Answer:
Step-by-step explanation:
Given
Required
PQ
Since Q is between the given points, then:
This gives:
Collect like terms
Next, solve for x
We have:
This gives:
Collect like terms
Divide by 2
So:
The transformation that would map the parallelogram onto itself is the rotation of 180 degrees about the point (2, 2)
<h3>What is a
transformation?</h3>
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is the transformation that does not change the shape or size of a figure. Examples of rigid transformations are <em>translation, reflection and rotation</em>.
The transformation that would map the parallelogram onto itself is the rotation of 180 degrees about the point (2, 2)
Find out more on transformation at: brainly.com/question/4289712
#SPJ1
Answer:
x = 49°
Step-by-step explanation:
The sine of an angle is equal to the cosine of its complement:
x = 90° -41° = 49°
P I hope this helps sorry if it didn’t
Answer:
- dimensions: 12 ft by 5 ft
- area: 60 ft²
Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
_____
<em>Comment on finding the area</em>
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
