<span>3y+2x=6
5y-2x=10
--------------add
8y = 16
y = 2
</span>3y+2x=6
3(2)+2x=6
6 + 2x = 6
2x = 0
x = 0
answer: x = 0 and y = 2 or (0,2)
Answer:
187 units²
Step-by-step explanation:
break the figure into two rectangles
one 16 by 7 , the other 25 by 3
a = (16 * 7) + (25 * 3)
a = 187
5y - 5= 22
or
5(y)-5=22
Hope that helps!
Answer:
12 inches
Step-by-step explanation:
Let b represent the base
h represents the height
area of the parallelogram = base * height = 216 square inches
From the question'
b = 18 + 3h
Slot in the value of b
216 = (18 + 3h) * h
expand
216 = 18h + 3h^2
subtract 216 from both sides
0 = 18h + 3h^2 - 216
rearrange
3h^2 + 18h - 216 = 0
divide through by 3
h^2 + 6h - 72 = 0
Now, lets solve!
h^2 + 6h - 12h - 72 = 0
h( h + 6 ) - 12(h + 6) = 0
(h - 12) (h + 6) = 0
h - 12 = 0
h = 12
and
h + 6 = 0
h = - 6
Taking the positive value of h
Hence, the height is 12 inches
Lets check
when h = 12 inches
Area of the parallelogram = 18* 12 = 216 square inches .... correct
when h = -6inches
A = 18 * -6 ≠ 216 square inches
So height is 12 inches
The given conclusion that ABCD is a square is not valid.
Given that, AC⊥BD and AC≅BD.
We need to determine if the given conclusion is valid.
<h3>What are the properties of squares?</h3>
A square is a closed figure with four equal sides and the interior angles of a square are equal to 90°. A square can have a wide range of properties. Some of the important properties of a square are given below.
- A square is a quadrilateral with 4 sides and 4 vertices.
- All four sides of the square are equal to each other.
- The opposite sides of a square are parallel to each other.
- The interior angle of a square at each vertex is 90°.
- The diagonals of a square bisect each other at 90°.
- The length of the diagonals is equal.
Given that, the diagonals of a quadrilateral are perpendicular to each other and the diagonals of a quadrilateral are equal.
Now, from the properties of a square, we understood that the diagonals of a square are perpendicular to each other and the diagonals of a square are equal.
So, the given quadrilateral can be a square. But only with these two properties can not conclude the quadrilateral is a square.
Therefore, the given conclusion that ABCD is a square is not valid.
To learn more about the properties of a square visit:
brainly.com/question/20377250.
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