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Marysya12 [62]
2 years ago
8

Find the value of k such that x-2 is a factor of 3x³-kx²+5x+k​

Mathematics
1 answer:
Nuetrik [128]2 years ago
6 0

Answer:

\displaystyle k = \frac{34}{3}

Step-by-step explanation:

We are given the polynomial:

\displaystyle P(x) = 3x^3 - kx^2 + 5x + k

And we want to determine the value of <em>k</em> such that (<em>x</em> - 2) is a factor of the polynomial.

Recall that the Factor Theorem states that a binomial (<em>x</em> - <em>a</em>) is a factor of a polynomial P(x) if and only if P(a) = 0.

Our binomial factor is (<em>x</em> - 2). Thus, <em>a</em> = 2.

Hence, by the Factor Theorem, P(2) must equal zero.

Find P(2):

\displaystyle \begin{aligned} P(2) &= 3(2)^3 - k(2)^2 + 5(2) + k \\ \\ &= 3(8) - 4k + 10 + k \\ \\ &= 34 - 3k  \end{aligned}

This must equal zero. Hence:

\displaystyle \begin{aligned} 34 - 3k &= 0 \\ \\ -3k &= -34 \\ \\ k = \frac{34}{3}  \end{aligned}

In conclusion, <em>k</em> = 34/3.

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Step-by-step explanation:

n/12=10

n=10*12

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You purchased concentrated cleaner that must be diluted (watered down)
abruzzese [7]

Answer:

The volume of the concentrated 80 gallons mixture is 20 gallons

The volume of water in the 80 gallons mixture is 60 gallons

Step-by-step explanation:

The given parameters are;

The content of Container A = The cleaner

The concentration of the cleaner = 20% solution

The content of Container B = Pure water

The concentration of the desired solution = 5%

The volume of the required solution = 80 gallons

Let x represent the volume of the concentrated solution and y represent the volume of water in the 80 gallons mixture

Therefore, we have;

20/100 × x + y×0 = 5/100×80

x + y = 80

y = 80 - x

20/100 × x + (80 - x)×0 = 5/100×80

0.2·x = 4

x = 4/0.2 = 20

x = 20 gallons

y = 80 - x = 80 - 20 = 60

y = 60 gallons

The volume of the concentrated solution (80 gallons mixture) = x = 20 gallons

The volume of water in the 80 gallons mixture = y = 60 gallons.

8 0
3 years ago
Which is bigger 5miles and 8 ft or 8,800yards
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3. What are the intersection points of the line whose equation is y=3x +3 and the
densk [106]

Answer:

Points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

Step-by-step explanation:

Equation of the circle → (x - 2)² + y² = 25 ---------(1)

                                   → (x - 2)² + (y - 0)² = 5²

By comparing this equation with the standard equation of the circle,

(x - a)² + (y - b)²= r²

Here (a, b) is the center and r is the radius of the circle.

Therefore, center of the circle is (2, 0) and radius = 5 units

Second equation is a linear equation → y = 3x + 3 -------(2)

x-intercept of the equation → x = -1

y-intercept of the equation → y = 3

By graphing these equations we can get the point of intersections.

Solving these equations algebraically,

Substitute the value of y from equation (2) in the equation (1),

(x - 2)² + (3x + 3)² = 25

x² - 4x + 4 + 9x² + 18x + 9 = 25

10x² + 14x - 12 = 0

5x² + 7x - 6 = 0

x = \frac{-7\pm \sqrt{7^2-4(5)(-6)}}{2(5)}

x = \frac{-7\pm \sqrt{169}}{10}

x = \frac{-7\pm13}{10}

x = -2, 0.6

From equation (2),

y = -3, 4.8

Therefore, points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

6 0
3 years ago
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