Linear equations are equations that have constant slopes
The linear equation that represents the table is (a) y = 7x +4
<h3>How to determine the linear equation</h3>
Start by calculating the slope (m) using:
So, we have:
Simplify
The equation is then calculated as:
So, we have:
Open the brackets
Hence, the linear equation that represents the table is (a) y = 7x +4
Read more about linear equations at:
brainly.com/question/14323743
A (4,8) and b (7,2) and let c (x,y)
A , B and C are col-linear ⇒⇒⇒ ∴ slope of AB = slope of BC
slope of AB = (2-8)/(7-4) = -2
slope of BC = (y-2)/(x-7)
∴ (y-2)/(x-7) = -2
∴ (y-2) = -2 (x-7) ⇒⇒⇒ equation (1)
<span>The distance
between two points (x₁,y₁),(x₂,y₂) = d
</span>
The ratio of AB : BC = 3:2
AB/BC = 3/2
∴ 2 AB = 3 BC
= <span>
eliminating the roots by squaring the two side and simplifying the equation
∴ 4 * 45 = (x-7)² + (y-2)² ⇒⇒⇒ equation (2)
substitute by (y-2) from equation (1) at </span><span>equation (2)
4 * 45 = 5 (x-7)²
solve for x
∴ x = 9 or x = 5
∴ y = -2 or y = 6
The point will be (9,-2) or (5,6)
the point (5,6) will be rejected because it is between A and B
So, the point C = (9,-2)
See the attached figure for more explanations
</span>
Answer: the radius is 2.61 cm
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
From the information given,
Volume = 156 cm³
Height = 7.3 cm
Therefore,
156 = 3.14 × r² × 7.3
156 = 22.922r²
r² = 156/22.922 = 6.81
Taking square root of both sides of the equation, it becomes
r = 2.61 cm
Looks like the PMF is supposed to be
which is kinda weird, but it's not entirely clear what you meant...
Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:
Next,
If
, then
, where we take the positive root because we know
can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that
can take on the values
,
, and
. At these values of
, we would have the same probability as we did for the respective value of
. That is,
Part (5) is incomplete, so I'll stop here.
I just realized I forgot a whole unit we did this year, but a(n)=5n-12
is the explicit form if that helps at all