find the 17th term of the arithmetic sequence whose common difference is d=3 and whose first term is a1=5.
1 answer:
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Answer:
B) consistent, dependent
Step-by-step explanation:
The given system is
45x - 30y = -90
-12x + 8y = 24
Let us make y the subject in both equations to get:
Top equation
Bottom equation
We can see that both equations are identically the same.
There is going to be infinitely many solutions.
We say the system is consistent and dependent.
The correct choice is B
Answer:
The approximate difference between m∠C and m∠A is 45° to the nearest degree
Step-by-step explanation:
* Lets talk about the right triangle
- It has one right angle and two acute angles
- The side opposite the the right angle is called hypotenuse
- The other sides are called the legs of the right angle
- In ΔABC
∵ AC is the hypotenuse
∴ ∠B is the right angle
∴ AB and BC are the legs of the right angle
∴ Angles A and C are the acute angles
∵ m∠B = 90°
- The sum of the measures of the interior angles of a Δ is 180°
∴ m∠A + m∠C = 180° - 90° = 90°
- We will use trigonometry to find the measures of angles A and C
- sin A is the ratio between the opposite side to angle ∠A and the
hypotenuse
∵ BC is the opposite side of angle A
∴ sin A = BC/AC
∵ BC = 5 cm
∵ AC = 13 cm
∴ sin A = 5/13
- Lets find m∠∠A by using sin ^-1
∴ m∠A =
- Lets use the rule of the sum of angles A and C to find the measure
of the angle C
∵ m∠A + m∠C = 90°
∴ 22.62° + m∠C = 90 ⇒ subtract 22.62 from both sides
∴ m∠C = 67.38°
- Lets find the difference between m∠C and m∠A
∴ The approximate difference between m∠C and m∠A is:
67.38° - 22.62° = 44.78° ≅ 45° to the nearest degree