Answer:
Please check the explanation.
Step-by-step explanation:
<u>Calculating the area of the outer rectangle:</u>
Given
- The length outer rectangle = l = 3x - 1
- The width of outer rectangle = w = 5x + 2
Thus,
The area of the outer rectangle:
<u>Calculating the area of the inner rectangle:</u>
Given
- The length inner rectangle = l = x + 7
- The width of inner rectangle = w = x
Thus,
The area of the outer rectangle:
A = wl
= x(x+7)
= x² + 7
<u>Calculating the area of the shaded region:</u>
As
The area of the outer rectangle = 15x² + x - 2
The area of the inner rectangle = x² + 7
- The area of the shaded region can be determined by subtracting the area of the inner rectangle from the area of the outer rectangle.
Thus,
shaded region Area = Outer Rectangle Area - Inner Rectangle Area
= 15x² + x - 2 - (x² + 7)
= 15x² + x - 2 - x² - 7
= 14x² + x - 9
Therefore, the Area of the shaded region is: 14x² + x - 9
Answer:
Volume = 175 cm³
Step-by-step explanation:
We can picture this image as a whole rectangular prism, with a part that has been cut out of it.
Step 1: Volume of original prism
We are going to solve the volume of the original prism, with the dimensions of 9, 7, and 5
Step 2: Volume of part cut out
We are solving the volume of that part that has been cut out ( missing space)
- V = 5 * (9-2) * (7-3)
- V = 5 * 7 * 4
- V = 140
Step 3: Total Volume
Now we just subtract the cutout part from the original volume
Volume = 175 cm³
Note, we could have also found the volume by splitting this shape into two prisms with dimensions (9 * 3 * 5) and (4 * 5 * 2). This way would also get us:
- V = (9 * 3 * 5) + (4 * 5 * 2)
- V = 135 + 40
- V = 175
-Chetan K
You answer will be C, Angle Side Angle (ASA). Since you are given two lines parallel, then you know angle BCE and angle CEF are congruent using the reason of "If two lines are parallel then the alternate interior angles are congruent" (they are congruent because they are alternate interior angles). Also, angle CBF and angle BFE are congruent because they are both alternate interior angles.
P.S. the first pair of alternate interior angles is created by parallel lines BC and EF and the intersecting line BF. And the second pair is created by parallel lines BC and EF and intersecting line CE.
Answer:
Plzzz
Step-by-step explanation:
Zoom innnn plzz
Given :-
To find :-
Solution :-
<u>According</u><u> to</u><u> Question</u><u>,</u>
- x = 3 + √8
- 1/x = 1/3-√8
- 1/x = 1(3+√8)/(3+√8)(3-√8)
- 1/x = 3+√8/3²-(√8)²
- 1/x = 3+√8/9-8
- 1/x = 3 + √8
<u>So </u><u> </u><u>that</u><u> </u><u>,</u>
- x² + 1/x²
- (x + 1/x)² - 2
- ( 3+√8+3-√8)²-2
- 9² - 2
- 81 - 2
- 79
