Simplifying
5x + 2 = 3x + -4
Reorder the terms:
2 + 5x = 3x + -4
Reorder the terms:
2 + 5x = -4 + 3x
Solving
2 + 5x = -4 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
2 + 5x + -3x = -4 + 3x + -3x
Combine like terms: 5x + -3x = 2x
2 + 2x = -4 + 3x + -3x
Combine like terms: 3x + -3x = 0
2 + 2x = -4 + 0
2 + 2x = -4
Add '-2' to each side of the equation.
2 + -2 + 2x = -4 + -2
Combine like terms: 2 + -2 = 0
0 + 2x = -4 + -2
2x = -4 + -2
Combine like terms: -4 + -2 = -6
2x = -6
Divide each side by '2'.
x = -3
Simplifying
x = -3
Answer:
Exponential function is:
y = 100 (1.03)ˣ
Step-by-step explanation:
We know that the exponential growth function is of the form
y = a (1 + r)ˣ
Here:
a = initial value
r = growth rate
x = number of time intervals that have passed
Given that A new savings account is opened with 400. Thus,
a = 400
Given that a new saving account gains 3% every year.
r = 3% = 0.03
now substituting a = 400 and r = 0.03 in the function
y = a (1 + r)ˣ
y = 100 (1 + 0.03)ˣ
y = 100 (1.03)ˣ
Therefore, exponential function is:
y = 100 (1.03)ˣ
<em>Please note that the growth factor i.e. 1.03 is greater than 1, so the exponential function represents exponential growth.</em>
The perimeter of a triangle is:
P = a + b + c
We are given that:
b = a + 3
c = 2 a – 3
Therefore:
68 = a + a + 3 + 2 a – 3
68 = 4 a
a = 17
and,
b = a + 3 = 20
<span>c = 2a – 3 = 31</span>
