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3 years ago

If 2 is one root of the equation 4x3 + kx - 24 = 0, then the value of k is

Mathematics

1 answer:

Leokris [45]3 years ago

3 0

Answer:

Step-by-step explanation:

We are given the equation:

$\displaystyle 4x^3 + kx - 24 = 0$

And that x = 2 is a root. And we want to determine the value of k.

By definition, since x = 2 is a root of the equation, when x = 2, the equation must equal zero:

$\displaystyle 4(2)^3 + k(2) - 24 = 0$

Solve for k:

$\displaystyle \begin{aligned} 4(2)^3 + k(2) - 24 & = 0 \\ \\ 32 + 2k - 24 & = 0 \\ \\ 2k + 8 & = 0 \\ \\ k & = - 4\end{aligned}$

Hence, the value of k is -4.

In conclusion, our answer is B.

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Y_Kistochka [10]

1. I feel the need to explain things first before I write the numeric value.
Let x be the total number of students in the school. 25% of this value is given to be 35.
(0.25)x = 35
The value of x is 140. 75% of this value is the answer which is equal to 105.

2. Let y be the alternative schools. With this, the number of charter schools is 2x - 6 which is equal to 52
2x - 6 = 52
The value of x is 29. Therefore, there are 29 charter schools.

4 0

4 years ago

An architect is designing square windows with an area of(x2 + 16x +64) ft?. The dimensions of the

Darina [25.2K]

A) The dimensions are (x+10) by (x+10).

B) The perimeter is given by 4x+40.

C) The perimeter when x is 4 is 56.

The quadratic can be factored by finding factors of c, the constant, that sum to b, the coefficient of x. Our c is 100 and our b is 20; we want factors of 100 that sum to 20. 10*10=100 and 10+10=20, so those are what we need. This gives us (x+10)(x+10 for the factored form.

Since the dimensions are all (x+10), and there are 4 sides, the perimeter is given by 4(x+10). Using the distributive property we have 4*x+4*10=4x+40.

To find the perimeter when x=4, substitute 4 into our perimeter expression:

4*4+40=16+40=56.

6 0

3 years ago

Read 2 more answers

Solve the system of linear equations.

sweet-ann [11.9K]

Answer:

dependent system
x = 2 -a
y = 1 +a
z = a

Step-by-step explanation:

Let's solve this by eliminating z, then we'll go from there.

Add 6 times the second equation to the first.

(3x -3y +6z) +6(x +2y -z) = (3) +6(4)

9x +9y = 27 . . . simplify

x + y = 3 . . . . . . divide by 9 [eq4]

Add 13 times the second equation to the third.

(5x -8y +13z) +13(x +2y -z) = (2) +13(4)

18x +18y = 54

x + y = 3 . . . . . . divide by 18 [eq5]

Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:

y = 3 -x . . . . solve eq5 for y

x +2(3 -x) -z = 4 . . . . substitute into the second equation

-x +6 -z = 4

x = 2 - z . . . . . . add x-4

y = 3 -(2 -z)

y = z +1

So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...

x = 2 -a

y = 1 +a

z = a

_____

Check

First equation:

3(2-a) -3(a+1) +6a = 3

6 -3a -3a -3 +6a = 3 . . . true

Second equation:

(2-a) +2(a+1) -a = 4

2 -a +2a +2 -a = 4 . . . true

Third equation:

5(2-a) -8(a+1) +13a = 2

10 -5a -8a -8 +13a = 2 . . . true

Our solution checks algebraically.

6 0

3 years ago

Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Castel can dig the same hole in six hours. How long will it tak

aleksley [76]

.
Rates:
Ryan: 1 hole per 5 hours
Castel: 1 hole per 6 hours
.
Let x = time if working together
then
x(1/5 + 1/6) = 1
x(6 + 5) = 30
11x = 30
x = 30/11
x = 2.7273 hours
or
x = 2 hours and 44 minutes

3 0

3 years ago

Read 2 more answers

If a theater holds 1800 and sells 1/3 of its seats how many tickets does it sell

kozerog [31]

Hey!

A theater holds 1,800 seats. It sells 1/3 of it. That means you have to find 1/3 of 1,800

$\frac{1800}{1} \times \frac{1}{3} = \frac{1800}{3} = 600$

That means the theater sells 600 seats.

$\framebox{Answer = 600 seats}$

7 0

4 years ago