All categories

3 years ago

30 POINTS!!! Please help

Mathematics

2 answers:

puteri [66]3 years ago

8 0

Answer:

f(x) = x³ + 6x² + 13x + 10

Step-by-step explanation:

Note that complex roots occur in conjugate pairs, thus

x = - 2 + i is a root then x = - 2 - i is also a root

The roots are x = - 2, x = - 2 + i, x = - 2 - i, then the factors are

(x + 2), (x - (- 2 + i)) , (x - (- 2 - i)), that is

(x + 2), (x + 2 - i)(x + 2 + i)

The polynomial is the product of the factors

f(x) = (x + 2)(x + 2 - i)(x + 2 + i) ← expanding

= (x + 2)(x² + 2x + xi + 2x + 4 + 2i - xi - 2i - i²) → i² = - 1

= (x + 2)(x² + 4x + 4 + 1)

= (x + 2)(x² + 4x + 5) ← distribute

= x³ + 4x² + 5x + 2x² + 8x + 10 ← collect like terms

= x³ + 6x² + 13x + 10

WITCHER [35]3 years ago

6 0

Answer:

f(x) = x³ + 6x² + 13x + 10

Step-by-step explanation:

You might be interested in

A regular hexagon is shown below. Find the value of X

Varvara68 [4.7K]

Answer:

$x=9$

Step-by-step explanation:

The expression is for the interior angle of the hexagon; one interior angle is equal to $(11x+21)^o$ .

Since an interior angle of a hexagon measures 120°, we have the equality

$(11x+21)=120$ .

Now it is just a matter of solving for $x:$

$11x=120-21\\\\11x=99\\\\x=\frac{99}{11} \\\\\boxed{x=9}$

3 0

3 years ago

A shipping container is in the shape of a right rectangular prism with a length of 2 feet, a width of 3 feet, and a height of 5

7nadin3 [17]

Answer:

13 pounds

Step-by-step explanation:

volume = base area × height

area of a rectangular triangle = a×b/2

Vp = (2×3/2) × 5 = 3×5 = 15 ft³

weight of contents = 15 × 0.84 = 12.6 pounds = 13 pounds rounded.

4 0

3 years ago

If you rent a car for one day and drive it for 100 miles the cost is $40:00 if you drive it 220 miles the cost is 46.00 use the

gladu [14]

If you divide $6.00 by 120, you come up with 5 cents per mile. So the slope of the line (m) would be 0.05, or 1/20.

We also know that it costs $40.00 at 100 miles, so when x=100, y=40. If you multiply 100 by 0.05 you get 5, which means the rate goes up $5.00 for every 100 miles. So if you take your original y=40 ($40.00 for 100 miles) and subtract 5, that means y=35 for 0 miles, and that gives you your zero-intercept (b).

So your equation would be y = 1/20x + 35

Now, if x = 300 miles, then

y= 1/20*300 + 35

y = 15 + 35

y = 50, therefore it would cost $50.00 to drive the rental car 300 miles.

8 0

3 years ago

Read 2 more answers

1-3. Find the center point, the radius and the diameter for the following equation: x² + y2 = 16

kogti [31]

Answer:

Center: (0, 0)

Radius: 4

Step-by-step explanation:

Circle Standard Equation: (x - h)² + (y - k)² = r²

(h, k) is center

r is radius

We see that our <em>h</em> and our <em>k</em> are both 0.

∴ Our center is (0, 0), origin.

We see that our r² = 16

√r² = √16

∴ Our radius is equal to 4

3 0

3 years ago

Which statement best represents the distance on a number line between -14 and -5

antiseptic1488 [7]

-5 - (-14)
-5 + 14 (due to same, change, change rule)
9
The distance is 9 units.

6 0

4 years ago