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3 years ago

15/23 Marks

Mathematics

1 answer:

olganol [36]3 years ago

3 0

Answer: a) 6, 0, 10 b) yellow/orange line

Step-by-step explanation:

a) Plug the x in the y functions, y = 2x² + x

when x = -2, y = 2(-2)² + (-2) = 8 - 2 = 6

when x = 0, y = 2(0)² + (0) = 0 + 0 = 0

when x = 2, y = 2(2)² + (2) = 8 + 2 = 10

b) By looking the table, the equation has a point (0,0), only blue and yellow/orange line has the passed the point (0,0), so we delete the red line option.

And we choose a point (1,3), then only yellow/orange line has passed the point (1,3). So the yellow/orange line fits the equation.

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What’s the first step in multiplying a monomial by any polynomial

suter [353]

Answer:

distribute the monomial into the polynomial and be careful of sign errors

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and t

WINSTONCH [101]

Answer:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

$\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}$

Seperate the differential equation and solve for the constant C.

$\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}$

You have 100 rodents when:

$100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months$

You have 1000 rodents when:

$1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months$

7 0

2 years ago

Ron needed to buy a new jacket for his upcoming ski trip. The ticket price of the jacket was $199.00. After the sales tax was ad

Levart [38]

Answer: 5%

Step-by-step explanation:

Given that:

Ticket price of jacket = $199

Final price after addition of sales tax = $208.95

Percentage sales tax on the jacket =?

Final price after addition of sales tax = price of jacket + amount of sales tax paid

208.95 = 199 + amount of sales tax paid

amount of sales tax paid = 208.95 - 199

amount of sales tax paid = $9.95

Let Percentage of sales tax = x

(x / 100) * 199 = 9.95

199x / 100 = 9.95

199x = 995

x = 5

Hence percent sales tax paid = 5%

8 0

3 years ago

Can someone help me please? Am I right or no?

Juliette [100K]

The figure consists of three objects, a rectangle, a trapezoid, a triangle

Find the area of the rectangle
The rectangle is 16 in long and 9 in wide
a₁ = l × w
a₁ = 16 × 9
a₁ = 144 in²

Find the area of the trapezoid
The base of trapezoid is 31 in and 16 in, and the height is 35 - 20 = 15 in.
a₂ = 1/2 × (a + b) × h
a₂ = 1/2 × (31 + 16) × 15
a₂ = 1/2 × 47 × 15
a₂ = 352.5 in²

Find the area of the triangle
The base of the triangle is 31 in, the height is 20 in
a₃ = 1/2 × b × h
a₃ = 1/2 × 31 × 20
a₃ = 310 in²

Add the area together
a = a₁ + a₂ + a₃
a = 144 + 352.5 + 310
a = 806.5

The answer is 806.5 in²

4 0

2 years ago

Simplify (x^-5) (x^2)*

Pani-rosa [81]

Answer:

1/x^3

Step-by-step explanation:

foil method

6 0

3 years ago