Answer:
Ann us correct. It's a quadratic function.
Step-by-step explanation:
Given equation is,
y = 3x(x - 7)
By converting this equation into the standard quadratic equation,
y = 3x² - 21x
Highest exponent of the polynomial equation is 2 (Exponent of highest degree variable x²). This decides that the given function is a quadratic function.
Therefore, Ann is correct. It's a quadratic function.
You have the correct answer. Nice work. If you need to see the steps, then see below
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First we need to find the midpoint of H and I
The x coordinates of the two points are -4 and 2. They add to -4+2 = -2 and then cut that in half to get -1
Do the same for the y coordinates: 2+4 = 6 which cuts in half to get 3
So the midpoint of H and I is (-1,3). The perpendicular bisector will go through this midpoint
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Now we must find the slope of segment HI
H = (-4,2) = (x1,y1)
I = (2,4) = (x2,y2)
m = (y2 - y1)/(x2 - x1)
m = (4 - 2)/(2 - (-4))
m = (4 - 2)/(2 + 4)
m = 2/6
m = 1/3
Flip the fraction to get 1/3 ---> 3/1 = 3
Then flip the sign: +3 ----> -3
So the slope of the perpendicular bisector is -3
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Use m = -3 which is the slope we found
and (x,y) = (-1,3), which is the midpoint found earlier
to get the following
y = mx+b
3 = -3*(-1)+b
3 = 3+b
3-3 = 3+b-3
0 = b
b = 0
So if m = -3 and b = 0, then y = mx+b turns into y = -3x+0 and it simplifies to y = -3x
So that confirms you have the right answer. I've also used GeoGebra to help confirm the answer (see attached)
Answer:
The expected value for an event with outcomes:
{x₁, x₂, ..., xₙ}
Each one with probability:
{p₁, p₂, ..., pₙ}
Is just:
Ev = x₁*p₁ + ... + xₙ*pₙ
here we have two outcomes:
x₁ = the object worths $25
x₂ = the object is worth $4.
Each one with probability p₁ and p₂ respectively, such that:
p₁ + p₂ = 1
Then the expected value is:
Ev = p₁*($25) + p₂*($4)
Now we want to know how should be the probabilities, such that buying the object for $16 is whort.
Well, the purchase will be whort if the expected value is larger than $16.
This is equivalent to:
p₁*($25) + p₂*($4) - $16 > $0
Knowing that:
p₁ + p₂ = 1
we can rewrite:
p₂ = 1 - p₁
replacing that in the above inequality we get:
p₁*($25) + ( 1 - p₁)*($4) - $16 > $0
Now we can solve this for p₁
p₁*($25 - $4) + $4 - $16 > $0
p₁*$21 - $12 > $0
p₁*$21 > $12
p₁ > $12/$21 = 0.571
The probability of the object being authentic should be larger than 0.571 to take the gamble.
Answer:
Height is 21cm
Step-by-step explanation:
Volume of the cylinder = 1029pi
Base area = 7x7xpi = 49pi
Therefor the height = 1029pi/49pi=1029/49 = 21cm
Answer:
15%
Step-by-step explanation:
A holiday is reduced from £540 to £459
Reduction = £540 - £459
= £81
Percentage reduction = reduction/initial amount x 100%
That’s £81/£540 x 100%
0.15 x 100%
15%
The percentage reduction in price is 15%