm³

In short, Your Answer would be Option A

Hope this helps!</span>

6 0

3 years ago

Read 2 more answers

The cost for Andrea to produce several units of a certain item is $336 plus $12 per unit. She sells this item for $28 per unit.

Morgarella [4.7K]

Profit will be achieved when the money earned is greater than the money spent so,
336 + (n*12) = n*28 any subsequent units sold would result in profit
336 = 28n - 12n
336 = 16n
=> n = 336/16 = 21
21 units must be sold to draw even any more would result in profit

3 0

3 years ago

Please help :) I have no clue & math isn’t my strong subject.

melisa1 [442]

Equation of a line that is perpendicular to given line is $y=\frac{-7}{4} x+\frac{7}{4}$ .