The length of a right triangle is 32 cm in the height is 10 cm what is the area of the triangle
1 answer:
You might be interested in
The last three terms of the given binomial expansion are 40x²y³ + 10xy⁴ + y⁵
<h3>Binomial expansion</h3>From the question, we are to determine the last three terms of the binomial expansion 32x⁵ + 80x⁴y + 80x³y² + __ + __ + __
The highest power of the expansion is 5
Using the binomial expansion theorem
(m +n)⁵ = m⁵ + 5m⁴n + 10m³n² + 10m²n³ + 5mn⁴ + n⁵
Now, we will determine the values of m and n by comparison
By comparison,
m⁵ = 32x⁵
m⁵ = (2x)⁵
∴ m = 2x
Also,
5m⁴n = 80x⁴y
Divide both sides by 5, to get
m⁴n = 16x⁴y
Put m = 2x into the equation
(2x)⁴n = 16x⁴y
16x⁴n = 16x⁴y
∴ n = y
Thus, the expression being expanded is (2x + y)⁵
By binomial expansion, the expansion of (2x + y)⁵ is
(2x + y)⁵ = (2x)⁵ + 5(2x)⁴y + 10(2x)³(y)² + 10(2x)²(y)³ + 5(2x)(y)⁴ + y⁵
(2x + y)⁵ = 32x⁵ + (5×16)x⁴y + (10×8)x³(y)² + (10×4)x²(y)³ + (5×2)x(y)⁴ + y⁵
(2x + y)⁵ = 32x⁵ + 80x⁴y + 80x³y² + 40x²y³ + 10xy⁴ + y⁵
Hence, the last three terms of the given binomial expansion are 40x²y³ + 10xy⁴ + y⁵
Learn more on Binomial expansion here: brainly.com/question/13602562
#SPJ1
Jason's data distribution is symmetrical and shows no outliers; Shane's data distribution is uniform and shows no outliers also. Therefore, the correct observation about the data sets that is correct is:<em> Option B.</em>
<h3>Symmetrical and Uniform Data Distribution on a Dot Plot</h3>- If the data plotted on the dot plot shows a bell shape curve and can be divided into equal halves by a vertical line, the data distribution is symmetrical.
- When the data is spread equally across the range with no clear peaks, the data distribution is uniform.
<h3>What are Outliers?</h3>
Outliers are values that are far from the middle and are entirely different from the rest of the data.
The dot plots for sales made by Jason and Shane are shown in the image attached below.
Jason's data distribution is symmetrical and shows no outliers; Shane's data distribution is uniform and shows no outliers also. Therefore, the correct observation about the data sets that is correct is:<em> Option B.</em>
Learn more about data distribution on:
