Answer:
21
Step-by-step explanation:
![4x + 24 = 7x - 49 \\ then \: collect \: the \: same \: variable \\ 4x - 7x = - 49 - 24 \\ x = - 63 \div - 3 = 21](https://tex.z-dn.net/?f=4x%20%2B%2024%20%3D%207x%20-%2049%20%20%5C%5C%20then%20%5C%3A%20collect%20%5C%3A%20the%20%5C%3A%20same%20%5C%3A%20variable%20%5C%5C%204x%20-%207x%20%3D%20%20-%2049%20-%2024%20%5C%5C%20x%20%3D%20%20-%2063%20%5Cdiv%20%20-%203%20%3D%2021)
Answer:
C. Ari and Matthew collide at 4.8 seconds.
Explanation:
Ari and Matthew will collide when they have the same x and y position. Since Ari's path is given by
x(t) = 36 + (1/6)t
y(t) = 24 + (1/8)t
And Matthew's path is given by
x(t) = 32 + (1/4)t
y(t) = 18 + (1/4)t
We need to make x(t) equal for both, so we need to solve the following equation
Ari's x(t) = Matthew's x(t)
36 + (1/6)t = 32 + (1/4)t
Solving for t, we get
36 + (1/6)t - (1/6)t = 32 + (1/4)t - (1/6)t
36 = 32 + (1/12)t
36 - 32 = 32 + (1/12)t - 32
4 = (1/12)t
12(4) = 12(1/12)t
48 = t
It means that after 48 tenths of seconds, Ari and Mattew have the same x-position. To know if they have the same y-position, we need to replace t = 48 on both equations for y(t)
Ari's y position
y(t) = 24 + (1/8)t
y(t) = 24 + (1/8)(48)
y(t) = 24 + 6
y(t) = 30
Matthew's y position
y(t) = 18 + (1/4)t
y(t) = 18 + (1/4)(48)
y(t) = 18 + 12
y(t) = 30
Therefore, at 48 tenths of a second, Ari and Mattew have the same x and y position. So, the answer is
C. Ari and Matthew collide at 4.8 seconds.
The next three terms of sequence are 65, 129 and 257
<em><u>Solution:</u></em>
<em><u>Given sequence is:</u></em>
2, 3, 5, 9, 17, 33
We have to find the next three terms in sequence
<em><u>Let us find the logic used in this sequence</u></em>
![2 + 2^0 = 2 + 1 = 3\\\\3 + 2^1 = 3 + 2 = 5\\\\5 + 2^2 = 5 + 4 = 9\\\\9 + 2^3 = 9 + 8 = 17\\\\17 + 2^4 = 17 + 16 = 33](https://tex.z-dn.net/?f=2%20%2B%202%5E0%20%3D%202%20%2B%201%20%3D%203%5C%5C%5C%5C3%20%2B%202%5E1%20%3D%203%20%2B%202%20%3D%205%5C%5C%5C%5C5%20%2B%202%5E2%20%3D%205%20%2B%204%20%3D%209%5C%5C%5C%5C9%20%2B%202%5E3%20%3D%209%20%2B%208%20%3D%2017%5C%5C%5C%5C17%20%2B%202%5E4%20%3D%2017%20%2B%2016%20%3D%2033)
Thus the sequence is increasing by 2 raised to power 0, 1, 2 and so on
<em><u>Thus the next three terms are found by:</u></em>
![33 + 2^5 =33 + 32= 65\\\\65 + 2^6 = 65 + 64 = 129\\\\129 + 2^7 = 129 + 128 = 257](https://tex.z-dn.net/?f=33%20%2B%202%5E5%20%3D33%20%2B%2032%3D%2065%5C%5C%5C%5C65%20%2B%202%5E6%20%3D%2065%20%2B%2064%20%3D%20129%5C%5C%5C%5C129%20%2B%202%5E7%20%3D%20129%20%2B%20128%20%3D%20257)
Thus the next three terms of sequence are 65, 129 and 257
Answer:
[1, 3]
Step-by-step explanation:
g(x) = f(2x), so g(x) is f(x) compressed horizontally by a factor of 2. Vertically, it is not changed.
Therefore, the ranges are identical.