Work is provided in the image attached.
Answer:
x = 25, y = 9
Step-by-step explanation:
Since the triangles are congruent then corresponding angles and sides are congruent, thus
∠ O = ∠ P , substitute values
6y - 14 = 40 ( add 14 to both sides )
6y = 54 ( divide both sides by 6 )
y = 9
and
NG = IT , that is
x - 2y = 7 ( substitute y = 9 into the equation )
x - 2(9) = 7
x - 18 = 7 ( add 18 to both sides )
x = 25
Answer:
2
Step-by-step explanation:
|a+x|/2 − |a−x|/2 , if a=−2; x=−6
Evaluate this expression
Simply plug in the numbers
| -2 + -6 | /2 - |-2 - -6|/2
|-8| /2 - |4|/2
4 - 2
2
Answer:
in steps
Step-by-step explanation:
base width: 1/2 x 5 = 2.5
base length: 1/2 x 4 = 2
height: 1/2 x 3 = 1.5
Volume: lwh = 2.5 x 2 x 1.5 = 7.5 in³
We can find m∠BCD like follows: m∠BCD=90°-45°=45<span>°
Now, m</span><span>∠DBC= 180°-(90°+45°)=45°
Remember that </span>
![sin \alpha = \frac{opposite leg}{hypotenuse}](https://tex.z-dn.net/?f=sin%20%5Calpha%20%3D%20%5Cfrac%7Bopposite%20leg%7D%7Bhypotenuse%7D%20)
, so
![oppositeleg=(hypotenuse)(sin \alpha )](https://tex.z-dn.net/?f=oppositeleg%3D%28hypotenuse%29%28sin%20%5Calpha%20%29)
We know that hypotenuse= BC= 3in and
![\alpha](https://tex.z-dn.net/?f=%20%5Calpha%20)
=∠DBC)=45°, so replacing the values we get:
![CD=3sin(45)=2.12](https://tex.z-dn.net/?f=CD%3D3sin%2845%29%3D2.12)
We can conclude that the segment CD is 2.12 in