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3 years ago

Expand completely using the Binomial Theorem (3y - x)^4

Mathematics

1 answer:

AleksAgata [21]3 years ago

4 0

Answer:

In standard form it is x^4 - 12x^3y + 54x^2y^2 - 108x y^3 + 81y^4.

Step-by-step explanation:

(3y)^4 + 4C1(3y)^3(-x) + 4C2(3y)^2(-x)^2 + 4C3(3y)(-x)^3 + (-x)^4

= 81y^4 - 108y^3x + 54y^2x^2 - 12yx^3 + x^4

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The graph represents this system of equations:

Kipish [7]

Answer:

(2.5, - 2)

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

(2.5, - 2 ) ← point of intersection

3 0

3 years ago

Read 2 more answers

The baker broke each of the cookies in half. She counted 6

densk [106]

Answer:

Step-by-step explanation:

6/2=3

six halves of cookies put the halves into pairs and you get 3

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3 years ago

Determine the value of x to the nearest thousandth in the equation 8(2)^x+3=48

solong [7]

You probably mean either

$8\cdot2^x + 3 = 48$

$8\cdot2^{x+3} = 48$

Write 8 = 2³, so that in the first interpretation,

$8\cdot2^x = 2^3 \cdot 2^x = 2^{x + 3}$

and in the second,

$8\cdot2^{x+3} = 2^3 \cdot 2^{x+3} = 2^{x + 6}$

Then in the first interpretation, we have

$2^{x + 3} + 3 = 48 \implies 2^{x + 3} = 45 \implies x + 3 = \log_2(45) \implies x = \log_2(45) - 3 \approx \boxed{2.492}$

Otherwise, the second interpretation gives

$2^{x + 6} = 48 \implies x + 6 = \log_2(48) \implies x = \log_2(48) - 6 \approx -0.415$

8 0

3 years ago

What is the slope of a line y=7.8x+62

dexar [7]

Answer:

m = 7.8

Step-by-step explanation:

Its the slope. Its the number next to the x.

3 0

3 years ago

Micah is writing a function that models the height a dolphin reaches when it propels itself from underwater to the surface, leap

stepladder [879]

Answer:

The dolphin will be above the surface of the water for 2 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

The height of the dolphin after t seconds is given by:

$h(t) = -16t^2 + 96t - 128$

According to Micha's model, how long will the dolphin be above the surface of the water?

It stays above the surface of the water between the first and the second root. Initially, it is below water, when the first time for which $h(t) = 0$ it crosses the surface upwards, and then the second time for which $h(t) = 0$ it crosses the surface downwards.