C
alternate interior angles theorem: If a transversal intersects two parallel lines, then the alternate interior angles are congruent. thus, if the alternate interior angles are congruent, then the lines are parallel.
all the angles are congruent, so m || n and p || q.
Answer:
5 packages
Step-by-step explanation:
each would have five if they made 5 sandwhiches
The given polynomial function has 1 relative minimum and 1 relative maximum.
<h3>What are the relative minimum and relative maximum?</h3>
- The relative minimum is the point on the graph where the y-coordinate has the minimum value.
- The relative maximum is the point on the graph where the y-coordinate has the maximum value.
- To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)
<h3>Calculation:</h3>
The given function is
f(x) = 2x³ - 2x² + 1
derivating the above function,
f'(x) = 6x² - 4x
At slope = 0, f'(x) = 0 (for maximum and minimum values)
⇒ 6x² - 4x = 0
⇒ 2x(3x - 2) = 0
2x = 0 or 3x - 2 = 0
∴ x = 0 or x = 2/3
Then the y-coordinates are calculated by substituting these x values in the given function,
when x = 0;
f(0) = 2(0)³ - 2(0)² + 1 = 1
So, the point is (0, 1)
when x = 2/3;
f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27
So, the point is (2/3, 19/27)
Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.
So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.
Thus, option A is correct.
Learn more about the relative minimum and maximum here:
brainly.com/question/9839310
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Answer: 16 students receive passing grades out of those 16 , 11 Students receive perfect math & 8 perfect spelling
8 is you answer
Draw 16 circles that would rep the students
Count up to 11 with 1 mark in each bubble that would rep the perfect math
Then count 8 and put 1 Mark in the Bubble and you'll see that 8 Students Received 2 Awards
Step-by-step explanation:
Answer:
Cleanser that costs 50 cents is 1400 liters, Cleanser that costs 80 cents is 600 liters.
Step-by-step explanation:
We can solve this by using <em>simultaneous equations</em>:
- Let us express the question in terms of equations
Let a be cleanser at 50 cents and let b be the cleanser at 80 cents.
Equation 1: 0.5a + 0.8b = 0.59(a+b)
Equation 2: a + b = 2000
From equation 2, a = 2000 - b (Let's call this equation 3)
2. Substituting equations 2 and 3 in Equation 1:
0.5a + 0.8b = 0.59(a+b)
0.5(2000 - b) + 0.8b = 0.59(2000)
1000 - 0.5b + 0.8b = 1180
0.3b = 180
b = 600
Substitute in equation 3:
a = 2000 - 600
a = 1400
As a note, I formed equation 1 because I know for a fact the cost per liter of a and b. I also know it is sold at 0.59 cents per liter. We are selling 2000 liters in this instance, therefore 0.59(2000) = 1180, which in this case is the selling price.
