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3 years ago

What is (1/4) to the fourth power

Mathematics

1 answer:

dolphi86 [110]3 years ago

3 0

$\frac{1}{4} ^4= \frac{1}{256}$

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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

_____

<em>Check</em>

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

Solving for Y. Write the following equations in slope-intercept form.

asambeis [7]

1) 3x - 2y = -16 Subtract 3x from both sides
-2y = -3x - 16 Divide both sides by -2
y = $\frac{3}{2}$ x + 8

2) 9x - 7y = -7 Subtact 9x from both sides
-7y = -8x - 7 Divide both sides by -7
y = $\frac{8}{7}$ + 1

3) x - 3y = 6 Subtract x from both sides
-3y = -x + 6 Divide both sides by -3
y = $\frac{1}{3}$ - 2

4 0

3 years ago

P(A) = 0.14. P(B) = 0.24, and P(A and B) = 0.19. Find P(A given B). Round your

Ket [755]

Answer: The required probability is 0.79

Step-by-step explanation:

Given: P(A) = 0.14

P(B) = 0.24

P(A and B) = 0.19

To find: P(A given B)

The conditional probability of an event A is the probability that the event will occur given the knowledge of an already occurred event B and is denoted by

$P(A/B)$ or $P(A \text { given } B)$ where the value of $P(A/B)= \dfrac{P(A \text { and } B)}{P(B)}$