Answer:
<h2>m∠BWP = 46°</h2>
Step-by-step explanation:
YZXW is a quadrangle.
We know: Angles i quadrangle add up to 360°.
Therefore we have the equation:
m∠DYP + m∠CZR + m∠AXS + m∠BWQ = 360°
Substitute given measures of angles:
46° + 76° + 104° + m∠BWQ = 360°
226° + m∠BWQ = 360° <em>subtract 226° from both sides</em>
m∠BWQ = 134°
∠BWQ and ∠BWP are supplementary angles (add up to 180°).
Therefore
m∠BWP = 180° - 134°
m∠BWP = 46°
Other method.
m∠CZR + m∠AXS = 76° + 104° = 180°
Conclusion: YZXW is a trapezoid. Therefore CD is parallel to AB.
Therefore ∠DYP and ∠BWP are corresponding angles.
Corresponding angles have equal measures.
Therefore m∠BWP = m∠DYP = 46°
Answer:
25x^2 -40x + 16
Step-by-step explanation:
(5x-4)^2
(5x-4)(5x-4)
FOIL
first 5x*5x =25x^2
outer 5x*-4 = -20x
inner 5x*-4 = -20x
last = -4*-4 = 16
Add them together
25x^2 -20x -20x+ 16
Combine like terms
25x^2 -40x + 16
Answer:
56 - 9π
Step-by-step explanation:
To find the area of the shaded region, you must find the area of the rectangle then subtract the area of the circle inside.
Area of the Rectangle: length x width
8*7=56
Area of the circle: πr^2
π*3^2 = 9π
Area of shaded region = 56 - 9π
Answer:
398 ft²
Step-by-step explanation:
Assuming you have correctly described the total area in terms of non-overlapping triangles and a rectangle, you can put the dimensions into the appropriate area formula and add up the pieces.
Triangle area = 1/2·bh
Rectangle area = bh
___
So, the <em>first triangle</em> has an area of ...
1/2·(20 ft)(20 ft) = 200 ft²
The <em>second triangle</em> has an area of ...
1/2·(6 ft)(6 ft) = 18 ft²
The <em>rectangle</em> has an area of ...
(30 ft)(6 ft) = 180 ft²
And the area total is ...
200 ft² +18 ft² +180 ft² = 398 ft²
