Write a polynomial if least degree with roots 9 and -6

Mathematics

1 answer:

klio [65]3 years ago

8 0

Answer:

x² -3x - 54

Step-by-step explanation:

given roots of a polynomial are 9 and -6

this means that (x-9) and (x+6) are factors of the polynomial.

To get the polynomial with the least degree, simply multiply the two factors to obtain a quadratic expression (degree 2)

(x-9) (x+6)

= x² + 6x -9x -54

= x² -3x - 54

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Look at the pic below and please help.

marshall27 [118]

Answer:

1) Equation's:

y = 500 + 15x

y = 350 + 18x

2) Number of guest and the charge:

Cost is same for both at 50 meals. The cost is $1250.

Part 1

Turn sentences into equation's (Let 'y' be total cost and x per meal) :

(i) charges $500 and $15 per meal

y = 500 + 15x

(ii) charges $350 and $18 per meal

y = 350 + 18x

Part 2

y = y

500 + 15x = 350 + 18x

18x - 15x = 500 - 350

3x = 150

x = 150/3

x = 50

Charge at guest's 50 meal:

y = 500 + 15(50)

y = $1250

Point : (50, 1250)

3 0

3 years ago

Doomtown is 300 miles due west of Sagebrush and Joshua is due west of Doomtown. At 9 a.m. Mr. Archer leaves Sagebrush for Joshua

e-lub [12.9K]

Refer to the diagram shown below.

Let the distance that Sassoon travels is d miles.
Let his average speed be x mph.
The time of travel is from 1 p.m. to 4 p.m., which is 3 hours.
Therefore
3x = d (1)

The distance that Archer travels is (d + 300) miles.
The time of travel is from 9 a.m. to 4 p.m., which is 7 hours.
The average traveling speed is (x + 20) mph, therefore
7(x + 20) = d + 300
That is,
7x + 140 = d + 300
7x = d + 160 (2)

Subtract (1) from (2).
7x - 3x = d + 160 - d
4x = 160
x = 40 mph (Sassoon's average speed)
x+20 = 60 mph (Archer's average speed)
From (1), obtain d = 120 mi

Answer:
Archer's speed is 60 mph.
Sassoon's speed is 40 mph.