Answer:
The 21st term is 137.
Step-by-step explanation:
Arithmetic progression:
In an arithmetic progression the difference between consecutive terms is always the same, and its called common difference.
The nth term is given by:
In which 
is the first term and d is the common difference.
The first two terms are -3, 4.
This means that 
So
The 21st term is
The 21st term is 137.
Answer:
Step-by-step explanation:
As the two figure are the image and pre-image of a dilation.
Considering the left sided triangle is original and right sided triangle ( smaller one) is the image.
As one of the sides of the left triangle (original figure) is 4 in. And the corresponding length of the side on the right triangle (image of the figure) is 2 in.
It means the image of the side (2 in) is obtained when the side (4 in) of the original object is dilated by a scale factor of 1/2. In other words, the side of the image (2 in) is obtained multiplying the side (4 in) of original figure by 1/2. i.e. 4/2 = 2 in
Lets determine the missing side of the right side triangle by the same rule.
As the original object has one of the sides is 5 in and the corresponding side of the image has x in. As the original figure is dilated by a scale factor of 1/2. so the missing side of x will be: x = 5/2 = 2.5
So, the value of x will be 2.5
Similarly, the original object has one of the sides with length (y + 1 in). As the As the original figure is dilated by a scale factor of 1/2. As the corresponding length of the side of the image triangle is 3 in.
so
y + 1 = 2(3) ∵ 3 in (image side) is multiplied by 2
y + 1 = 6
y = 6 - 1
y = 5
So, the value of y = 5
Therefore,
Answer:
x = 2y + 1 + (z/2)
Step-by-step explanation:
Just manipulate the equation to isolate x.
