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olchik [2.2K]
1 year ago
5

Expand the function. (2x+y)^(7)

Mathematics
1 answer:
iragen [17]1 year ago
6 0

The binomial (2 · x + y)⁷ in expanded form by 128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷.

<h3>How to expand the power of a binomial</h3>

Herein we have the seventh power of a binomial, whose expanded form can be found by using the binomial theorem and Pascal's triangle. Hence, we find the following expression for the expanded form:

(2 · x + y)⁷

(2 · x)⁷ + 7 · (2 · x)⁶ · y + 21 · (2 · x)⁵ · y² + 35 · (2 · x)⁴ · y³ + 35 · (2 · x)³ · y⁴ + 21 · (2 · x)² · y⁵ + 7 · (2 · x) · y⁶ + y⁷

128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷

Then, the binomial (2 · x + y)⁷ in expanded form by 128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷.

To learn more on binomials: brainly.com/question/12249986

#SPJ1

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wariber [46]

Answer:

57 ft²

Step-by-step explanation:

Lol I always found the area formula for a parallelogram to be interesting- it's like a rectangle, just the base times the height.

So to find this, you would subtract the area of the parallelogram by the area covered by the car.

(17ft · 9ft) - (16ft ·6ft) = 153ft² - 96ft²

= 57 ft²

Lol don't forget the units! A few of my teachers have been really picky about it, where if you don't include units, the entire answer is wrong : ( but either way, it's a good habit to pick up!

3 0
3 years ago
In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for
tatuchka [14]

Answer:

With a .95 probability, the margin of error is = 0.392

Step-by-step explanation:

Given -

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period.

Sample size ( n ) =81

Standard deviation (\sigma ) = 1.8 hours

\alpha = 1 -.95 =.05

Z_{\frac{\alpha }{2}} = Z_{\frac{.05 }{2}} = 1.96           (Using Z table)

With a .95 probability, the margin of error is

Margin of error  =  Z_{\frac{\alpha }{2}}\frac{\sigma }{\sqrt{n}}

                          = Z_{\frac{.05 }{2}} \frac{1.8 }{\sqrt{81}}

                           = 1.96\times 0.2

Margin of error   = 0.392

   

8 0
3 years ago
A steel company is making flat rectangular frames as a part of a new product they are launching. Each frame will be cut out of a
Luda [366]

The area of steel before cutting:

Area =(11+2x)*(6+2x)cm²

= 4x^{2}+22x+12x+66

Hence, Area=4x^{2}+34x+66

Area of steel after cutting out the 11*6 inside dimensions.

4x^{2}+34x+66-(11*6)=4x^{2}+34x

As the area should be close to 28 cm square, so equation becomes:

4x^{2}+34x=28 or 4x^{2}+34x-28=0

Now for the answer, kindly see the image attached. It gives x=0.76

Hence, the answer is 0.76 cm.


7 0
3 years ago
A shipment of 20 DVDs has arrived at a video rental store. Based on past experience, the manager knows that 10% of all new DVDs
aleksley [76]

Answer:

The probability is 0.081

Step-by-step explanation:

Here, we want to calculate the probability that the 3rd inspection will be defective.

What this means is that the first two would

not be defective.

Probability of having a defective DVD = 10% = 10/100 = 0.1

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So the probability of third being defective = Probability of first not defective * Probability of second not defective * Probability of third defective

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━━━━━━━☆☆━━━━━━━

▹ Answer

<em>(-2, 1)</em>

▹ Step-by-Step Explanation

4x + 3y = -5

-2x + 2y = 6

4x + 3y = -5

x = -3 + y

4(-3 + y) + 3y = -5

y = 1

x = -3 + 1

x = -2

(x, y) = (-2, 1)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

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4 years ago
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