4.5(4-x) + 36 = 202 - 2.5(3x + 28)
Distributive property
18 - 4.5x + 36 = 202 - 7.5x - 70
Combine like terms
-4.5x + 54 = -7.5x + 132
Add 7.5x to both sides
3x = 78
Divide both sides by 3
x = 26
Answer:
- diagram is below
- 6, 11, 16, 21
- s[n] = s[n-1] +5
- 26, 31, 36
Step-by-step explanation:
a) See below for the next diagram in sequence.
__
b) The numbers of straws in each diagram are ...
6, 11, 16, 21, ...
__
c) Each term is 5 more than the previous one, so the recursive rule for the number of straws is ...
s[1] = 6
s[n] = s[n-1] +5
__
d) The next three terms of the sequence are ...
..., 26, 31, 36, ...
Answer:
2.35 miles
Step-by-step explanation:
According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.
<h3>How to apply translations on a given function</h3>
<em>Rigid</em> transformations are transformation such that the <em>Euclidean</em> distance of every point of a function is conserved. Translations are a kind of <em>rigid</em> transformations and there are two basic forms of translations:
Horizontal translation
g(x) = f(x - k), k ∈
(1)
Where the translation goes <em>rightwards</em> for k > 0.
Vertical translation
g(x) = f(x) + k, k ∈
(2)
Where the translation goes <em>upwards</em> for k > 0.
According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.
To learn more on translations: brainly.com/question/17485121
#SPJ1
F(x) =16ˣ and g(x) = 16⁽ˣ/₂⁾
Since 16 = 2⁴, then we can write:
f(x) =2⁽⁴ˣ⁾ and g(x) = 2⁽⁴ˣ/₂⁾ = 2²ˣ
for x = 1 f(x) = 2⁴ = 16
for x = 1 g(x) = 2² = 4
(√16 = 4)
for x = 2 f(x) = 2⁸ = 256
for x = 2 g(x) = 2⁴ =16
(√256) = 16
for x = 3 f(x) = 2¹² = 4096
for x = 1 g(x) = 2⁶ = 64
(√4096 = 64)
We notice that:
The output values of g(x) are the square root of the output values of f(x) for the same value of x.