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nordsb [41]
3 years ago
5

Which is equivalent to (4xy-3x)^2, and what type of special product is it?

Mathematics
2 answers:
mars1129 [50]3 years ago
8 0

It's not the difference of squares, rather it is the square of a difference. That leaves a perfect square trinomial, which narrows your selection to two choices. An expression with 2 terms is not a trinomial, so that further narrows your selection. The appropriate choice is

... (4xy -3z)² = 16x²y² -24xyz +9z², a perfect square trinomial

_____

The expression you have in your problem statement has no z term, so none of the choices is applicable to that one.

maria [59]3 years ago
5 0

Answer:

The correct option is 4.

Step-by-step explanation:

The given expression is

(4xy-3z)^2

Algebraic formula:

(a-b)^2=a^2-2ab+b^2

It is a perfect square trinomial.

Using algebraic formula, we get

(4xy-3z)^2=(4xy)^2-2(4xy)(3z)+(3z)^2

(4xy-3z)^2=16x^2y^2-24xyz+9z^2

Therefore option 4 is correct.

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Which of the following is equivalent to tan2θcos(2θ) for all values of θ for which tan2θcos(2θ) is defined?
Aloiza [94]

Answer:

2sin²θ - tan²θ

Step-by-step explanation:

Given

tan²θcos(2θ)

Required

Simplify

We start by simplifying cos(2θ)

cos(2θ) = cos(θ+θ)

From Cosine formula

cos(A+A) = cosAcosA - sinAsinA

cos(A+A) = cos²A - sin²A

By comparison

cos(2θ) = cos(θ+θ)

cos(2θ) = cos²θ - sin²θ ----- equation 1

Recall that cos²θ + sin²θ = 1

Make sin²θ the subject of formula

sin²θ = 1 - cos²θ

Substitute sin²θ = 1 - cos²θ in equation 1

cos(2θ) = cos²θ - (1 - cos²θ)

cos(2θ) = cos²θ - 1 +cos²θ

cos(2θ) = cos²θ + cos²θ - 1

cos(2θ) = 2cos²θ - 1

Substitute 2cos²θ - 1 for cos(2θ) in the given question

tan²θcos(2θ) becomes

tan²θ(2cos²θ - 1)

Open brackets

2cos²θtan²θ - tan²θ

------------------------

Simplify tan²θ

tan²θ = (tanθ)²

Recall that tanθ =  sinθ/cosθ

So, we have

tan²θ = (sinθ/cosθ)²

tan²θ = sin²θ/cos²θ

------------------------

Substitute sin²θ/cos²θ for tan²θ

2cos²θtan²θ - tan²θ becomes

2cos²θ(sin²θ/cos²θ) - tan²θ

Open bracket (cos²θ will cancel out cos²θ) to give

2(sin²θ) - tan²θ

2sin²θ - tan²θ

Hence, the simplification of tan²θcos(2θ) is 2sin²θ - tan²θ

Option E is correct

7 0
3 years ago
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lesya692 [45]

Answer:

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Step-by-step explanation:

4 0
3 years ago
What is the domain and range of each function graohed below?
andriy [413]
Domain is the x values you can use
range is the y values



a.
the domain
hmm, seems to be all real numbers except for at x=0, it gets really close tho
so D=(-∞,0)U(0,∞)

range is all real numbers except for y=0, it gets really close tho
R=(-∞,0)U(0,∞)



b.
domain
that empty circle means something like < or >
goes from 5 to 6, not including 5
so domain is D=(5,6]

range is from -4 to 2, not including -4
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3 years ago
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Explain how you could use the objects to act out this problem
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Use some bricks and paint. paint the bricks
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What are the missing statement and reason in step 2 of the proof? Statement: ∠ABC ≅ ∠BCD, ∠BAD ≅ ∠ADC Reason: For parallel lines
ICE Princess25 [194]

Answer:

Statement: AB=CD, BC=AD

Reason: By definition of parallelogram .

Statement: AC=AC

Reason: Reflexive property of equality.

Step-by-step explanation:

1.Statement: \angle ABC\cong \angle BCD,\angle BAD\cong \angle ADC.

Reason: For parallel lines cut by a transversal , corresponding angles are congruent.

2.Statement:AB=CD,BC=AD

Reason: By definition of parallelogram.

3.Statement: AC=AC

Reason: Reflexive property of equality.

4.Statement: \triangle ABC\cong \triangle CDA.

Reason: SSS criterion for congruence.

5.Statement:AB\cong CD, BC\cong AD.

Reason: Given .

6.Statement: AB\parallel CD, BC\parallel AD.

Reason: By definition of parallelogram.

7.Statement: \angle BAC\cong \angle ACD.

Reason: Alternate Interior Angles Theorem.

7 0
3 years ago
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