When NN is construsted, batch size is not defined and place holder is used and its summary(tensorfow) shows the batch size as None.
This is useful because you can change batch size later.
In case of a simple model with 10 input features, 1 hidden layers with 10 neurons and output layer, the shape of the hidden layer would be (None, 10), which means if the batch size is 20, the hidden layer would have the shape of (20, 10).
When the model is used to predict for a single output, with shape(10, 1), how does the math work?