Step-by-step explanation:
Simplifying 4x4 + -12x2 + 8 = 0 Reorder the terms: 8 + -12x2 + 4x4 = 0 Solving 8 + -12x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -3x2 + x4) = 0 Factor a trinomial. 4((1 + -1x2)(2 + -1x2)) = 0 Factor a difference between two squares. 4(((1 + x)(1 + -1x))(2 + -1x2)) = 0 Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1
Solution
x = {-1.414213562, 1.414213562, -1, 1}
Answer: The next number in the given pattern is 11.
Step-by-step explanation: We are given to find the next number in the following pattern :
1 5 3 7 5 9 7 . . .
Let a(n) denotes the n-th number of the give pattern.
Then, we see the following rule if followed by the consecutive terms :
Therefore, the next term will be the sum of the 7-th number and 4. That is
Thus, the next number in the given pattern is 11.
Answer:
x=24,50n+30,00m
Step-by-step explanation:
In this equation n stands for the total amount of shirts sold and m for the total amount of jeans sold.
Based on the calculations, the equation of the triangle's line of symmetry is equal to: B. y = x - 1.
<h3>How to determine the equation of the triangle's line of symmetry?</h3>
First of all, we would determine the midpoint where the line of symmetry passes through points A and B:
Midpoint at point A = (3 + 7)/2 = 10/2 = 5.
Midpoint at point B = (6 + 2)/2 = 8/2 = 4.
Point D = (5, 4)
Mathematically, the standard equation of a line is given by y = ax + b.
D(5, 4); 4 = 5a + b ....equation 1.
C(4, 3); 3 = 4a + b ....equation 2.
Subtracting eqn. 2 from eqn. 1, we have:
1 = a
Next, we would find the value of b:
4 = 5a + b
4 = 5(1) + b
b = 4 - 5
b = -1.
Therefore, the equation of the triangle's line of symmetry is given by:
y = ax + b
y = x(1) + (-1)
y = x - 1.
Read more on line of symmetry here: brainly.com/question/10152876
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