Answer:
Center = (5, -2) and radius = √33
Step-by-step explanation:
The equation of a circle is given by the formula;
(x-a)² + (y-b)² = r² ; where (a,b) is the center of the circle and r is the radius of the circle.
In this case;
2x² - 20x + 2y² + 8y =40 ;
Dividing both sides of the equation by 2 we get;
x² - 10x + y² + 4y = 20
we can then use the completing the square on both x and y terms.
x² - 10x + y² + 4y = 20
x² + 2(-5)x + 25 + y² + 2(2) y + 4 = 20 +9 + 4
In standard form we get;
(x-5)² + (y+2)² = 33
Therefore;
Center = (5, -2) and radius = √33
Answer:
The measurements of the sides and angles of triangle ABC are the exact same as the measurements in the three images.
Step-by-step explanation:
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<span>The wallet contains 4 $1 bills, 4 $5 bills, and 4 quarters.
$1 </span>× 4 = $4
$5 × 4 = $20
$0.25 × 4 = $1
$4 + $20 = $24, $24 + $1 = $25.
Answer: the probability that a randomly selected Canadian baby is a large baby is 0.19
Step-by-step explanation:
Since the birth weights of babies born in Canada is assumed to be normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = birth weights of babies
µ = mean weight
σ = standard deviation
From the information given,
µ = 3500 grams
σ = 560 grams
We want to find the probability or that a randomly selected Canadian baby is a large baby(weighs more than 4000 grams). It is expressed as
P(x > 4000) = 1 - P(x ≤ 4000)
For x = 4000,
z = (4000 - 3500)/560 = 0.89
Looking at the normal distribution table, the probability corresponding to the z score is 0.81
P(x > 4000) = 1 - 0.81 = 0.19
So since -2, 0, 1 are the roots:
Therefore x = -2, x = 0 , x = 1
Implies that:
x = 2 x - 2 = 0
x = 0 x = 0
x = 1 x - 1 = 0
Therefore (x - 2)x(x - 1) = 0
(x - 2)(x - 1) = x(x - 1) - 2(x - 1) = x² - x - 2x + 2 = x² - 3x + 2
(x - 2)x(x - 1) = 0
(x - 2)(x - 1)x = 0
(x² - 3x + 2)x = 0
x*x² - x*3x + x*2 = 0
x³ - 3x² + 2x = 0
This is the polynomial with the least degree, because it possible for another polynomial with higher power to still have the same root.
x³ - 3x² + 2x = 0 is the polynomial.
I hope this helps.
