Consider the graph of f(x) = 2x 3 – 3x 2 – 14x. On a coordinate plane, a graph increases through (negative 2, 0) to (negative 1, 10), decreases through (0, 0) to (2, negative 24), and then increases through (3.5, 0) through (4, 20). Based on the graph, what is the solution to 2x 3 – 3x 2 ≥ 14x?
Answers
Answer:
Answer D
Step-by-step explanation:
Final answer:
The solution to the inequality 2x³ – 3x² – 14x ≥ 0, as indicated by the graph provided, is given by the intervals of x where the function is increasing. Therefore, the solution is comprised of the intervals [-2, -1] and [3.5, ∞].
Explanation:
The solution to 2x³ – 3x² ≥ 14x can be found by solving the inequality. First, let's rearrange the inequality to: 2x³ – 3x² – 14x ≥ 0. This equation represents where the function is positive (above the x-axis) on the graph. Therefore, we must identify the intervals of x where the function increases or decreases.
Based on the description of the graph, the function increases in the intervals (-2, -1) and (3.5, ∞) and decreases in the interval (-1, 3.5). So, the solution to the inequality would be the union of the intervals where the function increases: [-2, -1] U [3.5, ∞].
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Let X = lemonade
Let Y = peanuts
On Saturday, Marcus sold 5 more cups of lemonade than bags of peanuts
So, X = Y + 5 and he earned 7.05
Forming the equation.
[(Y+5)*0.75] + (Y*0.35) = 7.05
0.75Y + 3.75 + 0.35Y = 7.05
1.1Y = 7.05 - 3.75
1.1Y = 3.3
Y = 3
So the number of cups of lemonade is Y + 5 = 3 + 5 = 8
So there are 8 cups.
Answers
Answer:
total tip: 32.5*20/100=6.5
Step-by-step explanation:
Answers
8 (2 + y) - 2y = 22
16 + 8y - 2y = 22
6y = 22 - 16
6y = 6
y = 1
And x = 2 + y = 2 + 1 = 3
Therefore, in (x, y) format . . . (3, 1)
Answer:answer is 3,1 on plato
Step-by-step explanation:trust me I literally just took it and it says correct
3. Indicate whether each of the three reciprocal functions (cosecant, secant, and cotangent) is a periodic function. If so, state the period of each.
4. List the domain and range for the secant and cotangent functions. (Use "pi" for π.)
5. Compare the graphs of the cosecant and secant functions. How are they different? How are they similar?
Answers
Step-by-step explanation:
1. All the trigonometric values can be found using the unit circle. See attached table.
2. Graph:
desmos.com/calculator/10n7yrm3tm
3. All trig functions are periodic functions. The period of secant and cosecant is 2π. The period of cotangent is π.
4. Using the table from step 1 and the graph from step 2, secant has a domain of x ≠ pi/2, 3pi/2 and a range of x ≤ -1, x ≥ 1. Cotangent has a domain of x ≠ 0, pi, 2pi and a range of -∞ < x < ∞.
5. Graph:
desmos.com/calculator/tldiqt7qra
Cosecant has the same graph as secant shifted π/2 to the right. So they have different domains, but the same range.
Answers
You can do this because when you cut the rectangle in half with the diagonal, it forms a right triangle, making the diagonal the hypotenuse (c).
Diagonal: 62.48 inches
Answers
So all the numbers divisible by 8, 15, and 21 are all the multiples of 280.
The smallest 6-digit number is 100,000 .
100,000 / 280 = 357.1 , so the next whole-number multiple is the 358th one.
280 x 358 = 100,240 .
You can tell right away that this is the smallest one that qualifies,
because if you take away 280 and go to the next smaller multiple,
it won't have 6 digits anymore.