Answer:
y = -x + 5
y = x/2 + 3/2
Step-by-step explanation:
First we calculate the slope as difference between coordinates
a) P₁ ( -1 , 6 ) P₂ ( 3 , 2 )
m = Δy/Δx ⇒ m = ( y₂ - y₁ ) / ( x₂ - x₁ ) ⇒ m = (2 -6 ) / (3 -(-1))
m = -4 /4
m = -1
Now we have:
y - y₁ = m ( x - x₁ ) ⇒ y - 6 = (-1) ( x - (-1))
y - 6 = -1 * ( x + 1 ) ⇒ y - 6 = - x - 1
y = -x + 5
In the second case
Q₁ ( -3 , 0 ) Q₂ ( 5 , 4 )
Again we calculate the slope
m = Δy / Δx ⇒ m = ( 4 - 0 ) / ( 5 - (-3)) ⇒ m = 4 / 8 ⇒ m = 1/2
m = 1/2 or x = 0,5
And
y - y₁ = 1/2 ( x - x₁ ) ⇒ y - y₁ = 1/2 ( x - (-3)) ⇒ y - 0 = 1/2 * x + 3/2
y = x/2 + 3/2
Answer:
2(4x + 1)(x + 1)
Step-by-step explanation:
Given
8x² + 10x + 2 ← factor out 2 from each term
= 2(4x² + 5x + 1)
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 1 = 4 and sum = + 5
The factors are + 1 and + 4
Use these factors to split the x - term
4x² + x + 4x + 1 ( factor the first/second and third/fourth terms )
= x(4x + 1) + 1 (4x + 1) ← factor out (4x + 1)
= (4x + 1)(x + 1), thus
4x² + 5x + 1 = (4x + 1)(x + 1) and
8x² + 10x + 2 = 2(4x + 1)(x + 1) ← in factored form
Answer:
D.) 0.9990
Step-by-step explanation:
Given :
Number of questions = 10
True or False questions ; probability of success, p = 1/2 = 0.5
Using binomial distribution :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
Probability of getting atleast one correct answer :
P(x ≥ 1) = p(1) + p(2) +... P(x = 10)
Using a binomial probability calculator :
P(x ≥ 1) = 0.9990
Let t = the number of days the mouse travels
Let D = the distance that the mouse traveled
The mouse travels at a rate of 1.5 miles per day, so R = 1.5 mi/day
The equation is:
Distance (D) = Rate (R) x Time (t)
SO:
Distance (D) = 1.5 mi./day X Time (t)
January : 31 days.
February : February is the second and shortest month of the year in the Julian and Gregorian calendar with 28 days in common years and 29 days in leap years, with the quadrennial 29th day being called the leap day. It is the first of five months to have a length of less than 31 days, and the only month to have less than 30 days
March : 31 days.
April : 30 days.
May : 31 days.
June : 30 days.
July : 31 days.
August : 31 days.
Septembers : 30 days.
October : 31 days.
November : 30 days.
December : 31 days.
Hope this helps!
