Answer:
The new area is 1800feet^2
Step-by-step explanation:
Step one:
Given data
The length and width or a rectangular courtyard is 40 feet and 30 feet
we can calculate the area of the courtyard as
Area= 40*30
Area= 1200 feet^2
when the extra 15 feet is added to the width
the new width is= 30+15= 45feet
The new area is
Area= 40*45
Area= 1800 feet^2
in all the area will increase by 1800-1200= 600feet
The length of the rope needed is 15 feet
Given the following parameters;
- Height of the pole = 9 foot
- The distance from the <u>rope away from the base </u>of the pole is 12 feet
Required
To get the length of the rope, you will use the pythagoras theorem expressed as:
Substituting the given parameters:
c² = 9² + 12²
c² =81 + 144
c² = 225
c = √225
c = 15 feet
Therefore the length of the rope needed is 15 feet
Learn more on Pythagoras theorem here: brainly.com/question/231802
Answer:
Step-by-step explanation:
f-1(x) is the inverse of f(x)
to find the inverse let’s set the equation up like this
y = 4x -2
now we’ll switch x and y
x = 4y -2
and solve for y
x + 2 = 4y
x/4 + 2/4 = y
the inverse is
y = x/4 + 1/2
this equation is written in y = mx + b form
where b = y intercept
so the y intercept is 1/2
Let's see what the options look like when we multiply the expressions in brackets:
(first, i multiply both parts of the second bracked by the first part of the first bracket, and then the same with the second part of the first bracket:
<span>(1) (3x - 3)(x - 2))
3x2 +6x -3x +6// this is not correct
(2) (3x + 3)(x - 2) </span>
3x2-6x+3x-6//this is not correct
(3)
3(x + 1)(x - 2)
3(x2-2x+x-2)//simplifying:
3(x2-x-2)//multiplying:
3x2-3x-6)
- so this is not correct either
(4) 3(x - 1)(x - 2)
3(x2-2x - x + 2)
3(x2-3x +2)
3x2-9x +6 - well, here is our winner!
