Hello!
Simplifying
5x2 + -7x + -3 = 8
Reorder the terms:
-3 + -7x + 5x2 = 8
Solving
-3 + -7x + 5x2 = 8
Solving for variable 'x'.
Reorder the terms:
-3 + -8 + -7x + 5x2 = 8 + -8
Combine like terms: -3 + -8 = -11
-11 + -7x + 5x2 = 8 + -8
Combine like terms: 8 + -8 = 0
-11 + -7x + 5x2 = 0
Begin completing the square. Divide all terms by
5 the coefficient of the squared term:
Divide each side by '5'.
-2.2 + -1.4x + x2 = 0
Move the constant term to the right:
Add '2.2' to each side of the equation.
-2.2 + -1.4x + 2.2 + x2 = 0 + 2.2
Reorder the terms:
-2.2 + 2.2 + -1.4x + x2 = 0 + 2.2
Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2
Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2
The x term is -1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.
Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49
Reorder the terms:
0.49 + -1.4x + x2 = 2.2 + 0.49
Combine like terms: 2.2 + 0.49 = 2.69
0.49 + -1.4x + x2 = 2.69
Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 2.69
Calculate the square root of the right side: 1.640121947
Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.
Subproblem 1
x + -0.7 = 1.640121947
Simplifying
x + -0.7 = 1.640121947
Reorder the terms:
-0.7 + x = 1.640121947
Solving
-0.7 + x = 1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7
Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7
Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947
Simplifying
x = 2.340121947
Subproblem 2
x + -0.7 = -1.640121947
Simplifying
x + -0.7 = -1.640121947
Reorder the terms:
-0.7 + x = -1.640121947
Solving
-0.7 + x = -1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7
Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.640121947 + 0.7
x = -1.640121947 + 0.7
Combine like terms: -1.640121947 + 0.7 = -0.940121947
x = -0.940121947
Simplifying
x = -0.940121947
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, -0.940121947}
2x + 9 = -65
2x = -65 - 9
2x = -74
x = -74/2
x = -37
So, your final answer is -37
Hope this helps!
Answer:
1 pink marble
Step-by-step explanation:
If Jamie selected 10 times the pink marble in a total of 420 tries, we can assume that the proportion of pink marble in the total number of marbles is:
10 / 420 = 1/42
So to predict a good number of pink marbles in the total 40 marbles, we just need to multiply the 40 marbles by the proportion found above:
pink marble = 40 * (1/42) = 0.9524
As this number needs to be a whole number, a good assumption is that there is 1 pink marble in the 40 marbles.
Answer:
Last choice. d.
Step-by-step explanation:
We are given the first term and the sixth term.
The first term is 
.
The sixth them is 
.
Let's solve for the common ratio, r.
Divide both sides by -9:
Take the fifth root of both sides:
So the common ratio is 4.
Answer:
A cross section is a surface or shape that is exposed by making a straight cut through something especially at right angles to an axis.
