diff --git a/Library/Homebrew/utils/autoremove.rb b/Library/Homebrew/utils/autoremove.rb
index cb34473286..3a53c5d745 100644
--- a/Library/Homebrew/utils/autoremove.rb
+++ b/Library/Homebrew/utils/autoremove.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 module Utils
@@ -25,7 +25,7 @@ module Utils
     def formulae_with_no_formula_dependents(formulae)
       return [] if formulae.blank?
 
-      dependents = []
+      dependents = T.let([], T::Array[Formula])
       formulae.each do |formula|
         dependents += formula.runtime_formula_dependencies
 
@@ -33,7 +33,7 @@ module Utils
         next if Tab.for_keg(formula.any_installed_keg).poured_from_bottle
 
         formula.deps.select(&:build?).each do |dep|
-          suppress(FormulaUnavailableError) { dependents << dep.to_formula }
+          Kernel.suppress(FormulaUnavailableError) { dependents << dep.to_formula }
         end
       end
       formulae - dependents
diff --git a/Library/Homebrew/utils/curl.rb b/Library/Homebrew/utils/curl.rb
index 80cf0517dc..049f889e96 100644
--- a/Library/Homebrew/utils/curl.rb
+++ b/Library/Homebrew/utils/curl.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "open3"
@@ -243,8 +243,8 @@ module Utils
       return unless url.start_with? "http"
 
       secure_url = url.sub(/\Ahttp:/, "https:")
-      secure_details = nil
-      hash_needed = false
+      secure_details = T.let(nil, T.nilable(T::Hash[Symbol, T.untyped]))
+      hash_needed = T.let(false, T::Boolean)
       if url != secure_url
         user_agents.each do |user_agent|
           secure_details = begin
@@ -267,7 +267,7 @@ module Utils
         end
       end
 
-      details = nil
+      details = T.let(nil, T.nilable(T::Hash[Symbol, T.untyped]))
       user_agents.each do |user_agent|
         details =
           curl_http_content_headers_and_checksum(
@@ -414,7 +414,7 @@ module Utils
             # Unknown charset in Content-Type header
           end
         end
-        file_contents = File.read(file.path, **open_args)
+        file_contents = File.read(T.must(file.path), **open_args)
         file_hash = Digest::SHA2.hexdigest(file_contents) if hash_needed
       end
 
@@ -430,7 +430,7 @@ module Utils
         responses:      responses,
       }
     ensure
-      file.unlink
+      T.must(file).unlink
     end
 
     def curl_supports_tls13?
@@ -547,7 +547,7 @@ module Utils
       return response unless response_text.match?(HTTP_STATUS_LINE_REGEX)
 
       # Parse the status line and remove it
-      match = response_text.match(HTTP_STATUS_LINE_REGEX)
+      match = T.must(response_text.match(HTTP_STATUS_LINE_REGEX))
       response[:status_code] = match["code"] if match["code"].present?
       response[:status_text] = match["text"] if match["text"].present?
       response_text = response_text.sub(%r{^HTTP/.* (\d+).*$\s*}, "")
diff --git a/Library/Homebrew/utils/curl.rbi b/Library/Homebrew/utils/curl.rbi
new file mode 100644
index 0000000000..e69d89d750
--- /dev/null
+++ b/Library/Homebrew/utils/curl.rbi
@@ -0,0 +1,6 @@
+# typed: strict
+
+module Utils::Curl
+  include Kernel
+  requires_ancestor { SystemCommand::Mixin }
+end
diff --git a/Library/Homebrew/utils/formatter.rb b/Library/Homebrew/utils/formatter.rb
index 3b7caae2b3..870364c142 100644
--- a/Library/Homebrew/utils/formatter.rb
+++ b/Library/Homebrew/utils/formatter.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "utils/tty"
@@ -91,11 +91,11 @@ module Formatter
     end
 
     fallback.call if objects.empty?
-    fallback.call if respond_to?(:tty?) ? !tty? : !$stdout.tty?
+    fallback.call if respond_to?(:tty?) ? !T.unsafe(self).tty? : !$stdout.tty?
 
     console_width = Tty.width
     object_lengths = objects.map { |obj| Tty.strip_ansi(obj).length }
-    cols = (console_width + gap_size) / (object_lengths.max + gap_size)
+    cols = (console_width + gap_size) / (T.must(object_lengths.max) + gap_size)
 
     fallback.call if cols < 2
 
@@ -109,14 +109,14 @@ module Formatter
     output = +""
 
     rows.times do |row_index|
-      item_indices_for_row = row_index.step(objects.size - 1, rows).to_a
+      item_indices_for_row = T.cast(row_index.step(objects.size - 1, rows).to_a, T::Array[Integer])
 
-      first_n = item_indices_for_row[0...-1].map do |index|
-        objects[index] + "".rjust(col_width - object_lengths[index])
+      first_n = T.must(item_indices_for_row[0...-1]).map do |index|
+        objects[index] + "".rjust(col_width - object_lengths.fetch(index))
       end
 
       # don't add trailing whitespace to last column
-      last = objects.values_at(item_indices_for_row.last)
+      last = objects.values_at(item_indices_for_row.fetch(-1))
 
       output.concat((first_n + last)
             .join(gap_string))
diff --git a/Library/Homebrew/utils/formatter.rbi b/Library/Homebrew/utils/formatter.rbi
new file mode 100644
index 0000000000..e9038dd0f3
--- /dev/null
+++ b/Library/Homebrew/utils/formatter.rbi
@@ -0,0 +1,5 @@
+# typed: strict
+
+module Formatter
+  include Kernel
+end