Step-by-step explanation:
Complete the proof of the Pythagorean theorem is given below.
Statement Reason
1. ΔABC is a right triangle, with a 1. Given
right angle at ∠C
2. Draw an altitude from point C 2. From a point not on a line, exactly
to AB one perpendicular can be drawn through the point to the line
3. ∠CDB and ∠CDA are right 3. Definition of altitude
angles
4. ∠BCA ≅ ∠BDC 4. All right angles are congruent
5. ∠B ≅ ∠B 5. 
6. ΔCBA ~ ΔDBC 6. AA Similarity Postulate
7. 
7. 
8. 
8. 
9. ∠CDA ≅ ∠BCA 9. 
10. ∠A ≅ ∠A 10.
11. ΔCBA ~ ΔDBA 11. AA Similarity Postulate
12. 
12. 
13. 
13.
14. 
14. 
15. 
15. Distributive Property
16. 
16. 
17. 
18. 
Answer:
a) x > − 24 
b) x < − 3
c) q < 56
Step-by-step explanation:
a) −2/5x−9<9/10
<=> 2/5x + 9 > − 9/10
<=> 2/5x > − 9/10 − 9
<=> 2×2/2×5x > − 9/10 − 9×10/10
<=> 4/10x > − 99/10
<=> x > − 99/4
<=> x > − 24
b) 4x+6<−6
<=> 4x < − 6 − 6
<=> 4x < − 12
<=> x < − 12/4
<=> x < − 3
c) q+12−2(q−22)>0
<=> q+12−2q −2×(−22)>0
<=> (q−2q) + (12+ 44) >0
<=> −q + 56 >0
<=> q < 56
Answer:
Area of ABCD = 959.93 units²
Step-by-step explanation:
a). By applying Sine rule in the ΔABD,
Sin∠DBA = 
m∠DBA = 
m∠DBA = 45.64°
Therefore, m∠ADB = 180° - (110° + 45.64°) = 24.36°
m∠ADB = 24.36°
c). Area of ABCD = Area of ΔABD + Area of ΔBCD
Area of ΔABD = AD×BD×Sin(
)
= 35×46Sin(12.18)
= 339.68 units²
Area of ΔBCD = BD×BC×Sin(
)°
= 46×27×(0.4994)
= 620.25 units²
Area of ABCD = 339.68 + 620.25
= 959.93 units²
The isosceles triangle has two sides congruent which mean they are equal. If two sides are equal, it also means that two angles are equal.
For triangle XYZ, we have angles shown below:
∠X + ∠Y + ∠Z = 180°
If ∠Y = a°, then we can have the expression for ∠X such as shown below:
∠X + a° + ∠Z =180°
∠X= 180° - a° - ∠Z
If ∠Z = ∠Y, then we have the final expression:
∠X = 180° -2a°
Answer:
x - 8 = 0
Step-by-step explanation:
Since, the cube root of a number is 2.
Let the number be x.
Therefore,
![\sqrt[3]{x} = 2 \\ cubing \: both \: sides \\ {( \sqrt[3]{x})}^{3} = {(2)}^{3} \\ x = 8 \\ x - 8 = 0](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%7D%20%20%3D%202%20%5C%5C%20%20cubing%20%5C%3A%20both%20%5C%3A%20sides%20%5C%5C%20%20%7B%28%20%5Csqrt%5B3%5D%7Bx%7D%29%7D%5E%7B3%7D%20%20%3D%20%20%7B%282%29%7D%5E%7B3%7D%20%20%5C%5C%20%20%20x%20%3D%208%20%5C%5C%20%20x%20-%208%20%3D%200)
