Solve for x over the real numbers:
2 x^2 - 4 x - 3 = 0
Divide both sides by 2:
x^2 - 2 x - 3/2 = 0
Add 3/2 to both sides:
x^2 - 2 x = 3/2
Add 1 to both sides:
x^2 - 2 x + 1 = 5/2
Write the left hand side as a square:
(x - 1)^2 = 5/2
Take the square root of both sides:
x - 1 = sqrt(5/2) or x - 1 = -sqrt(5/2)
Add 1 to both sides:
x = 1 + sqrt(5/2) or x - 1 = -sqrt(5/2)
Add 1 to both sides:
Answer: x = 1 + sqrt(5/2) or x = 1 - sqrt(5/2)
with the pythagorean theorem

using the formula of the quadratic equation

the length cannot be negative, therefore x=7
length of the shorter leg is: 7ft
length of the longer leg is: 3+3(7)= 24ft
length of the hypotenuse is: 4+3(7)= 25ft
Answer:
some information is missing, so I looked for similar questions and found the attached image:
since each recipe requires ¹/₂ cup of butter, you are able to make 12 ÷ ¹/₂ = 24 recipes with one container of butter (assuming you have all the other ingredients).
One-half, ¹/₂, is a fraction that can also be written in decimal form as 0.5. Two times ¹/₂ is equal to 1, and similarly, twenty four times ¹/₂ is equal to 12.
Answer:
the slope is -8/5
Step-by-step explanation:
we need to get the equation in the form
y= mx+b where m is the slope and b is the y intercept
8x + 5y =40
subtract 8x from each side
8x-8x + 5y = -8x +40
5y = -8x+40
divide each side by 5
5y/5 = -8x /5 + 40/5
y = -8/5 x +8
the slope is -8/5 and the y intercept is 8
Answer:
Step-by-step explanation:
2x+90=7x
2x=7x-90
2x-7x=-90
-5x+-90
x=18