Answer:
BC = 30
Step-by-step explanation:
If the three points are collinear, it means they lie on the same straight line.
Now B lies between A and C
By mathematical convention;
AC = AB + BC
This means;
48 = 2x + 2 + 3x + 6
48 = 5x + 8
48-8 = 5x
5x = 40
x = 40/5
x = 8
From the question BC = 3x + 6
Substitute the value of x; 3(8) + 6 = 24 + 6 = 30
Answer:
OPTION D: NEITHER
Step-by-step explanation:
The given equation is: 7x - 2y = - 5
To find a solution to this, we substitute the options and compare LHS and RHS.
OPTION A: (1, 5)
LHS = 7(1) - 2(5) = 7 - 10 = -3
RHS = - 5
LHS
RHS.
So, this option is eliminated.
OPTION B: (-1, 1)
LHS = 7(-1) - 2(1) = -7 - 2 = - 9
RHS = - 5
Again, LHS
RHS.
So, this Option is eliminated as well.
OPTION C: It says both A and B. Clearly, this is eliminated as well.
Therefore, the answer is: OPTION D: NEITHER.
NOTE: This is a two variable equation. So, we need a minimum of two equations to determine the solution. Since, only one equation is given here, we use the help of options.
Answer:
1) ΔACD is a right triangle at C
=> sin 32° = AC/15
⇔ AC = sin 32°.15 ≈ 7.9 (cm)
2) ΔABC is a right triangle at C, using Pythagoras theorem, we have:
AB² = AC² + BC²
⇔ AB² = 7.9² + 9.7² = 156.5
⇒ AB = 12.5 (cm)
3) ΔABC is a right triangle at C
=> sin ∠BAC = BC/AB
⇔ sin ∠BAC = 9.7/12.5 = 0.776
⇒ ∠BAC ≈ 50.9°
4) ΔACD is a right triangle at C
=> cos 32° = CD/15
⇔ CD = cos32°.15
⇒ CD ≈ 12.72 (cm)
Step-by-step explanation:
It has to be the first one