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Natasha2012 [34]
3 years ago
8

Simplify. Your answer should contain only positive exponents.

Mathematics
1 answer:
saveliy_v [14]3 years ago
6 0

Answer:

Step-by-step explanation:

7.

2y² * 3x = 6xy²

8.

4v³ * vu²

= 4 \times 1 \times (v^{3+1})( u^2)

= 4v⁴u²

9.

4a³b² * 3a⁻⁴b⁻³

= 4 \times 3 \times a^{(3+(-4))} \times b ^{(2+(-3))}

= 12a⁻¹b⁻¹

= \dfrac{1}{12ab}

10.

x²y⁻⁴ * x³y²

= x^{2+3}y^{(-4)+2}

= x^{5}y^{-2}

= x^{5} \times \dfrac{1}{y^{2}}

11.

(x²)⁰ = 1

12.

(2x²)⁻⁴

= (2^{-4} \times x^2^{(-4)})

= \dfrac{1}{16x^8}

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Which of the following statement(s) describes the rate of change of f over the interval 1.5 ≤ x ≤ 3? Select all that apply.
Vesnalui [34]

2 Answers: Choice B and Choice C

The rate of change is 2.

The rate of change is constant.

======================================================

Explanation:

The first point on the left is when x = 1.5 and it has a height of y = 1

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So is the point (3,4) for similar reasoning.

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m = (y2-y1)/(x2-x1)

m = (4-1)/(3-1.5)

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Since the slope stays at 2 on the interval 1.5 ≤ x ≤ 3, this means we consider the slope to be constant. If the curve bended at all on this interval, then it wouldn't be a constant slope.

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2 years ago
Write and equation of the translated or rotated graph in general form (picture below)
WINSTONCH [101]

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

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∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

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∵ We have term xy that means we rotated the graph about

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∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

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∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

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* Lets substitute x' and y' in the 1st answer

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∴ (\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=

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- The purple is the equation xy = -8

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Hope it helps :)

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