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hammer [34]
3 years ago
7

What is the factored form 6n4-24n3+ 18n?

Mathematics
1 answer:
Svetach [21]3 years ago
8 0
<span>6n^4 - 24n^3 + 18n
= 6n(n^3 - 4n^2 + 3)

hope it helps</span>
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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
A recipe calls for 3/4 of a cup of flour to make 5/8 of a pound of bread
schepotkina [342]

Answer:

\huge\boxed{\sf 1 \ pound \ of \ dough = 1\frac{1}{5}  \ cup \ of \ flour}

Step-by-step explanation:

\displaystyle \underline{Given \ that:}\\\\\frac{5}{8} \ pound \ of \ dough = \frac{3}{4} \ cup\ of \ flour\\\\Multiply \ 8 \ to \ both \ sides\\\\5 \ pounds \ of \ dough = \frac{3}{4} \times 8 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 3 \times 2 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 6 \ cups \ of \ flour\\\\Divide \ both \ sides \ by \ 5\\\\1 \ pound \ of \ dough = \frac{6}{5}  \ cup \ of \ flour\\\\\boxed{1 \ pound \ of \ dough = 1\frac{1}{5}  \ cup \ of \ flour}\\\\

\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
8 0
2 years ago
Calculate the area of triangle ABC with altitude BD, given A (−6, 0), B (0, 0), C (0, 6), and D (−3, 3).
nata0808 [166]

Answer:

  • 18 unit²

Step-by-step explanation:

If BD is altitude then AC is the base.

<u>The length of AC is:</u>

  • AC = \sqrt{6^2+6^2} = 6\sqrt{2}

<u>The length of BD is:</u>

  • BD = \sqrt{3^2 + 3^2} = 3\sqrt{2}

<u>The area is:</u>

  • A = 1/2bh
  • A = 1/2 * 6\sqrt{2} *3\sqrt{2} = 18 unit²
4 0
3 years ago
Read 2 more answers
Write 1/4 as a decimal.
n200080 [17]

Answer:

0.25

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What’s the distance between the points (-7,-4) and (-5,-4)?
Radda [10]

Answer:

2 units

Step-by-step explanation:

Distance

= \sqrt{(-4 - (-4))^2 + (-7 - (-5))^2}

= \sqrt{0^2 + (-2)^2}

= \sqrt{(-2)^2}

= 2

3 0
3 years ago
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