m = 5 and n = 3
let f(x) = 2x³ - mx² + nx - 2 , then
f( - 1 ) = - 2 - m - n - 2 = - 12
f(2 ) = 16 - 4m + 2n - 2 = 0
Tidying up the 2 equations
- m - n = - 8 → (1)
- 4m + 2n = - 14 → ( 2)
multiply equation ( 1) by 2
- 2m - 2n = - 16 → ( 3 )
add ( 2 ) and ( 3 ) term by term
-6m = - 30 ⇒ m = 5 ( substitute m = 5 into (2 )
- 20 + 2n = - 14
2n = 6 ⇒ n = 3
Answer:
x=110, y=50
Step-by-step explanation:
Draw a line perpendicular to the base CD from point A. The point of intersection is E. Angle AED=90 degrees. This is a right angle triangle. A triangle has a total angle of 180 degrees. Angle DAE is then 180-(90+70) = 20. The bases of a trapezoid are parallel to each other, making angle EAB a right angle. Add 90 + 20, and you'll get 110 degrees. This is the value of x.
Draw another line perpendicular to the base CD, this time from point B. The point of intersection is F. Angle ABF is 90 degrees. Angle FBC is 130-90=40. Angle BFC is also 90 degrees. You once again find the difference of the numbers from 180. 180-(40+90)=180-130=50. y=50 degrees.
Answer: The number pi is an irrational number
Step-by-step explanation:
Pi is irrational because it will never end and at the same time doesnt have a pattern in which the numbers repeat. Here are some of the numbers in pi 3.14159265359
Answer:
Approximately 7.8 units
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
From the graph, we can see that A is (0,0). Let's let this be x₁ and y₁.
B is (-5,6). Let's let this be x₂ and y₂. So, substitute:
Simplify:
Square:
Add:
Take the square root. Use a calculator:
So, the distance between them is about 7.8 units.
And we're done!
Answer:
p=0.05882
Step-by-step explanation:
Probability is the likelihood of an event occurring.
-A standard deck of cards has 4 kings.
#After one card is removed, 51 remains of which 3 are kings:
Hence, the probability that the second card is king is 0.05882
