Jerold D. Fisher entered a plea agreement and pled guilty to submitting fraudulent tax returns to the Internal Revenue Service. In return, the Government promised, among other things, not to charge Mr. Fisher with any further crimes arising out of the same underlying conduct. Following the plea agreement and before sentencing, the district court found Mr. Fisher had breached the plea agreement and released the Government from its no-new-charges obligation. The Government then indicted Mr. Fisher on related structuring charges. The court subsequently reversed itself and reinstated the plea agreement, but the Government did not dismiss the new indictment.
At sentencing on the tax fraud charge, Mr. Fisher asked the district court to find that the Government (1) had breached the plea agreement by failing to dismiss the structuring charges, and (2) had engaged in vindictive prosecution. The court sentenced Mr. Fisher to 41 months in prison without ruling on either of those requests.
Mr. Fisher now appeals, arguing the district court committed procedural error by declining to decide his governmental breach claim. Because that claim is moot, we lack jurisdiction over it. To the extent Mr. Fisher attempts to raise a similar argument regarding his vindictive prosecution claim, he has forfeited that claim and waived it through inadequate briefing. We therefore grant the Government’s motion to dismiss this appeal.
I. BACKGROUND
1. The Original Indictment and Plea Agreement
On May 1, 2013, a federal grand jury indicted Mr. Fisher on two counts of violating 18 U.S.C. § 287, which prohibits knowingly presenting “false, fictitious, or fraudulent” claims to any agency or department of the United States. According to the indictment, Mr. Fisher filed false Forms W-2 purporting to show that Fisher Alfalfa Farms, of which he claimed to be the registered agent, had paid him $8,877,934 in wages and withheld $3,997,436 in employment taxes for tax years 2006 through 2009. He also allegedly submitted fraudulent Forms 1040 for himself. Based on these fabricated documents, the U.S. Treasury sent him checks and electronic -transfers totaling $3,866,021.
On February 14, 2014, Mr. Fisher and the Government entered into a plea agreement, under which the Government dismissed Count 1 in return for a guilty plea to Count 2. Mr. Fisher’s promises in the plea agreement included the following:
c. The defendant agrees to fully and completely assist the United States in the identification and recovery of forfei-table assets, either domestic or foreign, which have been acquired directly or indirectly through the unlawful activities of the defendant.
d. The defendant agrees to cooperate fully with the United States Attorneys Office and to provide a financial statement on a form approved by the USAO that discloses all assets in which *985defendant has any interest or over which the defendant exercises control, directly or indirectly, including those held by a spouse, nominee or other third party, as well as any transfer of assets that has taken place in the last 5 years.
e. The defendant agrees to submit to an examination, which may be taken under oath and may include a polygraph examination.
g. The defendant agrees to not encumber, transfer, or dispose of any monies, property or assets under defendant’s custody or control, without written approval from the United States Attorneys Office.
ROA, Vol. 1 at 48-49. In return, the Government agreed (1) not to “file any additional charges against the defendant, or any one acting in concert with the defendant, arising out of the facts forming the basis for the present indictment,” (2) to recommend a sentence of 36 months, and (3) to recommend a two-or three-level reduction for acceptance of responsibility under United States Sentencing Guidelines Manual (“U.S.S.G”) § 3E1.1. ROA, Vol. 1 at 52. These obligations were “contingent upon the defendant’s continuing manifestation of acceptance of responsibility as determined by-the United States”:
In the event the Court finds the defendant has breached this plea agreement or otherwise failed to adhere to its terms, the United States shall not be bound by this paragraph' and may pursue any additional charges arising from the criminal activity under investigation as well as any perjury, false statement, or obstruction of justice charges which may have occurred.
ROA, Vol. 1 at 52-53. The Government also bound itself “not to use new information the defendant provides about the defendant’s own criminal conduct except as specifically authorized by U.S.S.G. § 1B1.8,” which permits the use of “self-incriminating information” against a cooperating defendant in limited circumstances. ROA, Vol. 1 at 53; U.S. Sentencing Guidelines Manual § IB 1.8 (U.S. Sentencing Comm’n 2014).
Finally, the plea agreement contained a waiver of Mr. Fisher’s right to “appeal or collaterally attack any matter in connection with this prosecution, [his] conviction, or the components of the sentence to be imposed.” ROA, Vol. 1 at 55. The waiver contained an exception that permitted Mr. Fisher to bring “claims with regards to ineffective assistance of counsel or prose-cutorial misconduct.” ROA, Vol. 1 at 56.
2. Initial Sentencing Hearing
As provided by the plea agreement, the Government deposed Mr. Fisher on May 6, 2014. On May 27, 2014, the district court conducted a brief sentencing hearing, at which neither party objected to the presentence report. The district court calculated the Guidelines range as 41 to 51 months and announced that it tentatively intended to impose the 36-month sentence jointly recommended by the parties. After explaining its reasons for that sentence, however, the court asked the Government how much of Mr. Fisher’s unlawfully obtained money had been recovered. The Government responded that despite making “diligent efforts to try to locate assets,” it had only “recovered a fraction of the $4 million.” ROA, Vol. 3 at 11-12.
Unconvinced that the stolen funds were “gone to the wind,” the district court continued the sentencing to give Mr. Fisher "an opportunity to “think about it some more and think about maybe there’s some other information he might be able to offer.” ROA, Vol. 3 at 13. “[A]s it stands right now,” the court explained, “I’m not *986willing, without any further explanation, to honor the parties’ agreement to sentence Mr. Fisher to under the guideline range. I’m just not. Not with this amount of loss.” ROA, Vol. 3 at 13-14. Mr. Fisher, as he was being led from the courtroom, exclaimed to the court, “Three million was lost in the stock market. They know that.” ROA, Vol. 3 at 15.
3. Government’s Motion to Find Mr. Fisher in Breach of the Plea Agreement
The Government subsequently filed a Motion to Determine If Defendant Has Breached His Plea Agreement. The Government sought to be released from paragraph 5 of the agreement — which concerns the filing of additional charges, Mr. Fisher’s recommended sentence, and acceptance of responsibility — on the ground that Mr. Fisher had not manifested acceptance of responsibility. In particular, the Government claimed that Mr. Fisher “ha[d] obfuscated on the issue of his assets and ha[d] failed to provide documentation, as requested, to establish that he lost $3,000,000 in the stock market as he represented to the Court in his aborted sentencing hearing on May 27, 2014.” ROA, Vol. 1 at 99. The Government also alleged “Fisher ha[d] been trying to get assistance from one or more fellow inmates at [Corrections Corporation of America] to help him move money that he ha[d] under his control covertly.” ROA, Vol. 1 at 99-100.
4. Second Sentencing Hearing
At a second sentencing hearing on July 7, 2014, the Government presented testimony from IRS Special Agent Lamont Wynn. Special Agent Wynn made allegations against Mr. Fisher based on information from Mr. Fisher’s fellow inmate who was a cooperating witness in a different case.
First, Special Agent Wynn testified that according to the informant, Mr. Fisher had been making phone calls using other prisoners’ personal identification numbers (PINs) to prevent Government monitoring of his calls. The informant had reported that.on one such call, Mr. Fisher instructed his girlfriend, Renita Lewis, to sell weight-lifting equipment he had purchased with tax fraud proceeds. Second, Special Agent Wynn claimed Mr. Fisher had been tutoring other inmates on how to obtain tax refunds, both legally and illegally.
5. Third Sentencing Hearing
At a third sentencing hearing on July 28, 2014, the Government submitted a transcript of a May 9, 2014 phone call Mr. Fisher placed to Ms. Lewis, using another prisoner’s PIN. Mr. Fisher started that call by telling Ms. Lewis, “Twelve with one of the long things,” then spoke in what appears to be code for several minutes, ROA, Ex. 1, to disguise, the Government argued, his efforts- to dispose of assets through Ms. Lewis. At the end of the call, Mr. Fisher said if his family did not pay a $350 outstanding warrant for his arrest,
well they will see what $350 will cost them. It’s going to cost motherfucking farm ground and five years in jail I can put them all away, there, so that’s fine with me. I’m not going to do any more time for their stupidity and everything and their bullshit and stuff.
ROA, Vol. 4 at 3. The Government claimed Mr. Fisher was threatening to turn his relatives in to the Government if they did not assist him with the warrant. According to the Government, Mr. Fisher’s threats suggested he and his family had been attempting to dispose of assets without the Government’s knowledge.
6. District Court Finds Mr. Fisher Breached the Plea Agreement
On August 27, 2014, the district court granted the Government’s motion to find *987Mr. Fisher in breach, concluding he “ha[d] failed to fully and honestly identify and disclose the location and or disposition of assets and property derived from the offense, only providing limited information of questionable credibility when pressed.” ROA, Yol. 1 at 380. Specifically, the court found Mr. Fisher had withheld all information about his stock market losses until after the May 27, 2014 sentencing hearing, failed to disclose that family members possessed some of his assets, and attempted to dispose of other assets through Ms. Lewis without the Government’s knowledge. Because it concluded Mr. Fisher had breached, the court released the Government from several of its obligations under the plea agreement, including its promise not to file new charges against Mr. Fisher.
7.New Charges Against Mr. Fisher and Ms. Lewis
On September 24, 2014, the Government indicted Mr. Fisher and Ms. Lewis on seven counts of structuring, in violation of 31 U.S.C. § 5324(a)(3). The indictment recited the facts of Mr. Fisher’s first case, including his submission of fraudulent tax returns and his agreement to plead guilty on February 14, 2014. It further alleged that Mr. Fisher and Ms. Lewis deposited his illegal tax proceeds into various bank accounts in a manner designed to “evad[e] the reporting requirements” that federal law imposes on financial institutions. Aplt. Br., Attach. C at 4-10; 31 U.S.C. § 5324(a).
The Government was free to seek this second indictment because the district court’s August 27, 2014 order lifted the restrictions imposed by paragraph five of the plea agreement. That order was based on the court’s belief that it was “not until the May 27 sentencing hearing [that] Defendant offer[ed], in an excited utterance as he left [the] courtroom, that he had lost monies in the stock market.” ROA,- Vol. 1 at 341. “And, in the aftermath of the May 27 hearing,” the court explained in its order, “Defendant for the first time produced records of stock market transactions that identified and quantified a net loss of $1.9 million in the stock market.” ROA, Vol. 1 at 341.
It turned out, however, that the district court was in error: both parties agree on appeal that the Government had been in possession of records from Mr. Fisher’s E‘"Trade accounts since 2010, and that those records show stock market losses of between $1.9 million and $2.2 million.
8. Mr. Fisher Moves for Reconsideration
Given the district court’s factual misunderstanding, on September 30, 2014, Mr. Fisher moved for reconsideration of the August 27 order. On October 28, 2014, the court granted Mr. Fisher’s motion. The court found that as a result of poor briefing from both parties, “[i]t was not made clear to the Court when deciding whether Defendant breached the Plea Agreement that the records [of Mr. Fisher’s E*Trade accounts] were provided before May 27.” ROA, Vol. 1 at 1457. Because the Government had in fact possessed those records before executing the plea agreement, the court concluded Mr. Fisher had not breached and “the Government continues to be bound by the terms of the Plea Agreement at sentencing.” ROA, Vol. 1 at 1460.
9. Motion for Variance
Mr. Fisher filed a Motion for a Guideline Variance to a Sentence of Time Served on November 3, 2014. He argued the Government had breached the plea agreement by filing a new indictment based in part on evidence obtained during Mr. Fisher’s *988May 6, 2014 deposition. As a remedy for this breach, Mr. Fisher sought only to be relieved of his obligations under paragraphs l(c)-(g) of the plea agreement, which required him to cooperate with the Government in disclosing and recovering assets.
In addition, Mr. Fisher’s motion accused the Government of engaging in vindictive prosecution. He alleged, in particular, that the Government had brought the structuring charges to punish Mr. Fisher for refusing to plead guilty in a 2012 case; the Government had continued to investigate Mr. Fisher, even prior to his alleged breach of the tax fraud plea agreement, because it intended all along to obtain an additional indictment against him; and during his deposition, the Government had attempted to trick Mr. Fisher into lying so that it could bring perjury charges against him. The sole remedy he sought for the alleged prosecutorial vindictiveness was a sentence of time served.
10. Fourth and Final Sentencing Hearing
The district court held its fourth and final sentencing hearing on November 3, 2014. At that hearing, the court said the arguments raised in Mr. Fisher’s motion for variance affected only the structuring case against Mr. Fisher, not the instant tax fraud case, and that Mr. Fisher should therefore raise those concerns only in the second case, which was before a different judge.
The Government announced it did not intend to seek Mr. Fisher’s cooperation going forward. The court agreed that once a sentence was handed down in the tax fraud case, the Government could not seek to enforce paragraphs l(c)-(g) of the plea agreement.
The district court imposed a sentence of 41 months in prison followed by three years of supervised release, as well as $4,039,781 in restitution.to the IRS. When defense counsel inquired whether Mr. Fisher’s vindictive-prosecution claim had factored into the final sentence, the court responded:
I decided it would be more appropriate in the other case. I don’t think I have sufficient evidence to grant a variance on that basis.. I think it’s more appropriately taken up in the other case where it can be fully heard. And I think the appropriate remedy could be had in that case, everything from dismissal to remedies short of that.
ROA, Vol. 3 at 142-43.
On November 4, 2014, the day after the final sentencing hearing, the Government moved to dismiss the structuring charges against Mr. Fisher and Ms. Lewis.
11. Mr. Fisher’s Appeal
Mr. Fisher filed a timely notice of appeal on November 12, 2014. On December 10, 2014, the Government moved to enforce Mr. Fisher’s appeal waiver under 10th Circuit Rule 27.2(A)(1)(d). The Government’s motion also sought dismissal of the appeal under 10th Circuit Rule 27.2(A)(1)(b), which provides for “summary disposition because of a supervening change of law or mootness.” After Mr. Fisher responded, his appeal was referred to this panel.
II. DISCUSSION
Mr. Fisher made two arguments in his motion for variance and at the sentencing hearing before the district court. First, he argued the .Government had breached the plea agreement. On appeal, he argues the district court erred when it declined to rule on this issue. The problem with this argument is that Mr. Fisher has already obtained all the relief he requested for the Government’s alleged breach, rendering *989that issue moot. Accordingly, we grant the Government’s motion to dismiss the breach issue as moot.
Second, Mr. Fisher argued in district court that he should be sentenced to time served because the Government engaged in vindictive prosecution. On appeal, although he may, as with his breach issue, be alleging the district court erred by refusing to decide this issue, he has failed to brief it adequately. We therefore do not consider it.
A. Government Breach Claim Is Moot
Mr. Fisher contends the district court erred by failing to rule on his request to find the Government in breach of the plea agreement for failing to dismiss the second indictment before he was sentenced. He argues the “Government’s breach of its plea agreement obligations requires remand for resentencing before a different judge.” Aplt. Br. at 22.
We may reach the merits of Mr. Fisher’s appeal only if (1) Mr. Fisher’s appeal waiver is unenforceable, and (2) his claims are not moot. “The mootness question necessarily constitutes our threshold inquiry, because the existence of a live case or controversy is a constitutional prerequisite to the jurisdiction of the federal courts.” In re L.F. Jennings Oil Co., 4 F.3d 887, 889 (10th Cir.1993) (quotation omitted). We review mootness de novo as a legal question. Id.
1. Mootness Standard
“Article III of the United States Constitution limits the jurisdiction of federal courts to the adjudication of ‘Cases’ or ‘Controversies.’ ” Jordan v. Sosa, 654 F.3d 1012, 1019 (10th Cir.2011) (quoting U.S. Const. art. III, § 2, cl. 1). This case-or-controversy limitation requires that parties continue to have a personal stake in the outcome of a lawsuit during all stages of litigation, including appellate review. See United States v. Juvenile Male, — U.S. -, 131 S.Ct. 2860, 2864, 180 L.Ed.2d 811 (2011); Spencer v. Kemna, 523 U.S. 1, 7, 118 S.Ct. 978, 140 L.Ed.2d 43 (1998); S. Utah Wilderness All. v. Smith, 110 F.3d 724, 727 (10th Cir.1997) (“Article III mootness is ‘the doctrine of standing set in a time frame: The requisite personal interest that must exist at the commencement of the litigation (standing) must continue throughout its existence (mootness).’ ” (quoting Arizonans for Official English v. Arizona, 520 U.S. 43, 68 n. 22, 117 S.Ct. 1055, 137 L.Ed.2d 170 (1997))).
“We have held a case or controversy no longer exists when it is impossible to grant any effectual relief.” Chihuahuan Grasslands All. v. Kempthorne, 545 F.3d 884, 891 (10th Cir.2008); see also S. Utah Wilderness All., 110 F.3d at 727 (“[T]o be cognizable, a suit must be ‘a real and specific controversy admitting of specific relief through a decree of a conclusive character.’ ” (quoting Preiser v. Newkirk, 422 U.S. 395, 401, 95 S.Ct. 2330, 45 L.Ed.2d 272 (1975))). A claim is moot if a party has already obtained the only relief it seeks. See S. Utah Wilderness All., 110 F.3d at 727 (affirming district court’s finding that case was moot where “the only relief sought ... has already been obtained”).
2. Analysis
Mr. Fisher’s claim for government breach of the' plea agreement is moot. He has already received all the relief he requested for that alleged breach.
Federal Rule of Criminal Procedure 32(i)(3)(B) provides that “[a]t sentencing,the court ... must—for any disputed portion of the presentence report or other controverted matter—rule on the dispute or determine that a ruling is unnecessary *990either because the matter will not affect sentencing, or because the court will not consider the matter in sentencing.” Mr. Fisher contends the court violated this rule when it declined to decide his “disputed” motion to find the Government had breached the plea agreement and instead determined the alleged governmental breach should be addressed in his structuring case.
This claim is moot because, even if the district court erred in declining to decide this issue, or even if the court had determined the Government had breached the plea agreement, Mr. Fisher received everything he requested by way of relief. He asked the district court only for release from paragraphs l(c)-(g) of the plea agreement, which concern his cooperation obligations, as the sole remedy for the Government’s alleged breach.1
At the sentencing hearing, Mr. Fisher obtained release from his cooperation obligations. The prosecutor announced that the Government had “no intention of asking [Mr. Fisher] to cooperate any further” and that it “d[id] not intend to take his deposition, [and] d[id] not intend for him to provide any more information.” ROA, Vol. 3 at 126. Although the parties did not execute any formal amendment of the plea agreement to clarify that Mr. Fisher’s duty to cooperate terminated with the entry of judgment, the entirety of the transcript indicates that it did. The district court confirmed this interpretation when it told defense counsel that the Government had “conceded that they are no longer able to enforce any obligation on Mr. Fisher’s part to continue to cooperate in the identification and recovery of assets.” ROA, Vol. 3 at 132 (116:19-22).
Mr. Fisher has obtained “the only relief [he] sought” for the Government’s alleged breach of the plea agreement. S. Utah Wilderness All., 110 F.3d at 727. That relief renders his breach claim moot and divests us of subject matter jurisdiction over the breach issue. Id. Accordingly, we have neither the need nor the authority to decide whether Mr. Fisher has waived his right to bring this appeal on the breach claim or whether his claim is meritorious.
B. Vindictive Prosecution Claim Was Waived and Forfeited
We do not consider Mr. Fisher’s vindictive prosecution claim because he has waived it through inadequate briefing. In any event, this claim also was forfeited in district court.2
*9911. Mr. Fisher Waived His Vindictive Prosecution Claim
a. Requirement to Present Arguments in the Opening Brief
We have said that the “first task of an appellant is to explain to us why the district court’s decision was wrong.” Nixon v. City & Cty. of Denver, 784 F.3d 1364, 1366 (10th Cir.2015). We cannot rule on those issues the appellant does not bring to our attention. For this reason, 10th Circuit Rule 28(a)(8) instructs that the “appellant’s brief must contain, under appropriate headings and in the order indicated ... appellant’s contentions and the reasons for them, with citations to the authorities and parts of the record on which the appellant relies.”
“Consistent with this requirement, we routinely have declined to consider arguments that are not raised, or are inadequately presented, in an appellant’s opening brief.” Bronson v. Swensen, 500 F.3d 1099, 1104 (10th Cir.2007). The latter half of this formulation is as important as the former. While the “omission of an issue in an opening brief generally forfeits appellate consideration of that issue,” Kitchen v. Herbert, 755 F.3d 1193, 1208 (10th Cir.2014) (quotation omitted), it is equally true that an “issue mentioned in a brief on appeal, but not addressed, is waived,” Utah Envtl. Cong. v. Bosworth, 439 F.3d 1184, 1194 n. 2 (10th Cir.2006); see also Muscogee (Creek) Nation v. Pruitt, 669 F.3d 1159, 1166 (10th Cir.2012) (“[I]ssues designated for review are lost if they are not actually argued in the party’s brief.” (quotation omitted)). And the appellant must present his claims in a way that does not compel us to scavenge through his brief for traces of argument. See Nixon, 784 F.3d at 1370 (declining to address an argument in part because it was “misleadingly placed under a heading for a different issue”).
b. Analysis
In district court, Mr. Fisher claimed vindictive prosecution at the same time he moved to find the Government in breach of the plea agreement. The portion of his opening appeal brief that addresses Rule 32, however, only argues that the district court erroneously failed to rule on his government breach claim. There is no argument the district court also violated Rule 32 by sidestepping a ruling on his vindictive prosecution claim.' See Aplt. Br. at 23 (“Clearly, raising governmental breach of the present plea agreement needs to be resolved prior to sentencing.”), 24 (“The issue raised here, breach of a plea agreement, is not trivial, and required a ruling from the district court.”).
Read generously, several stray sentences elsewhere in Mr. Fisher’s brief could be construed to present an argument that the district court should have ruled on his vindictive prosecution claim. See, e.g., Aplt. Br. at 24-25 (“The district court’s error in this case stems from its erroneous belief that sentencing Fisher would moot the underlying obligations of the plea agreement, and that issues of vindictive prosecution and breach of the plea agreement by the Government didn’t have to be decided for purposes of this sentencing, but simply in the new indictment’s case before a different judge.” (emphasis in original)). But these scattered sentences fail to comply with 10th Circuit Rule 28(a)(8) because they do not “contain, under appropriate headings and in the order indicated ... appellant’s contentions and the reasons for them.” We therefore need not consider a Rule 32 argument regarding' Mr. Fisher’s vindictive prosecution claim. See Bronson v. Swensen, 500 F.3d at 1104.
Language in Mr. Fisher’s reply brief could be construed as an argument that *992the district court violated Rule 32 when it declined to rule on his vindictive prosecution claim. See Aplt. Reply Br. at 12 (disputing Government’s assertion that “defense trial counsel ... fail[ed] to object to the district court’s ruling that it was deferring the prosecutorial vindictiveness claim to the new case and court”). But this language does not present Mr. Fisher’s “contentions and the reasons for them” any more clearly than his opening brief. Mr. Fisher’s Rule 32 vindictive prosecution claim is not properly before us, and we do not consider it.
2. Mr. Fisher Forfeited His Vindictive Prosecution Claim in District Court
Mr. Fisher also forfeited his Rule 32 vindictive prosecution argument because he did not object to the lack of a Rule 32 ruling in the district court and does not argue for plain error on appeal. If a defendant “ha[s] not raised a separate objection to the district court’s failure to make an appropriate finding under [¶]... Rule 32(i)(3)(B) ], our review [i]s limited to determining whether this alleged failure to make a specific finding amounted to plain error.” United States v. Warren, 737 F.3d 1278, 1284 (10th Cir.2013) (second brackets in original) (internal quotation marks omitted). “[T]he failure to argue for plain error and its application on appeal ... surely marks the end of the road for an argument for reversal not first presented to the district court.” United States v. Lamirand, 669 F.3d 1091, 1099 n. 7 (10th Cir.2012) (ellipsis in original) (quotation omitted). Mr. Fisher never invoked Rule 32 before the district court. It was therefore Mr. Fisher’s burden to argue in his opening brief that the district court committed plain error. He failed to do so.
III. CONCLUSION
Based on the foregoing, we grant the Government’s motion to dismiss Mr. Fisher’s claim regarding breach of the plea agreement and affirm his sentence. We deny the Government’s motion to enforce the appeal waiver as moot.