Answer:
- The system has infinitely many solutions when a = 3/4 and b = 1/2
<h3>Given </h3>
System of linear equations
<h3>To find </h3>
- Values of a and b that leads to infinitely many solutions
<h3>Solution</h3>
The linear system of equations has infinitely many solutions when lines overlap, so both have same slope and y-intercept.
We can solve it in two different ways
1. Note that when the first equation is multiplied by 4, it has same value of constant as the second equation, which is 64.
- 4ax + 4by = 64
- 3x + 2y = 64
When compared it gives us:
- 4a = 3 ⇒ a = 3/4
- 4b = 2 ⇒ b = 2/4 = 1/2
2. Convert both equations from standard to slope-intercept form and compare:
- ax + by = 16
- by = -ax + 16
- y = - (a/b)x + 16/b
- 3x + 2y = 64
- 2y = - 3x + 64
- y = - (3/2)x + 32
Work out values of a and b:
- 16/b = 32 ⇒ b = 16/32 ⇒ b = 1/2
- - (a/b) = - 3/2 ⇒ a/b = 3/2 ⇒ a = 3b/2 ⇒ a = 3(1/2)/2 ⇒ a = 3/4
Answer:
1.932 days (or approximatelly 1 day, 22 hours and 22 minutes)
Step-by-step explanation:
The inicial concentration is 60,000, and this concentration triples every 4 days, so we can write the equation:
P = Po * r^t
where P is the final concentration after t periods of 4 days, Po is the inicial concentration and r is the ratio that the concentration increases (r = 3)
Then, we have that:
102000 = 60000 * 3^t
3^t = 102/60 = 1.7
log(3^t) = log(1.7)
t*log(3) = log(1.7)
t = log(1.7)/log(3) = 0.483
so the number of days that will take is 4*0.483 = 1.932 days (or approximatelly 1 day, 22 hours and 22 minutes)
Answer:
expresión 5
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
similar means resembling without being identical or same shape but different size. triangles are obviously the same shape and they're obviously different size.
