Answer:
The distance between the points is approximately 6.4
Step-by-step explanation:
The given coordinates of the points are;
(2, -2), and (6, 3)
The distance between two points, 'A', and 'B', on the coordinate plane given their coordinates, (x₁, y₁), and (x₂, y₂) can be found using following formula;

Substituting the known 'x', and 'y', values for the coordinates of the points, we have;

Therefore, the distance between the points, (2, -2), and (6, 3) = √(41) ≈ 6.4.
Answer:
x=−2
Step-by-step explanation: Step 1: Simplify both sides of the equation.
3(x−5)−3=5(x−2)+2x
(3)(x)+(3)(−5)+−3=(5)(x)+(5)(−2)+2x(Distribute)
3x+−15+−3=5x+−10+2x
(3x)+(−15+−3)=(5x+2x)+(−10)(Combine Like Terms)
3x+−18=7x+−10
3x−18=7x−10
Step 2: Subtract 7x from both sides.
3x−18−7x=7x−10−7x
−4x−18=−10
Step 3: Add 18 to both sides.
−4x−18+18=−10+18
−4x=8
Step 4: Divide both sides by -4.
−4x
−4
=
8
−4
x=−2
Answer:
(a) The slope of f(x) is greater than the slope of g(x)
(b) f(x) has a greater y intercept
Step-by-step explanation:
Given


Solving (a): Compare the slopes
The slope (m) of f(x) is calculated as;

This gives:


Substitute values for f(0) and f(1)



The slope of g(x) can be gotten using the following comparison


So:



Solving (b): Compare the y intercept
y intercept is when 
From the table of f(x)

From the equation of g(x)



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Answer:
? = 4.29
Step-by-step explanation:
Remark
Let x be the question mark. You get the proportionality by using the dimensions of the little triangle to the dimensions of the large triangle.
Equation
14/(14+ 4) = 15/(x + 15) Combine like terms on the left
14/18 = 15/(x + 15) Cross multiply
14*(x + 15) = 18 * 15 Simplify the right
14(x + 15) = 270 Divide by 14
x + 15 = 270 / 14
x + 15 = 19.29 Subtract 15 from both sides
x = 19.29 - 15
x = 4.29
Answer:
y = 
Step-by-step explanation:
Given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 5 when x = 6
k =
= 
y =
x ← equation of variation
When x = 5, then
y =
× 5 = 