Answer:
r = 2.5
Step-by-step explanation:
x is directly proportional to y. This can be written as,
x ∝ y
In terms of constant, the proportionality can be written as,
x = ry
Where r is the constant. The table has a set of values for x and y. Let's substitute the values in the first row into the equation with the constant.
10 = r × 4
r = 
r = 2.5
Lets check with the second row.
12.5 = r × 5
r = 
r = 2.5
Since both sets of values have the same answer for the constant, this means that the third row of values should probably have the same constant.
r = 2.5
In this item, we are not given with the figure but knowing that these lines ought to be perpendicular then we will be able to derive the relationship between the slopes of the line.
The slopes of the perpendicular line are the negative reciprocals of one another. If we represent the slopes of the lines as m₁ and m₂, the relationship can be written in the form,
(m₁)(m₂) = -1
We are given with one of the slopes. To determine the value of the second slope then,
m₂ = -1/m₁
m₂ = -1/(2/5)
m₂ = -5/2
<em>ANSWER: m₂ = -5/2</em>
Answer:
x² + y² = 42.25
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ← r is the radius
here r = 6.5, hence
x² + y² = 6.5², that is
x² + y² = 42.25 ← equation of circle
Answer:
Step-by-step explanation:
<u>Diagonal of a Square</u>
Given a square of length side a, the length of the diagonal is
The diagonal of a rectangle of sides x and y is
The sides have lengths 12 cm and 14 cm, the diagonal is
Since this value is the same of the diagonal of certain square, we can say
Dividing by 
Answer:
Step-by-step explanation:
In point slope form, the equation is y-7=(-10/3)(x+9). In slope-intercept form, it is y=(-10/3)x-23.
First find the slope of the line. The formula for slope is
m=(y₂-y₁)/(x₂-x₁)
Using our points, we have
m=(-3-7)/(-6--9) = -10/3
Plug this into point slope form:
y-y₁=m(x-x₁)
y-7=(-10/3)(x--9)
y-7=(-10/3)(x+9)
Using the distributive property:
y-7=(-10/3)*x+(-10/3)*9
y-7=(-10/3)x-90/3
y-7=(-10/3)x-30
Add 7 to both sides:
y=(-10/3)x-23
