The given pentagon can be divided into two figures : a triangle and rectangle as shown in figure.
Let us find area of each figure separately.
Triangle:
Area of triangle is given by:
where b=base and h=height
Height of triangle :
h=(3x+5)-(2x+1)
h=x+4
Base = 2x-2
Area of triangle= (x-1)(x+4) = x²+3x-4
Area of rectangle:
Area of rectangle is given by:
A=l*b
Area of rectangle = 4x²-2x-2
Area of pentagon = Area of triangle + Area of rectangle
Area of pentagon = x²+3x-4 + 4x²-2x-2
Area of pentagon = 5x²+x-6
If area of pentagon is 42 cm², then solving for x,
Factorising to get x,
x=-3.2 and x=3
If we take x as negative the side will be negative, so we neglect x=-3.2
So x=3 is the answer.
Hey there! I'm happy to help!
Imagine the line that is created when you connect the two points (the distance between the two points).
You can create a right triangle where this distance is the hypotenuse where the two legs are the change in x and y. So, if you take those changes in x and y, you can use the Pythagorean Theorem (a²+b²=c²) to find the distance between the two points, which is the hypotenuse.
Our change in x is 9 because 9-0 is 9.
We square it
9²=81
Our change in y is 5 as -1-(-6) or -1+6 is 5.
5²=25
We add these.
81+25=106
We square root and round to the nearest tenth.
√106≈10.3
So, our distance is 10.3.
This Pythagorean Theorem method actually gives us a formula called the distance formula that you can use to find the distance between points.
Have a wonderful day and keep on learning! :D
I believe a is the second and fourth options and b is the first and third
Answer:
Option A is correct.
The Solutions can be found for the equation 4x − 8 − 4x = 9 is, Zero
Step-by-step explanation:
Given the equation:
Like terms are those terms which have same variable to the same power.
Combine like terms;
⇒The equation does not have any solution
Therefore, the Solutions can be found for the equation 4x − 8 − 4x = 9 is, Zero
Answer:
2nd option is the correct answer
Step-by-step explanation:
3 times a number decreased by 6 is - 2
