Answer: x = 8/5
Explanation:
5x-2 = 6
5x = 6 + 2
5x = 8
x = 8/5
Answer:
the classmate is incorrect
Step-by-step explanation:
when you do the math for both inequalities they are equal to each other, despite the fact that one has multiplication and the other has addition.
Answer:
x = -3 and x = -3/2
Step-by-step explanation:
After writing down the polynomial, split it; put a line between 3x^2 and -18x. Look and 2x^3 + 3x^2 and -18x - 27 separately and factor them both:
p(x) = 2x^3 + 3x^2 <u>- 18x -27</u>
p(x) = x^2(2x+3) <u>-9(2x+3)</u>
Now notice how x^2 and -9 have the same factor (2x+3). That means x^2 and -9 can go together:
p(x) = (x^2 - 9)(2x+3)
Factor it once more because there's a difference of squares:
p(x) = (x+3)(x-3)(2x+3)
Now just plug in whatever makes the each bracket equal 0:
x = -3, x = 3, and x = -3/2
Those are your zeros.
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y = 7x - 4x²
<span>7x - 4x² = 0 </span>
<span>x(7 - 4x) = 0 </span>
<span>x = 0, 7/4 </span>
<span>Find the area of the bounded region... </span>
<span>A = ∫ 7x - 4x² dx |(0 to 7/4) </span>
<span>A = 7/2 x² - 4/3 x³ |(0 to 7/4) </span>
<span>A = 7/2(7/4)² - 4/3(7/4)³ - 0 = 3.573 </span>
<span>Half of this area is 1.786, now set up an integral that is equal to this area but bounded by the parabola and the line going through the origin... </span>
<span>y = mx + c </span>
<span>c = 0 since it goes through the origin </span>
<span>The point where the line intersects the parabola we shall call (a, b) </span>
<span>y = mx ===> b = m(a) </span>
<span>Slope = m = b/a </span>
<span>Now we need to integrate from 0 to a to find the area bounded by the parabola and the line... </span>
<span>1.786 = ∫ 7x - 4x² - (b/a)x dx |(0 to a) </span>
<span>1.786 = (7/2)x² - (4/3)x³ - (b/2a)x² |(0 to a) </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (b/2a)a² - 0 </span>
<span>1.786 = (7/2)a² - (4/3)a³ - b(a/2) </span>
<span>Remember that (a, b) is also a point on the parabola so y = 7x - 4x² ==> b = 7a - 4a² </span>
<span>Substitute... </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (7a - 4a²)(a/2) </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (7/2)a² + 2a³ </span>
<span>(2/3)a³ = 1.786 </span>
<span>a = ∛[(3/2)(1.786)] </span>
<span>a = 1.39 </span>
<span>b = 7(1.39) - 4(1.39)² = 2.00 </span>
<span>Slope = m = b/a = 2.00 / 1.39 = 1.44</span>
What the question and read the problem again please
