P(x) = 2x^4 - x^3 + 2x^2 - k where k is an unknown integer. P(x) divided by (x+1) has a remainder of 2. What is the value of k?

7. All of the following are perfect square trinomials EXCEPT one. Which is it?

wolverine [178]

Answer:

All answers EXCEPT answer C. are perfect square trinomials.

Step-by-step explanation:

A perfect square trinomial is polynomial that satisfies the following condition:

$(a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}$ , $\forall\,a,b\in\mathbb{R}$

Let prove if each option observe this:

a) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$

1) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$ Given

2) $(2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 2\cdot x$ , $b = 3\cdot y$ Definition of perfect square trinomial/Result.

b) $9\cdot a^{2}-36\cdot a + 36$

1) $9\cdot a^{2}-36\cdot a + 36$ Given.

2) $(3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 3\cdot a$ , $b = 6$ Definition of perfect square trinomial/Result.

c) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$

1) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$ Given

2) $x\cdot y\cdot (1-4\cdot x+4\cdot x)$ Distributive property.

3) $x\cdot y \cdot 1$ Existence of the additive inverse/Modulative property.

4) $x\cdot y$ Modulative property/Result.

d) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$

1) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$ Given

2) $(a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})$ Definition of power/Distributive, associative and commutative properties.

3) $a = a\cdot b$ , $b = 2\cdot a^{2}$ Definition of perfect square trinomial.

All answers EXCEPT answer C. are perfect square trinomials.

8 0

3 years ago

When given the lengths of the diagonals of a kite, which statement best explains how to find the area?

ANEK [815]

Answer:

D

Step-by-step explanation:

The area (A) of a kite is calculated as

A = $\frac{1}{2}$ × d₁ × d₂ ( d₁ and d₂ are the diagonals )

This can be represented as

Multiply the diagonals then divide by 2 → D

4 0

2 years ago

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On a piece of paper, use a protractor to construct right triangle ABC with AB=3 in. , m∠A=90° , and m∠B=45° .

kirza4 [7]

Answer:

1. A. AC=3IN

2. D AND C

Step-by-step explanation:

7 0

3 years ago

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An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. given the formula h = d tan θ, wher

zloy xaker [14]

Height covered by the plane=h= 500 feet

Distance covered by the plane along the ground=d= 2 mile

Now, convert the mile into feet,

1 mile = 5280 feet

2 mile = 10560 feet

Now, use the formula

h= d tanθ

tanθ= h/d

tanθ= 500/10560

tanθ= 25/528

Take the tan⁻¹ on both side,

θ= tan⁻¹(25/528)

θ =2.71°

5 0

3 years ago

Consider the function f(x) = 5x + 7. Which statement MUST be true? A) f(1) ? f(3) = f(3) ? f(1) B) f(1) ? f(3) = f(5) ? f(3) C)

kondor19780726 [428]

Answer:

The answers are as follows for the functions.

f(1) = 12

f(3) = 22

f(5) = 32

Step-by-step explanation:

To find any of these, simply input the value in for x in the equation given.

f(1)

f(x) = 5x + 7

f(x) = 5(1) + 7

f(x) = 5 + 7

f(x) = 12

You can repeat this for each of them and it will allow you to use all of the numbers in the equations given.

6 0

3 years ago

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