An = a1 + (n - 1)(d)
Where a1 is the first term and d is the common difference.
First find d, the common difference.
24, ____, 32
a3 a4 a5
Subtract 32-24 = 8
Subtract a5 - a3 = 2
Divide 8/2 = 4
d = 4
Use d and one of the values they give us to find a1.
a3 = 24
24 = a1 + (3 - 1)(4)
24 = a1 + 2(4)
24 = a1 + 8
Subtract 8 from both sides
16 = a1
an = 16 + (n - 1)(4)
Can also be written
an = 16 + 4n - 4
an = 4n + 12
Answer:
0
Step-by-step explanation:
Answer:
x = 5, -6
Step-by-step explanation:
Step 1: Write out equation
x² + 2x - 25 = x + 5
Step 2: Move everything to one side
x² + x - 30 = 0
Step 3: Factor
(x - 5)(x + 6) = 0
Step 4: Find roots
x - 5 = 0
x = 5
x + 6 = 0
x = -6
2x-5y=3.
-2x+4y=-14
-y=-11
y=11.
x - 22= 7
x= 29
2•(29)-5(11)=3
58-55=3
29-2(11)=7
29-22=7
There are several ways to answer this. All involve finding a way to calculate the area of shapes we're familiar with and using those areas to find the area of this unusual shape. I've included three different ways, all of which yield the same total area.
In the first case, you cut the shape into two shapes by drawing a perpendicular line from point C to segment AE. That will give you a square and a trapezoid. The area of the square is (2 m)(5 m) = 10 m², and the area of the trapezoid is (0.5)(9 m - 5 m)(4 m + 4 m - 2 m) = 12 m². So the area of the entire shape is 10 m² + 12 m² = 22 m².
In the second case, you cut the shape into two shapes by drawing a perpendicular line from point C to segment AB. That will give you a rectangle and a triangle. The area of the rectangle is (2 m)(9 m) = 18 m². The area of the triangle is (0.5)(4 m - 2 m)(9 m - 5 m) = 4 m². So the area of the entire shape is 18 m² + 4 m² = 22 m².
In the third case, you can imagine that this shape is a piece of a larger rectangle with sides 4 m and 9 m with an area of 36 m². The area of this shape would be the difference between 36 m² and the area of the imaginary trapezoid that fills in rest of the rectangle. That trapezoid would have an area of (0.5)(4 m - 2 m)(9 m + 5 m) = 14 m². So the area of the shape given would be 36 m² - 14 m² = 22 m².
In any case, the area of the shape is 22 m².