C
alternate interior angles theorem: If a transversal intersects two parallel lines, then the alternate interior angles are congruent. thus, if the alternate interior angles are congruent, then the lines are parallel.
all the angles are congruent, so m || n and p || q.
Answer:
Step-by-step explanation:
1) since the sixth term is 3 and the fifth term 24, the common ratio would be 3/24 = 1/8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
If t6 = 3,r = 1/8, then
3 = a × 1/8^(6 - 1) = a × (1/8)^5
a = 3/(0.125)^5 = 98304
The first term is 98304.
Second term is 98304 × 1/8 = 12288
Third term is 12288 × 1/8 = 1536
Third term is 1536 × 1/8 = 192
2) t1 = 4
t2 = - 3t(2- 1) = - 3t1 = - 3 × 4 = - 12
t3 = - 3t(3- 1) = - 3t2 = - 3 × - 12 = 36
t4 = - 3t(4- 1) = - 3t3 = - 3 × 36 = - 108
3) let the numbers be t2,t3 and t4
The sequence becomes
1/2, t2,t3, t4,8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
8 = 1/2 × r^(5 - 1)
8 = 1/2 × r^4
16 = r^4
2^4 = r^4
r = 2
t2 = 1/2 × 2 = 1
t3 = 1 × 2 = 2
t4 = 2 × 2 = 4
Answer: A
Step-by-step explanation: 3(x-1) becomes 3x -3 ≤ 4x. Put all like variables on the same side, meaning you'll subtract 3x from both sides giving you -3 ≤ x. You can flip the equation around to make it look exactly like x ≥ -3
Answer:
50 cm
Step-by-step explanation:
So the first step is to find the height, and to do that you know that the area of a triangle is height * base / 2 = area. Plugging in the numbers you have, you get:
Then, this becomes
Divide both sides by 24
Now you can use the base and the height to find the hypotenuse using the Pythagorean Theorem: 
Therefore the length of the hypotenuse is 50 cm
Answer:
(- 2, 4 )
Step-by-step explanation:
A translation of 5 units left means subtract 5 from the original x- coordinate.
A translation of 6 units up means add 6 to the original y- coordinate.
Thus
(3, - 2 ) → (3- 5, - 2 + 6 ) → (- 2, 4 )
