Answer:
x = 1 or x = -5/2
Step-by-step explanation:
Solve for x over the real numbers:
2 x^2 + 3 x - 2 = 3
Divide both sides by 2:
x^2 + (3 x)/2 - 1 = 3/2
Add 1 to both sides:
x^2 + (3 x)/2 = 5/2
Add 9/16 to both sides:
x^2 + (3 x)/2 + 9/16 = 49/16
Write the left hand side as a square:
(x + 3/4)^2 = 49/16
Take the square root of both sides:
x + 3/4 = 7/4 or x + 3/4 = -7/4
Subtract 3/4 from both sides:
x = 1 or x + 3/4 = -7/4
Subtract 3/4 from both sides:
Answer: x = 1 or x = -5/2
The last one. It's basically saying you're in God's hands.
Answer:
x = 6
Step-by-step explanation:
Since the line segment is an angle bisector then the following ratios are equal
= ( cross- multiply )
78(6x - 1) = 42(10x + 5) ← distribute parenthesis on both sides )
468x - 78 = 420x + 210 ( subtract 420x from both sides )
48x - 78 = 210 ( add 78 to both sides )
48x = 288 ( divide both sides by 48 )
x = 6
Answer:
(A)The area of the square is greater than the area of the rectangle.
(C)The value of x must be greater than 4
(E)The area of the rectangle is
Step-by-step explanation:
The Square has side lengths of (x - 2) units.
Area of the Square
The rectangle has a length of x units and a width of (x - 4) units.
Area of the Rectangle =
<u>The following statements are true:</u>
(A)The area of the square is greater than the area of the rectangle.
This is because the area of the square is an addition of 4 to the area of the rectangle.
(C)The value of x must be greater than 4
If x is less than or equal to 4, the area of the rectangle will be negative or zero.
(E)The area of the rectangle is
By definition of tangent,
tan(<em>A</em> - <em>π</em>/4) = sin(<em>A</em> - <em>π</em>/4) / cos(<em>A</em> - <em>π</em>/4)
Expand the numerator and denominator using the angle sum identities for sin and cos:
tan(<em>A</em> - <em>π</em>/4) = (sin(<em>A</em>) cos(<em>π</em>/4) - cos(<em>A</em>) sin(<em>π</em>/4)) / (cos(<em>A</em>) cos(<em>π</em>/4) + sin(<em>A</em>) sin(<em>π</em>/4))
Divide through everything on the right by cos(<em>A</em>) cos(<em>π</em>/4):
tan(<em>A</em> - <em>π</em>/4) = (sin(<em>A</em>) / cos(<em>A</em>) - sin(<em>π</em>/4) / cos(<em>π</em>/4)) / (1 + (sin(<em>A</em>) sin(<em>π</em>/4)) / (cos(<em>A</em>) cos(<em>π</em>/4)))
Simplify the sin/cos terms to tan:
tan(<em>A</em> - <em>π</em>/4) = (tan(<em>A</em>) - tan(<em>π</em>/4)) / (1 + tan(<em>A</em>) tan(<em>π</em>/4))
tan(<em>π</em>/4) = 1, so we're left with
tan(<em>A</em> - <em>π</em>/4) = (tan(<em>A</em>) - 1) / (1 + tan(<em>A</em>))
Replace tan(<em>A</em>) with -√15:
tan(<em>A</em> - <em>π</em>/4) = (-√15 - 1) / (1 - √15)
Then the last option is the correct one.