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charle [14.2K]
4 years ago
9

Factor 9x^2+66xy+121y^2

Mathematics
1 answer:
Korvikt [17]4 years ago
7 0
Answer: (3x + 11y)^2

Demonstration:

The polynomial is a perfect square trinomial, because:

1) √ [9x^2] = 3x

2) √121y^2] = 11y

3) 66xy = 2 *(3x)(11y)

Then it is factored as a square binomial, being the factored expression:

 [ 3x + 11y]^2

Now you can verify working backwar, i.e expanding the parenthesis.

Remember that the expansion of a square binomial is:

- square of the first term => (3x)^2 = 9x^2
- double product of first term times second term =>2 (3x)(11y) = 66xy
- square of the second term => (11y)^2 = 121y^2

=> [3x + 11y]^2 = 9x^2 + 66xy + 121y^2, which is the original polynomial.

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If the basalt at the top of the ancient valley below Vulcan's Throne yields a radiometric date (K-Ar) of 15,000 years, and the l
zepelin [54]

Answer:

1.69\times 10^3feet/million year

Step-by-step explanation:

We are given that

Elevation of top of basalt in valley =4100 feet

Elevation of bottom of basalt in valley =2100 feet

Age of top of basalt in valley=15000 years

Age of bottom of basalt in valley=1.2 million years=1.2\times 10^6 years=1200000 years

We have to find the rate of basalt filling in the valley in feet per million yeas

Rate of basalt filling in the valley=\frac{Elevation\;of\;top\;of\;basalt\;in\;valley-elevation\;of\;bottom\;of\;basalt\;in\;valley}{age\;of\;bottom\;of\;basalt\;in\;valley-age\;of\;top\;of\;basalt\;in\;valley}

Rate of basalt filling in the valley=\frac{4100-2100}{1200000-15000}=\frac{2000}{1185000}=1.69\times 10^{-3} feet/year

Rate of basalt filling in the valley=1.69\times 10^{-3}\times 10^{6}=1.69\times 10^3feet/million year

6 0
4 years ago
Please help really important for my grade :(
Licemer1 [7]

Answer:

≈ 50.7 cm²

Step-by-step explanation:

The area (A) of Δ XYZ is calculated as

A = \frac{1}{2} bh ( b is the base and h the perpendicular height ), that is

A = \frac{1}{2} × XY × YZ

Calculate YZ using the tangent ratio in the right triangle

tan40° = \frac{opposite}{adjacent} = \frac{YZ}{XY} = \frac{x}{11} ( multiply both sides by 11 )

11 × tan40° = x , that is

YZ ≈ 9.23 cm

Thus

A = \frac{1}{2} × 11 × 9.23 = 5.5 × 9.23 ≈ 50.7 cm² ( to 3 significant figures )

7 0
3 years ago
The product of x and its opposite is always 1.<br> O True<br> O False
kari74 [83]

Answer:

False

Step-by-step explanation:

x

The opposite of x is -x

x* -x = -x^2

This is not always 1

3 0
3 years ago
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Answer: i used paper and pen cause its faster than typing

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3 years ago
Difference between spoiled and spoiled rotten
Olegator [25]
I assume the difference between the two would be the spoiled person would be perceived that way from an outside view because when they break their phone, lets say, they're granted with a new one such as an iPhone7 when the original was a blackberry. While the spoiled rotten term would be for those who have behavioral issues when things like "No!" are said to them and a tantrum begins.
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