Explanation

Given that x + 1 is a factor of the polynomial x³ + ax² - x + 2, we know that (-1) is a root of the polynomial.

Let's plug in x = -1 into the polynomial:

(-1)³ + a(-1)² - (-1) + 2 = 0

-1 + a + 1 + 2 = 0

a + 2 = 0

Subtract 2 from both sides:

a = -2

Explanation

The given sequence is:

-31, -21, -11, -1, 9

Let's find the common difference (d):

d = (-21) - (-31) = 10

d = (-11) - (-21) = 10

d = (-1) - (-11) = 10

d = 9 - (-1) = 10

The sequence is an arithmetic progression (AP) with a common difference of 10.

The nth term of an AP is given by:

an = a + (n - 1)d

where a is the first term (-31), n is the term number (34), and d is the common difference (10).

a34 = -31 + (34 - 1) * 10

= -31 + 33 * 10

= -31 + 330

= 299

Explanation

Complementary angles are two angles whose sum is 90 degrees.

For example, 40° and 50° are complementary because 40° + 50° = 90°.

Explanation

Given equation:

0.5x + 1.1 = 2.3

Step-by-step:

Subtract 1.1 from both sides:

0.5x = 2.3 - 1.1 = 1.2

Divide both sides by 0.5:

x = 1.2 ÷ 0.5 = 2.4

Explanation

The tunic was a common garment worn by both men and women in ancient Rome.

It was a simple, knee-length piece of clothing, often belted at the waist.

Explanation

"With respect to" means concerning or regarding something.

It fits the context of linking the theory to its relevance to modern technology.

Explanation

"Pull himself together" means to regain emotional control after a stressful or difficult situation.

In this context, it refers to recovering from the grief of his mother's death.

Explanation

Golgi bodies (Golgi apparatus) modify, package, and transport proteins and lipids.

They are key in processing materials for secretion or use within the cell.

Explanation

Explanation

To find the cost of painting, we need to calculate the surface area of the cuboid:

Surface Area = 2(lw + lh + wh)

= 2(43.5 + 46 + 3.5*6)

= 2(14 + 24 + 21)

= 2 * 59

= 118 square meters

Now, cost of painting:

Cost = Surface Area * Rate

= 118 * 43.78

= 5166.04