Answer:
B
Step-by-step explanation:
![50+x \leq 50](https://tex.z-dn.net/?f=50%2Bx%20%20%5Cleq%20%2050)
Subtract 50 from both sides:
![50+x-50 \leq 50 - 50](https://tex.z-dn.net/?f=50%2Bx-50%20%20%5Cleq%20%2050%20-%2050)
![x \leq 0](https://tex.z-dn.net/?f=x%20%20%5Cleq%200)
hope this helps!
We look for the minimum of each function.
For f (x) = 3x2 + 12x + 16:
We derive the function:
f '(x) = 6x + 12
We match zero:
6x + 12 = 0
We clear the value of x:
x = -12/6
x = -2
We substitute the value of x in the equation:
f (-2) = 3 * (- 2) ^ 2 + 12 * (- 2) + 16
f (-2) = 4
For g (x) = 2sin(x-pi):
From the graph we observe that the minimum value of the function is:
y = -2
Answer:
A function that has the smallest minimum y-value is:
y = -2
The answer is <span>9.55 minutes
</span>
1. Turn 15 km into miles:
1 km = 0.621 mile
15 km = 15 * 0.621 mile = 9.315 miles
So, she ran 9.315 miles for 89 minutes
2. Calculate <span>how many minutes it took Jimena to run 1 mile during the race:
S</span>he ran 9.315 miles for 89 minutes.
She ran 1 mile for x minutes.
9.315 mi : 89 min = 1 mi : x
x = 89 min * 1 mi / 9.315 mi
x = 9.55 min
<span>Simplifying
3a2 + -2a + -1 = 0
Reorder the terms:
-1 + -2a + 3a2 = 0
Solving
-1 + -2a + 3a2 = 0
Solving for variable 'a'.
Factor a trinomial.
(-1 + -3a)(1 + -1a) = 0
Subproblem 1Set the factor '(-1 + -3a)' equal to zero and attempt to solve:
Simplifying
-1 + -3a = 0
Solving
-1 + -3a = 0
Move all terms containing a to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + -3a = 0 + 1
Combine like terms: -1 + 1 = 0
0 + -3a = 0 + 1
-3a = 0 + 1
Combine like terms: 0 + 1 = 1
-3a = 1
Divide each side by '-3'.
a = -0.3333333333
Simplifying
a = -0.3333333333
Subproblem 2Set the factor '(1 + -1a)' equal to zero and attempt to solve:
Simplifying
1 + -1a = 0
Solving
1 + -1a = 0
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1a = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1
Combine like terms: 0 + -1 = -1
-1a = -1
Divide each side by '-1'.
a = 1
Simplifying
a = 1Solutiona = {-0.3333333333, 1}</span>