Answer:
1481
Step-by-step explanation:
Answer:
3): 14
Step-by-step explanation:
The problem states that ABC and DEF are similar. Therefore, dsue to similar triangles, we have 7x/7=4/x, so x^2=4. Therefore, x=2 (because x cannot be negative). Therefore, AB = 7x = 7*2=14
Answer: C. Definition of an Altitude
Step-by-step explanation:
Given: In triangle MNO shown below, segment NP is an altitude from the right angle.
Let ∠MNP=x
Then ∠PNO=90°-x
Therefore in triangle MNO,
∠MPN=∠NPO =90° [by definition of Altitude]
[Definition of altitude : A line which passes through a vertex of a triangle, and joins the opposite side forming right angles. ]
Now using angle sum property in ΔMNP
∠MNP+∠MPN+∠PMN=180°
⇒x+90°+∠PMN=180°
⇒∠PMN=180°-90°-x
⇒∠PMN=90°-x
Now, in ΔMNO and ΔPNO
∠PMN=∠PNO=90°-x
and ∠MPN=∠NPO =90° [by definition of altitude]
Therefore by AA similarity postulate, we have
ΔMNO ≈ ΔPNO
Answer:
x = ± sqrt(43)
Step-by-step explanation:
2x^2 - 28 = x^2 + 15
Subtract x^2 from each side
2x^2-x^2 - 28 = x^2-x^2 + 15
x^2 -28 = 15
Add 28 to each side
x^2 - 28 +28= 15+28
x^2 = 43
Take the square root of each side
sqrt(x^2) = ± sqrt(43)
x = ± sqrt(43)
