Answer:
a = 1
Step-by-step explanation:
Given the point (a, 3) is on the line: 5x + y = 8.
Any point on the line satisfies the equation.
So, (a, 3) should satisfy the equation 5x + y = 8
Substituting x = a and y = 3, we get:
5(a) + 3 = 8
⇒ a = 1
Therefore, (1, 3) is the point on the line.
1/√2
Step-by-step explanation:
Imagine a right-angled triangle, for e.g. Triangle ABC,
Where
B = 90°
Remember your Toa Cah Soh.
sin 45° = opposite / hypotenuse
If theta = 45°
Angles A and C = 45° (Sum of angles in a triangle equal = 180°)
Since theta are the same, we can also deduce that the length AB and BC are the same.
Take for example AB = BC = 1 = opposite
By the Pythagorean theorem,
AB² + BC² = AC²
1² + 1² = AC²
2 = AC²
AC = √2 = hypotenuse
Therefore:
sin 45° = opposite / hypotenuse
sin 45° = 1/√2
Let length = l
width = w
length = 3 times width = 3w
Area of the land = 75 sq. m
Area = length × width = 3w×w = 75
3w²=75
w²=25
w=5 m
length = 3×15 = 15m
Now lets make the figure with the path of width x meters
(Refer the attached figure for easy understanding)
The inner length is the length of the rectangle reduced by x meters on either side due to the path
that is 15-x-x = 15-2x
the inner width is the width reduced by x meters in either side
= 5-x-x = 5-2x
Now lets calculate the inner area = inner length × inner width
(15-2x)×(5-2x)
= 
= 
sq. m
Now the function to calculate the cost
f(x) is given by $3.00 × area of the inner land
f(x) = 3 × {75-40x+4x²)
= 225-120x+12x²
or
= 12x²-120x+225
Answer:y=7
Step-by-step explanation:
Average rate of change is just the slope between the 2 points
we can do this the long way or the smart way
long way, find the 2 points and find the slope between them
when x=-5, f(-5)=-2(-5)+1=10+1=11
when x=1, f(1)=-2(1)+1=-2+1=-1
so the points are (-5,11) and (1,-1)
the slope between them is (-1-11)/(1-(-5))=(-12)/(1+5)=-12/6=-2
the answer is B, -2
smart way
recognize that that is a linear equation and the slope between any 2 points will be the m in y=mx+b
f(x)=-2x+1
the slope is -2
the average rate of change is -2
answer is B. -2
