Answer:
B) x = 3 or x = -5/2
Step-by-step explanation:
Solve for x over the real numbers:
2 x^2 - x = 15
Subtract 15 from both sides:
2 x^2 - x - 15 = 0
x = (1 ± sqrt((-1)^2 - 4×2 (-15)))/(2×2) = (1 ± sqrt(1 + 120))/4 = (1 ± sqrt(121))/4:
x = (1 + sqrt(121))/4 or x = (1 - sqrt(121))/4
sqrt(121) = sqrt(11^2) = 11:
x = (1 + 11)/4 or x = (1 - 11)/4
(1 + 11)/4 = 12/4 = 3:
x = 3 or x = (1 - 11)/4
(1 - 11)/4 = -10/4 = -5/2:
Answer: x = 3 or x = -5/2
Answer:
Yes
Step-by-step explanation:
Answer:
- 2 + 1i
Step-by-step explanation:
A complex number x + yi can be expressed in coordinate form as
x + yi → (x, y ), thus
- 7 + 4i → (- 7, 4 )
3 - 2i → (3, - 2 )
Given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
Here (x₁, y₁ ) = (- 7,4) and (x₂, y₂ ) = (3, - 2 )
midpoint = [ 0.5(- 7 + 3), 0.5(4 - 2) ] = [0.5(- 4), 0.5(2) ] = (- 2, 1 )
and (- 2, 1 ) → - 2 + 1i → - 2 + i
Answer:
27/31
Step-by-step explanation:
FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31
Answer:
Width = 7 cm
Length = 15 cm
Step-by-step explanation:
Let width = w
Length = w + 8
Area of rectangle = 105 sq. cm
length * breadth = 105
(w + 8)*w = 105
Use distributive property
w² + 8w = 105
w² + 8w - 105 = 0
Sum = 8
Product = -105
Factors = 15 , -7 {15 +(-7) = 8 & 15*(-7) = -105}
w² - 7m + 15m - 105 = 0
w(w - 7) + 15(m - 7) = 0
(w - 7)(w + 15) = 0
Ignore w + 15= 0 as measurements will not be in negative value
w - 7 = 0
w = 7
Width = 7 cm
Length = 7 + 8 = 15 cm