The polynomial that represents the area of the trapezoid shaped window is: 1/2(8x² - 14x - 15).
<h3>What is the
Area of a Trapezoid?</h3>
Area of trapezoid = 1/2(a + b)h, where a and b are length of the parallel sides, and h is the height.
Given:
a = 3x + 5
b = x - 2
h = 2x - 5
Thus:
Area of trapezoid = 1/2(3x + 5 + x - 2)(2x - 5)
Area of trapezoid = 1/2(4x + 3)(2x - 5)
Area of trapezoid = 1/2(8x² - 14x - 15)
Therefore, the polynomial that represents the area of the trapezoid shaped window is: 1/2(8x² - 14x - 15).
Learn more about area of trapezoid on:
brainly.com/question/1463152
Answer:
Options (A) and (D).
Step-by-step explanation:
Given expression is,
4x³ - 7x² -
+ 15
Characteristics of the give expression ,
Option (A).
Third term
of the expression is in the form a ratio.
True.
Option (B).
Entire expression is a difference.
False.
Option (C).
There are three terms.
False.
Option (D).
There are four terms in the given expression.
True.
Therefore, Options (A) and (D) will be the correct options.
Answer:
x= -10
Step-by-step explanation:.......
PEMDAS
Multiplication:
10* -4 / 3*9 = -40 / 27
Addition:
-40 / 27 + 7/6 find common denominator 108
-40*4 / 27*4 + 7*18 / 6*18
-160 / 108 + 126 / 108
-34 / 108
-17 / 54
Subtract:
-17 / 54 - 2/5 common denominator 270
17*5 / 54*5 - 2*54 / 5*54
-85 / 270 - 108 / 270
-193 / 270
-193/ 270 = -0.7148
-8 / 15 = -0.7148 :)
Answer:
S is not the subspace of 
Step-by-step explanation:
Let us suppose two vectors u and v belong to the S such that the property of xy≥0 is verified than
![v=\left[\begin{array}{c}0 \\1\end{array}\right]](https://tex.z-dn.net/?f=v%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Both the vectors satisfy the given condition as follows and belong to the S

Now S will be termed as subspace of R2 if
- u+v also satisfy the condition
- ku also satisfy the condition
Taking u+v
![u+v=\left[\begin{array}{c}-1 \\0\end{array}\right]+\left[\begin{array}{c}0 \\1\end{array}\right]\\u+v=\left[\begin{array}{c}-1+0 \\0+1\end{array}\right]\\u+v=\left[\begin{array}{c}-1 \\1\end{array}\right]](https://tex.z-dn.net/?f=u%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%20%5C%5C0%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D%5C%5Cu%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%2B0%20%5C%5C0%2B1%5Cend%7Barray%7D%5Cright%5D%5C%5Cu%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Now the condition is tested as

This indicates that the condition is not satisfied so S is not the subspace of 