Desmos, 90 82 59 bytes

f(m,d)=total([0,31,28,31,30,31,30,31,31,30,31,30][1...m])+d

Saved 23 bytes 'cause I was so dumb... I've been trying to do some clever list manipulation to save bytes, but it never came to my mind to just put the list itself.

Very Brief Explanation:

[0,31,28,31,30,31,30,31,31,30,31,30]: The number of days in each month(excluding December), with an extra 0 element at the beginning.

total( ... [1...m])+d: Sum of the first m elements of the list explained above, then add d.

Try It On Desmos!

Try It On Desmos! - Prettified

Desmos, 90 82 59 bytes

f(m,d)=total([0,31,28,31,30,31,30,31,31,30,31,30][1...m])+d

Saved 23 bytes 'cause I was so dumb... I've been trying to do some clever list manipulation to save bytes, but it never came to my mind to just put the list itself.

Very Brief Explanation:

[0,31,28,31,30,31,30,31,31,30,31,30]: The number of days in each month(excluding December), with an extra 0 element at the beginning.

total( ... [1...m])+d: Sum of the first m elements of the list explained above, then add d.

Try It On Desmos!

Try It On Desmos! - Prettified

Solution using Lynn's "closed form" formula, 34 bytes

f(m,d)=floor(275m/9)-30+d-mod(2,m)

Desmos, 90 82 bytes

f(m,d)=total((mod(join([0...7],[1...4]),2)+join([-30,0,-2],[0...9]0)+30)[1...m])+d

99% sure this can be golfed. I feel like there should be a more mathematical way to solve this?

Very Brief Explanation:

mod(join([0...7],[1...4]),2)+join([-30,0,-2],[0...9]0)+30: Constructs the list [0,31,28,31,30,31,30,31,31,30,31,30,31](The number of days in each month, with an extra 0 element at the beginning. In hindsight, I actually don't need the last element, but it doesn't save any bytes to fix.)

total(( ... )[1...m])+d: Sum of the first m elements of the list explained above, then add d.

Try It On Desmos!

Try It On Desmos! - Prettified

Desmos, 90 82 59 bytes

f(m,d)=total([0,31,28,31,30,31,30,31,31,30,31,30][1...m])+d

Saved 23 bytes 'cause I was so dumb... I've been trying to do some clever list manipulation to save bytes, but it never came to my mind to just put the list itself.

Very Brief Explanation:

[0,31,28,31,30,31,30,31,31,30,31,30]: The number of days in each month(excluding December), with an extra 0 element at the beginning.

total( ... [1...m])+d: Sum of the first m elements of the list explained above, then add d.

Try It On Desmos!

Try It On Desmos! - Prettified

Desmos, 90 82 bytes

f(m,d)=total((mod(join([0...7],[1...4]),2)+join([-30,0,-2],[0...9]0)+30)[1...m])+d

99% sure this can be golfed.

Try It On Desmos!

Try It On Desmos! - Prettified

Desmos, 90 82 bytes

f(m,d)=total((mod(join([0...7],[1...4]),2)+join([-30,0,-2],[0...9]0)+30)[1...m])+d

99% sure this can be golfed. I feel like there should be a more mathematical way to solve this?

Very Brief Explanation:

mod(join([0...7],[1...4]),2)+join([-30,0,-2],[0...9]0)+30: Constructs the list [0,31,28,31,30,31,30,31,31,30,31,30,31](The number of days in each month, with an extra 0 element at the beginning. In hindsight, I actually don't need the last element, but it doesn't save any bytes to fix.)

total(( ... )[1...m])+d: Sum of the first m elements of the list explained above, then add d.

Try It On Desmos!

Try It On Desmos! - Prettified