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artcher [175]
2 years ago
11

Write a polynomial function of least degree with integral coefficients that has the given zeros.

Mathematics
1 answer:
densk [106]2 years ago
4 0
The zeroes are
0, -5, 3 + i (and its conjugate)

The factors are
x (x + 5) (x - (3 + i)) (x - (3 - i))
Expanding...
(x² + 5x)((x - 3) - i) ((x - 3) + i)
(x² + 5x)((x - 3)² - i²)
(x² + 5x)(x² - 6x + 9 - (-1))
(x² + 5x)(x² - 6x + 10)
x⁴ - 6x³ + 10x² + 5x³ - 30x² + 50x
x⁴ - x³ - 20x² + 50x
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Lucy spent a total of $6.60 on 5 apples and a package of grapes. If the package of grapes cost $2.35, how much did each apple co
erastova [34]

Answer:

<h2>0.85</h2>

Step-by-step explanation:

apple cost = total cost - grapes package cost

5 apples cost = 6.60 - 2.35

= 4.25

per apple cost = 4.25 ÷ 5

= 0.85

<h2>MARK ME AS BRAINLIST</h2><h3>PLZ FOLLOW ME</h3>

4 0
3 years ago
Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance fr
AfilCa [17]

The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

  • Distance is defined to be the magnitude or size of displacement between two positions.
  • Note that the distance between two positions is not the same as the distance traveled between them.
  • Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

Learn more about distance

brainly.com/question/15172156

#SPJ4

7 0
2 years ago
Which function will have a change in direction?
Ivahew [28]

Answer:

Quadratic

Step-by-step explanation:

A linear equation is just a line and an exponential function goes in the same direction

A quadratic us a parabola which has a turning point

3 0
3 years ago
Use the slope formula to find the slope of the line through the points (−3,−6) and (0,3).
liubo4ka [24]
Slope= y/x so first let’s find the difference in the y coordinates. -6 and 3. -6 + 9= 3
So far we have 9/x, now on to the x coordinates. -3 and 0, -3 + 3 = 0
9/3 is the slope
now simplify and the slope is 3
4 0
2 years ago
Please help me due tonight
Fittoniya [83]

Answer:

7 1/15

Step-by-step explanation:

3 2/5 + 3 4/6 = 7 1/15

4 0
2 years ago
Read 2 more answers
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