Fred graphed the following equations on his graphing calculator. y...

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6. Since we have the system of two equations, the solution lies in intersection points between their graphs. We can
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      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (244μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (437μs)
      • creating: site.layouts.app (1.06ms)
      • composing: site.layouts.app (24μs)
      • creating: components.canonical (1.12ms)
      • composing: components.canonical (114μs)
      • creating: components.open-graph (1.09ms)
      • composing: components.open-graph (163μs)
      • creating: site.headers.header (3.21ms)
      • composing: site.headers.header (191μs)
      • Illuminate\Cache\Events\CacheHit (7.13ms)
      • creating: components.footer (320μs)
      • composing: components.footer (119μs)
      • Illuminate\Cache\Events\CacheHit (829μs)
      • Illuminate\Cache\Events\CacheMissed (243μs)
      • Illuminate\Database\Events\StatementPrepared (728μs)
      • Illuminate\Database\Events\QueryExecuted (1.24ms)
      • eloquent.retrieved: App\Models\SubjectCat (86μs)
      • Illuminate\Cache\Events\KeyWritten (643μs)
      • Illuminate\Cache\Events\CacheHit (394μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (401μs)
      • Illuminate\Cache\Events\CacheHit (900μs)
      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (298μs)
      • Illuminate\Cache\Events\CacheHit (408μs)
      • creating: components.forms.contact-us (217μs)
      • composing: components.forms.contact-us (207μs)
      • creating: components.forms.get-started (195μs)
      • composing: components.forms.get-started (272μs)
      • creating: components.forms.free-tool-download (112μs)
      • composing: components.forms.free-tool-download (66μs)
      • creating: components.forms.claim-free-worksheet (199μs)
      • composing: components.forms.claim-free-worksheet (72μs)
      • creating: components.forms.tutor-subscription-waitlist (104μs)
      • composing: components.forms.tutor-subscription-waitlist (131μs)
      • creating: components.forms.tutor-subscription-join (109μs)
      • composing: components.forms.tutor-subscription-join (63μs)
      • creating: components.forms.tutor-support (103μs)
      • composing: components.forms.tutor-support (66μs)
      • 311 x Illuminate\Cache\Events\CacheHit (20.38%)
        130ms
        20 x Illuminate\Database\Events\StatementPrepared (6.89%)
        43.95ms
        20 x Illuminate\Database\Events\QueryExecuted (4.28%)
        27.33ms
        11 x Illuminate\Cache\Events\KeyWritten (1.65%)
        10.54ms
        11 x Illuminate\Cache\Events\CacheMissed (1.6%)
        10.21ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.73%)
        4.69ms
        1 x creating: site.headers.header (0.5%)
        3.21ms
        1 x Illuminate\Routing\Events\Routing (0.26%)
        1.67ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.21%)
        1.32ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.18%)
        1.17ms
        1 x creating: components.canonical (0.18%)
        1.12ms
        1 x creating: components.open-graph (0.17%)
        1.09ms
        1 x creating: site.layouts.app (0.17%)
        1.06ms
        1 x composing: homework.show (0.11%)
        698μs
        1 x Illuminate\Routing\Events\RouteMatched (0.09%)
        559μs
        1 x creating: components.breadcrumbs (0.08%)
        491μs
        1 x creating: homework.show (0.08%)
        490μs
        1 x creating: components.footer (0.05%)
        320μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        280μs
        1 x eloquent.booting: App\Models\SubjectCat (0.04%)
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        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        244μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        239μs
        5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        237μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        233μs
        1 x creating: components.forms.contact-us (0.03%)
        217μs
        1 x composing: components.forms.contact-us (0.03%)
        207μs
        1 x composing: components.breadcrumbs (0.03%)
        199μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        199μs
        1 x creating: components.forms.get-started (0.03%)
        195μs
        1 x composing: site.headers.header (0.03%)
        191μs
        1 x composing: components.open-graph (0.03%)
        163μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        150μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        131μs
        1 x composing: components.footer (0.02%)
        119μs
        1 x composing: components.canonical (0.02%)
        114μs
        1 x creating: components.forms.free-tool-download (0.02%)
        112μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        109μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        104μs
        1 x creating: components.forms.tutor-support (0.02%)
        103μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        72μs
        1 x composing: components.forms.free-tool-download (0.01%)
        66μs
        1 x composing: components.forms.tutor-support (0.01%)
        66μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        63μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        63μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        62μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        48μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        42μs
        1 x composing: site.layouts.app (0%)
        24μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated47.79ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '60031' limit 1
        16.47mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 60031
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (4)
        1.2mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (60031)
        1.17mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.18mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 60031 and `subject` = 4 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        3.54mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 60031
        • 1: 4
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (4)
        2.42mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 60031 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.65mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 60031
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 60031 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        3.78mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 60031
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 60031 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.7mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.38mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.14mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.6mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.42mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.55mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.28mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.26mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.21mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.39mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.2mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.25mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      5HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
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          utm_source
          direct
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          PHPDEBUGBAR_STACK_DATA
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          status_text
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          content_type
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          request_request
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          request_headers
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          request_cookies
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